diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index 279c90fe..cef7fac9 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -945,525 +945,531 @@ 731 self.prange = prange 732 return 733 - 734 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None): + 734 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): 735 """Plots the correlator using the tag of the correlator as label if available. 736 737 Parameters 738 ---------- 739 x_range : list - 740 list of two values, determining the range of the x-axis e.g. [4, 8] + 740 list of two values, determining the range of the x-axis e.g. [4, 8]. 741 comp : Corr or list of Corr 742 Correlator or list of correlators which are plotted for comparison. 743 The tags of these correlators are used as labels if available. 744 logscale : bool - 745 Sets y-axis to logscale + 745 Sets y-axis to logscale. 746 plateau : Obs - 747 Plateau value to be visualized in the figure + 747 Plateau value to be visualized in the figure. 748 fit_res : Fit_result - 749 Fit_result object to be visualized + 749 Fit_result object to be visualized. 750 ylabel : str - 751 Label for the y-axis + 751 Label for the y-axis. 752 save : str - 753 path to file in which the figure should be saved + 753 path to file in which the figure should be saved. 754 auto_gamma : bool 755 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. 756 hide_sigma : float 757 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. 758 references : list 759 List of floating point values that are displayed as horizontal lines for reference. - 760 """ - 761 if self.N != 1: - 762 raise Exception("Correlator must be projected before plotting") - 763 - 764 if auto_gamma: - 765 self.gamma_method() - 766 - 767 if x_range is None: - 768 x_range = [0, self.T - 1] - 769 - 770 fig = plt.figure() - 771 ax1 = fig.add_subplot(111) - 772 - 773 x, y, y_err = self.plottable() - 774 if hide_sigma: - 775 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 776 else: - 777 hide_from = None - 778 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 779 if logscale: - 780 ax1.set_yscale('log') - 781 else: - 782 if y_range is None: - 783 try: - 784 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) - 785 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) - 786 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 787 except Exception: - 788 pass - 789 else: - 790 ax1.set_ylim(y_range) - 791 if comp: - 792 if isinstance(comp, (Corr, list)): - 793 for corr in comp if isinstance(comp, list) else [comp]: - 794 if auto_gamma: - 795 corr.gamma_method() - 796 x, y, y_err = corr.plottable() - 797 if hide_sigma: - 798 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 799 else: - 800 hide_from = None - 801 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 802 else: - 803 raise Exception("'comp' must be a correlator or a list of correlators.") - 804 - 805 if plateau: - 806 if isinstance(plateau, Obs): - 807 if auto_gamma: - 808 plateau.gamma_method() - 809 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 810 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 811 else: - 812 raise Exception("'plateau' must be an Obs") - 813 - 814 if references: - 815 if isinstance(references, list): - 816 for ref in references: - 817 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 818 else: - 819 raise Exception("'references' must be a list of floating pint values.") - 820 - 821 if self.prange: - 822 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 823 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 824 - 825 if fit_res: - 826 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 827 ax1.plot(x_samples, - 828 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 829 ls='-', marker=',', lw=2) - 830 - 831 ax1.set_xlabel(r'$x_0 / a$') - 832 if ylabel: - 833 ax1.set_ylabel(ylabel) - 834 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 835 - 836 handles, labels = ax1.get_legend_handles_labels() - 837 if labels: - 838 ax1.legend() - 839 plt.draw() - 840 - 841 if save: - 842 if isinstance(save, str): - 843 fig.savefig(save) - 844 else: - 845 raise Exception("'save' has to be a string.") + 760 title : string + 761 Optional title of the figure. + 762 """ + 763 if self.N != 1: + 764 raise Exception("Correlator must be projected before plotting") + 765 + 766 if auto_gamma: + 767 self.gamma_method() + 768 + 769 if x_range is None: + 770 x_range = [0, self.T - 1] + 771 + 772 fig = plt.figure() + 773 ax1 = fig.add_subplot(111) + 774 + 775 x, y, y_err = self.plottable() + 776 if hide_sigma: + 777 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 778 else: + 779 hide_from = None + 780 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 781 if logscale: + 782 ax1.set_yscale('log') + 783 else: + 784 if y_range is None: + 785 try: + 786 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 787 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 788 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 789 except Exception: + 790 pass + 791 else: + 792 ax1.set_ylim(y_range) + 793 if comp: + 794 if isinstance(comp, (Corr, list)): + 795 for corr in comp if isinstance(comp, list) else [comp]: + 796 if auto_gamma: + 797 corr.gamma_method() + 798 x, y, y_err = corr.plottable() + 799 if hide_sigma: + 800 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 801 else: + 802 hide_from = None + 803 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 804 else: + 805 raise Exception("'comp' must be a correlator or a list of correlators.") + 806 + 807 if plateau: + 808 if isinstance(plateau, Obs): + 809 if auto_gamma: + 810 plateau.gamma_method() + 811 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 812 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 813 else: + 814 raise Exception("'plateau' must be an Obs") + 815 + 816 if references: + 817 if isinstance(references, list): + 818 for ref in references: + 819 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 820 else: + 821 raise Exception("'references' must be a list of floating pint values.") + 822 + 823 if self.prange: + 824 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 825 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') + 826 + 827 if fit_res: + 828 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 829 ax1.plot(x_samples, + 830 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 831 ls='-', marker=',', lw=2) + 832 + 833 ax1.set_xlabel(r'$x_0 / a$') + 834 if ylabel: + 835 ax1.set_ylabel(ylabel) + 836 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 837 + 838 handles, labels = ax1.get_legend_handles_labels() + 839 if labels: + 840 ax1.legend() + 841 + 842 if title: + 843 plt.title(title) + 844 + 845 plt.draw() 846 - 847 def spaghetti_plot(self, logscale=True): - 848 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 849 - 850 Parameters - 851 ---------- - 852 logscale : bool - 853 Determines whether the scale of the y-axis is logarithmic or standard. - 854 """ - 855 if self.N != 1: - 856 raise Exception("Correlator needs to be projected first.") - 857 - 858 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) - 859 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 860 - 861 for name in mc_names: - 862 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 847 if save: + 848 if isinstance(save, str): + 849 fig.savefig(save) + 850 else: + 851 raise Exception("'save' has to be a string.") + 852 + 853 def spaghetti_plot(self, logscale=True): + 854 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 855 + 856 Parameters + 857 ---------- + 858 logscale : bool + 859 Determines whether the scale of the y-axis is logarithmic or standard. + 860 """ + 861 if self.N != 1: + 862 raise Exception("Correlator needs to be projected first.") 863 - 864 fig = plt.figure() - 865 ax = fig.add_subplot(111) - 866 for dat in data: - 867 ax.plot(x0_vals, dat, ls='-', marker='') - 868 - 869 if logscale is True: - 870 ax.set_yscale('log') - 871 - 872 ax.set_xlabel(r'$x_0 / a$') - 873 plt.title(name) - 874 plt.draw() - 875 - 876 def dump(self, filename, datatype="json.gz", **kwargs): - 877 """Dumps the Corr into a file of chosen type - 878 Parameters - 879 ---------- - 880 filename : str - 881 Name of the file to be saved. - 882 datatype : str - 883 Format of the exported file. Supported formats include - 884 "json.gz" and "pickle" - 885 path : str - 886 specifies a custom path for the file (default '.') - 887 """ - 888 if datatype == "json.gz": - 889 from .input.json import dump_to_json - 890 if 'path' in kwargs: - 891 file_name = kwargs.get('path') + '/' + filename - 892 else: - 893 file_name = filename - 894 dump_to_json(self, file_name) - 895 elif datatype == "pickle": - 896 dump_object(self, filename, **kwargs) - 897 else: - 898 raise Exception("Unknown datatype " + str(datatype)) - 899 - 900 def print(self, print_range=None): - 901 print(self.__repr__(print_range)) - 902 - 903 def __repr__(self, print_range=None): - 904 if print_range is None: - 905 print_range = [0, None] - 906 - 907 content_string = "" - 908 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here - 909 - 910 if self.tag is not None: - 911 content_string += "Description: " + self.tag + "\n" - 912 if self.N != 1: - 913 return content_string - 914 - 915 if print_range[1]: - 916 print_range[1] += 1 - 917 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 918 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 919 if sub_corr is None: - 920 content_string += str(i + print_range[0]) + '\n' - 921 else: - 922 content_string += str(i + print_range[0]) - 923 for element in sub_corr: - 924 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 925 content_string += '\n' - 926 return content_string - 927 - 928 def __str__(self): - 929 return self.__repr__() - 930 - 931 # We define the basic operations, that can be performed with correlators. - 932 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 933 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 934 # One could try and tell Obs to check if the y in __mul__ is a Corr and - 935 - 936 def __add__(self, y): - 937 if isinstance(y, Corr): - 938 if ((self.N != y.N) or (self.T != y.T)): - 939 raise Exception("Addition of Corrs with different shape") - 940 newcontent = [] - 941 for t in range(self.T): - 942 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 943 newcontent.append(None) - 944 else: - 945 newcontent.append(self.content[t] + y.content[t]) - 946 return Corr(newcontent) - 947 - 948 elif isinstance(y, (Obs, int, float, CObs)): - 949 newcontent = [] - 950 for t in range(self.T): - 951 if _check_for_none(self, self.content[t]): - 952 newcontent.append(None) - 953 else: - 954 newcontent.append(self.content[t] + y) - 955 return Corr(newcontent, prange=self.prange) - 956 elif isinstance(y, np.ndarray): - 957 if y.shape == (self.T,): - 958 return Corr(list((np.array(self.content).T + y).T)) - 959 else: - 960 raise ValueError("operands could not be broadcast together") - 961 else: - 962 raise TypeError("Corr + wrong type") - 963 - 964 def __mul__(self, y): - 965 if isinstance(y, Corr): - 966 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 967 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") - 968 newcontent = [] - 969 for t in range(self.T): - 970 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 971 newcontent.append(None) - 972 else: - 973 newcontent.append(self.content[t] * y.content[t]) - 974 return Corr(newcontent) - 975 - 976 elif isinstance(y, (Obs, int, float, CObs)): - 977 newcontent = [] - 978 for t in range(self.T): - 979 if _check_for_none(self, self.content[t]): - 980 newcontent.append(None) - 981 else: - 982 newcontent.append(self.content[t] * y) - 983 return Corr(newcontent, prange=self.prange) - 984 elif isinstance(y, np.ndarray): - 985 if y.shape == (self.T,): - 986 return Corr(list((np.array(self.content).T * y).T)) - 987 else: - 988 raise ValueError("operands could not be broadcast together") - 989 else: - 990 raise TypeError("Corr * wrong type") - 991 - 992 def __truediv__(self, y): - 993 if isinstance(y, Corr): - 994 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 995 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") - 996 newcontent = [] - 997 for t in range(self.T): - 998 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 999 newcontent.append(None) -1000 else: -1001 newcontent.append(self.content[t] / y.content[t]) -1002 for t in range(self.T): -1003 if _check_for_none(self, newcontent[t]): -1004 continue -1005 if np.isnan(np.sum(newcontent[t]).value): -1006 newcontent[t] = None -1007 -1008 if all([item is None for item in newcontent]): -1009 raise Exception("Division returns completely undefined correlator") -1010 return Corr(newcontent) -1011 -1012 elif isinstance(y, (Obs, CObs)): -1013 if isinstance(y, Obs): -1014 if y.value == 0: -1015 raise Exception('Division by zero will return undefined correlator') -1016 if isinstance(y, CObs): -1017 if y.is_zero(): -1018 raise Exception('Division by zero will return undefined correlator') -1019 -1020 newcontent = [] -1021 for t in range(self.T): -1022 if _check_for_none(self, self.content[t]): -1023 newcontent.append(None) -1024 else: -1025 newcontent.append(self.content[t] / y) -1026 return Corr(newcontent, prange=self.prange) -1027 -1028 elif isinstance(y, (int, float)): -1029 if y == 0: -1030 raise Exception('Division by zero will return undefined correlator') -1031 newcontent = [] -1032 for t in range(self.T): -1033 if _check_for_none(self, self.content[t]): -1034 newcontent.append(None) -1035 else: -1036 newcontent.append(self.content[t] / y) -1037 return Corr(newcontent, prange=self.prange) -1038 elif isinstance(y, np.ndarray): -1039 if y.shape == (self.T,): -1040 return Corr(list((np.array(self.content).T / y).T)) -1041 else: -1042 raise ValueError("operands could not be broadcast together") -1043 else: -1044 raise TypeError('Corr / wrong type') -1045 -1046 def __neg__(self): -1047 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1048 return Corr(newcontent, prange=self.prange) -1049 -1050 def __sub__(self, y): -1051 return self + (-y) -1052 -1053 def __pow__(self, y): -1054 if isinstance(y, (Obs, int, float, CObs)): -1055 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1056 return Corr(newcontent, prange=self.prange) -1057 else: -1058 raise TypeError('Type of exponent not supported') -1059 -1060 def __abs__(self): -1061 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1062 return Corr(newcontent, prange=self.prange) -1063 -1064 # The numpy functions: -1065 def sqrt(self): -1066 return self ** 0.5 -1067 -1068 def log(self): -1069 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1070 return Corr(newcontent, prange=self.prange) -1071 -1072 def exp(self): -1073 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1074 return Corr(newcontent, prange=self.prange) -1075 -1076 def _apply_func_to_corr(self, func): -1077 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1078 for t in range(self.T): -1079 if _check_for_none(self, newcontent[t]): -1080 continue -1081 if np.isnan(np.sum(newcontent[t]).value): -1082 newcontent[t] = None -1083 if all([item is None for item in newcontent]): -1084 raise Exception('Operation returns undefined correlator') -1085 return Corr(newcontent) -1086 -1087 def sin(self): -1088 return self._apply_func_to_corr(np.sin) -1089 -1090 def cos(self): -1091 return self._apply_func_to_corr(np.cos) + 864 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) + 865 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 866 + 867 for name in mc_names: + 868 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 869 + 870 fig = plt.figure() + 871 ax = fig.add_subplot(111) + 872 for dat in data: + 873 ax.plot(x0_vals, dat, ls='-', marker='') + 874 + 875 if logscale is True: + 876 ax.set_yscale('log') + 877 + 878 ax.set_xlabel(r'$x_0 / a$') + 879 plt.title(name) + 880 plt.draw() + 881 + 882 def dump(self, filename, datatype="json.gz", **kwargs): + 883 """Dumps the Corr into a file of chosen type + 884 Parameters + 885 ---------- + 886 filename : str + 887 Name of the file to be saved. + 888 datatype : str + 889 Format of the exported file. Supported formats include + 890 "json.gz" and "pickle" + 891 path : str + 892 specifies a custom path for the file (default '.') + 893 """ + 894 if datatype == "json.gz": + 895 from .input.json import dump_to_json + 896 if 'path' in kwargs: + 897 file_name = kwargs.get('path') + '/' + filename + 898 else: + 899 file_name = filename + 900 dump_to_json(self, file_name) + 901 elif datatype == "pickle": + 902 dump_object(self, filename, **kwargs) + 903 else: + 904 raise Exception("Unknown datatype " + str(datatype)) + 905 + 906 def print(self, print_range=None): + 907 print(self.__repr__(print_range)) + 908 + 909 def __repr__(self, print_range=None): + 910 if print_range is None: + 911 print_range = [0, None] + 912 + 913 content_string = "" + 914 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here + 915 + 916 if self.tag is not None: + 917 content_string += "Description: " + self.tag + "\n" + 918 if self.N != 1: + 919 return content_string + 920 + 921 if print_range[1]: + 922 print_range[1] += 1 + 923 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 924 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 925 if sub_corr is None: + 926 content_string += str(i + print_range[0]) + '\n' + 927 else: + 928 content_string += str(i + print_range[0]) + 929 for element in sub_corr: + 930 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 931 content_string += '\n' + 932 return content_string + 933 + 934 def __str__(self): + 935 return self.__repr__() + 936 + 937 # We define the basic operations, that can be performed with correlators. + 938 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. + 939 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. + 940 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 941 + 942 def __add__(self, y): + 943 if isinstance(y, Corr): + 944 if ((self.N != y.N) or (self.T != y.T)): + 945 raise Exception("Addition of Corrs with different shape") + 946 newcontent = [] + 947 for t in range(self.T): + 948 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): + 949 newcontent.append(None) + 950 else: + 951 newcontent.append(self.content[t] + y.content[t]) + 952 return Corr(newcontent) + 953 + 954 elif isinstance(y, (Obs, int, float, CObs)): + 955 newcontent = [] + 956 for t in range(self.T): + 957 if _check_for_none(self, self.content[t]): + 958 newcontent.append(None) + 959 else: + 960 newcontent.append(self.content[t] + y) + 961 return Corr(newcontent, prange=self.prange) + 962 elif isinstance(y, np.ndarray): + 963 if y.shape == (self.T,): + 964 return Corr(list((np.array(self.content).T + y).T)) + 965 else: + 966 raise ValueError("operands could not be broadcast together") + 967 else: + 968 raise TypeError("Corr + wrong type") + 969 + 970 def __mul__(self, y): + 971 if isinstance(y, Corr): + 972 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): + 973 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") + 974 newcontent = [] + 975 for t in range(self.T): + 976 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): + 977 newcontent.append(None) + 978 else: + 979 newcontent.append(self.content[t] * y.content[t]) + 980 return Corr(newcontent) + 981 + 982 elif isinstance(y, (Obs, int, float, CObs)): + 983 newcontent = [] + 984 for t in range(self.T): + 985 if _check_for_none(self, self.content[t]): + 986 newcontent.append(None) + 987 else: + 988 newcontent.append(self.content[t] * y) + 989 return Corr(newcontent, prange=self.prange) + 990 elif isinstance(y, np.ndarray): + 991 if y.shape == (self.T,): + 992 return Corr(list((np.array(self.content).T * y).T)) + 993 else: + 994 raise ValueError("operands could not be broadcast together") + 995 else: + 996 raise TypeError("Corr * wrong type") + 997 + 998 def __truediv__(self, y): + 999 if isinstance(y, Corr): +1000 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1001 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1002 newcontent = [] +1003 for t in range(self.T): +1004 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1005 newcontent.append(None) +1006 else: +1007 newcontent.append(self.content[t] / y.content[t]) +1008 for t in range(self.T): +1009 if _check_for_none(self, newcontent[t]): +1010 continue +1011 if np.isnan(np.sum(newcontent[t]).value): +1012 newcontent[t] = None +1013 +1014 if all([item is None for item in newcontent]): +1015 raise Exception("Division returns completely undefined correlator") +1016 return Corr(newcontent) +1017 +1018 elif isinstance(y, (Obs, CObs)): +1019 if isinstance(y, Obs): +1020 if y.value == 0: +1021 raise Exception('Division by zero will return undefined correlator') +1022 if isinstance(y, CObs): +1023 if y.is_zero(): +1024 raise Exception('Division by zero will return undefined correlator') +1025 +1026 newcontent = [] +1027 for t in range(self.T): +1028 if _check_for_none(self, self.content[t]): +1029 newcontent.append(None) +1030 else: +1031 newcontent.append(self.content[t] / y) +1032 return Corr(newcontent, prange=self.prange) +1033 +1034 elif isinstance(y, (int, float)): +1035 if y == 0: +1036 raise Exception('Division by zero will return undefined correlator') +1037 newcontent = [] +1038 for t in range(self.T): +1039 if _check_for_none(self, self.content[t]): +1040 newcontent.append(None) +1041 else: +1042 newcontent.append(self.content[t] / y) +1043 return Corr(newcontent, prange=self.prange) +1044 elif isinstance(y, np.ndarray): +1045 if y.shape == (self.T,): +1046 return Corr(list((np.array(self.content).T / y).T)) +1047 else: +1048 raise ValueError("operands could not be broadcast together") +1049 else: +1050 raise TypeError('Corr / wrong type') +1051 +1052 def __neg__(self): +1053 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1054 return Corr(newcontent, prange=self.prange) +1055 +1056 def __sub__(self, y): +1057 return self + (-y) +1058 +1059 def __pow__(self, y): +1060 if isinstance(y, (Obs, int, float, CObs)): +1061 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1062 return Corr(newcontent, prange=self.prange) +1063 else: +1064 raise TypeError('Type of exponent not supported') +1065 +1066 def __abs__(self): +1067 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1068 return Corr(newcontent, prange=self.prange) +1069 +1070 # The numpy functions: +1071 def sqrt(self): +1072 return self ** 0.5 +1073 +1074 def log(self): +1075 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1076 return Corr(newcontent, prange=self.prange) +1077 +1078 def exp(self): +1079 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1080 return Corr(newcontent, prange=self.prange) +1081 +1082 def _apply_func_to_corr(self, func): +1083 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1084 for t in range(self.T): +1085 if _check_for_none(self, newcontent[t]): +1086 continue +1087 if np.isnan(np.sum(newcontent[t]).value): +1088 newcontent[t] = None +1089 if all([item is None for item in newcontent]): +1090 raise Exception('Operation returns undefined correlator') +1091 return Corr(newcontent) 1092 -1093 def tan(self): -1094 return self._apply_func_to_corr(np.tan) +1093 def sin(self): +1094 return self._apply_func_to_corr(np.sin) 1095 -1096 def sinh(self): -1097 return self._apply_func_to_corr(np.sinh) +1096 def cos(self): +1097 return self._apply_func_to_corr(np.cos) 1098 -1099 def cosh(self): -1100 return self._apply_func_to_corr(np.cosh) +1099 def tan(self): +1100 return self._apply_func_to_corr(np.tan) 1101 -1102 def tanh(self): -1103 return self._apply_func_to_corr(np.tanh) +1102 def sinh(self): +1103 return self._apply_func_to_corr(np.sinh) 1104 -1105 def arcsin(self): -1106 return self._apply_func_to_corr(np.arcsin) +1105 def cosh(self): +1106 return self._apply_func_to_corr(np.cosh) 1107 -1108 def arccos(self): -1109 return self._apply_func_to_corr(np.arccos) +1108 def tanh(self): +1109 return self._apply_func_to_corr(np.tanh) 1110 -1111 def arctan(self): -1112 return self._apply_func_to_corr(np.arctan) +1111 def arcsin(self): +1112 return self._apply_func_to_corr(np.arcsin) 1113 -1114 def arcsinh(self): -1115 return self._apply_func_to_corr(np.arcsinh) +1114 def arccos(self): +1115 return self._apply_func_to_corr(np.arccos) 1116 -1117 def arccosh(self): -1118 return self._apply_func_to_corr(np.arccosh) +1117 def arctan(self): +1118 return self._apply_func_to_corr(np.arctan) 1119 -1120 def arctanh(self): -1121 return self._apply_func_to_corr(np.arctanh) +1120 def arcsinh(self): +1121 return self._apply_func_to_corr(np.arcsinh) 1122 -1123 # Right hand side operations (require tweak in main module to work) -1124 def __radd__(self, y): -1125 return self + y -1126 -1127 def __rsub__(self, y): -1128 return -self + y -1129 -1130 def __rmul__(self, y): -1131 return self * y +1123 def arccosh(self): +1124 return self._apply_func_to_corr(np.arccosh) +1125 +1126 def arctanh(self): +1127 return self._apply_func_to_corr(np.arctanh) +1128 +1129 # Right hand side operations (require tweak in main module to work) +1130 def __radd__(self, y): +1131 return self + y 1132 -1133 def __rtruediv__(self, y): -1134 return (self / y) ** (-1) +1133 def __rsub__(self, y): +1134 return -self + y 1135 -1136 @property -1137 def real(self): -1138 def return_real(obs_OR_cobs): -1139 if isinstance(obs_OR_cobs, CObs): -1140 return obs_OR_cobs.real -1141 else: -1142 return obs_OR_cobs -1143 -1144 return self._apply_func_to_corr(return_real) -1145 -1146 @property -1147 def imag(self): -1148 def return_imag(obs_OR_cobs): -1149 if isinstance(obs_OR_cobs, CObs): -1150 return obs_OR_cobs.imag -1151 else: -1152 return obs_OR_cobs * 0 # So it stays the right type -1153 -1154 return self._apply_func_to_corr(return_imag) -1155 -1156 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1157 r''' Project large correlation matrix to lowest states -1158 -1159 This method can be used to reduce the size of an (N x N) correlation matrix -1160 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1161 is still small. -1162 -1163 Parameters -1164 ---------- -1165 Ntrunc: int -1166 Rank of the target matrix. -1167 tproj: int -1168 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1169 The default value is 3. -1170 t0proj: int -1171 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1172 discouraged for O(a) improved theories, since the correctness of the procedure -1173 cannot be granted in this case. The default value is 2. -1174 basematrix : Corr -1175 Correlation matrix that is used to determine the eigenvectors of the -1176 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1177 is is not specified. -1178 -1179 Notes -1180 ----- -1181 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1182 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1183 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1184 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1185 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1186 correlation matrix and to remove some noise that is added by irrelevant operators. -1187 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1188 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1189 ''' -1190 -1191 if self.N == 1: -1192 raise Exception('Method cannot be applied to one-dimensional correlators.') -1193 if basematrix is None: -1194 basematrix = self -1195 if Ntrunc >= basematrix.N: -1196 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1197 if basematrix.N != self.N: -1198 raise Exception('basematrix and targetmatrix have to be of the same size.') -1199 -1200 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1201 -1202 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1203 rmat = [] -1204 for t in range(basematrix.T): -1205 for i in range(Ntrunc): -1206 for j in range(Ntrunc): -1207 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1208 rmat.append(np.copy(tmpmat)) -1209 -1210 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1211 return Corr(newcontent) -1212 -1213 -1214def _sort_vectors(vec_set, ts): -1215 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" -1216 reference_sorting = np.array(vec_set[ts]) -1217 N = reference_sorting.shape[0] -1218 sorted_vec_set = [] -1219 for t in range(len(vec_set)): -1220 if vec_set[t] is None: -1221 sorted_vec_set.append(None) -1222 elif not t == ts: -1223 perms = [list(o) for o in permutations([i for i in range(N)], N)] -1224 best_score = 0 -1225 for perm in perms: -1226 current_score = 1 -1227 for k in range(N): -1228 new_sorting = reference_sorting.copy() -1229 new_sorting[perm[k], :] = vec_set[t][k] -1230 current_score *= abs(np.linalg.det(new_sorting)) -1231 if current_score > best_score: -1232 best_score = current_score -1233 best_perm = perm -1234 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) -1235 else: -1236 sorted_vec_set.append(vec_set[t]) -1237 -1238 return sorted_vec_set -1239 -1240 -1241def _check_for_none(corr, entry): -1242 """Checks if entry for correlator corr is None""" -1243 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 -1244 +1136 def __rmul__(self, y): +1137 return self * y +1138 +1139 def __rtruediv__(self, y): +1140 return (self / y) ** (-1) +1141 +1142 @property +1143 def real(self): +1144 def return_real(obs_OR_cobs): +1145 if isinstance(obs_OR_cobs, CObs): +1146 return obs_OR_cobs.real +1147 else: +1148 return obs_OR_cobs +1149 +1150 return self._apply_func_to_corr(return_real) +1151 +1152 @property +1153 def imag(self): +1154 def return_imag(obs_OR_cobs): +1155 if isinstance(obs_OR_cobs, CObs): +1156 return obs_OR_cobs.imag +1157 else: +1158 return obs_OR_cobs * 0 # So it stays the right type +1159 +1160 return self._apply_func_to_corr(return_imag) +1161 +1162 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1163 r''' Project large correlation matrix to lowest states +1164 +1165 This method can be used to reduce the size of an (N x N) correlation matrix +1166 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1167 is still small. +1168 +1169 Parameters +1170 ---------- +1171 Ntrunc: int +1172 Rank of the target matrix. +1173 tproj: int +1174 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1175 The default value is 3. +1176 t0proj: int +1177 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1178 discouraged for O(a) improved theories, since the correctness of the procedure +1179 cannot be granted in this case. The default value is 2. +1180 basematrix : Corr +1181 Correlation matrix that is used to determine the eigenvectors of the +1182 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1183 is is not specified. +1184 +1185 Notes +1186 ----- +1187 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1188 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1189 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1190 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1191 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1192 correlation matrix and to remove some noise that is added by irrelevant operators. +1193 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1194 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1195 ''' +1196 +1197 if self.N == 1: +1198 raise Exception('Method cannot be applied to one-dimensional correlators.') +1199 if basematrix is None: +1200 basematrix = self +1201 if Ntrunc >= basematrix.N: +1202 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1203 if basematrix.N != self.N: +1204 raise Exception('basematrix and targetmatrix have to be of the same size.') +1205 +1206 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1207 +1208 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1209 rmat = [] +1210 for t in range(basematrix.T): +1211 for i in range(Ntrunc): +1212 for j in range(Ntrunc): +1213 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1214 rmat.append(np.copy(tmpmat)) +1215 +1216 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1217 return Corr(newcontent) +1218 +1219 +1220def _sort_vectors(vec_set, ts): +1221 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" +1222 reference_sorting = np.array(vec_set[ts]) +1223 N = reference_sorting.shape[0] +1224 sorted_vec_set = [] +1225 for t in range(len(vec_set)): +1226 if vec_set[t] is None: +1227 sorted_vec_set.append(None) +1228 elif not t == ts: +1229 perms = [list(o) for o in permutations([i for i in range(N)], N)] +1230 best_score = 0 +1231 for perm in perms: +1232 current_score = 1 +1233 for k in range(N): +1234 new_sorting = reference_sorting.copy() +1235 new_sorting[perm[k], :] = vec_set[t][k] +1236 current_score *= abs(np.linalg.det(new_sorting)) +1237 if current_score > best_score: +1238 best_score = current_score +1239 best_perm = perm +1240 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) +1241 else: +1242 sorted_vec_set.append(vec_set[t]) +1243 +1244 return sorted_vec_set 1245 -1246def _GEVP_solver(Gt, G0): -1247 """Helper function for solving the GEVP and sorting the eigenvectors. -1248 -1249 The helper function assumes that both provided matrices are symmetric and -1250 only processes the lower triangular part of both matrices. In case the matrices -1251 are not symmetric the upper triangular parts are effectively discarded.""" -1252 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] +1246 +1247def _check_for_none(corr, entry): +1248 """Checks if entry for correlator corr is None""" +1249 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1250 +1251 +1252def _GEVP_solver(Gt, G0): +1253 """Helper function for solving the GEVP and sorting the eigenvectors. +1254 +1255 The helper function assumes that both provided matrices are symmetric and +1256 only processes the lower triangular part of both matrices. In case the matrices +1257 are not symmetric the upper triangular parts are effectively discarded.""" +1258 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] @@ -2200,484 +2206,490 @@ 732 self.prange = prange 733 return 734 - 735 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None): + 735 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): 736 """Plots the correlator using the tag of the correlator as label if available. 737 738 Parameters 739 ---------- 740 x_range : list - 741 list of two values, determining the range of the x-axis e.g. [4, 8] + 741 list of two values, determining the range of the x-axis e.g. [4, 8]. 742 comp : Corr or list of Corr 743 Correlator or list of correlators which are plotted for comparison. 744 The tags of these correlators are used as labels if available. 745 logscale : bool - 746 Sets y-axis to logscale + 746 Sets y-axis to logscale. 747 plateau : Obs - 748 Plateau value to be visualized in the figure + 748 Plateau value to be visualized in the figure. 749 fit_res : Fit_result - 750 Fit_result object to be visualized + 750 Fit_result object to be visualized. 751 ylabel : str - 752 Label for the y-axis + 752 Label for the y-axis. 753 save : str - 754 path to file in which the figure should be saved + 754 path to file in which the figure should be saved. 755 auto_gamma : bool 756 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. 757 hide_sigma : float 758 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. 759 references : list 760 List of floating point values that are displayed as horizontal lines for reference. - 761 """ - 762 if self.N != 1: - 763 raise Exception("Correlator must be projected before plotting") - 764 - 765 if auto_gamma: - 766 self.gamma_method() - 767 - 768 if x_range is None: - 769 x_range = [0, self.T - 1] - 770 - 771 fig = plt.figure() - 772 ax1 = fig.add_subplot(111) - 773 - 774 x, y, y_err = self.plottable() - 775 if hide_sigma: - 776 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 777 else: - 778 hide_from = None - 779 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 780 if logscale: - 781 ax1.set_yscale('log') - 782 else: - 783 if y_range is None: - 784 try: - 785 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) - 786 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) - 787 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 788 except Exception: - 789 pass - 790 else: - 791 ax1.set_ylim(y_range) - 792 if comp: - 793 if isinstance(comp, (Corr, list)): - 794 for corr in comp if isinstance(comp, list) else [comp]: - 795 if auto_gamma: - 796 corr.gamma_method() - 797 x, y, y_err = corr.plottable() - 798 if hide_sigma: - 799 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 800 else: - 801 hide_from = None - 802 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 803 else: - 804 raise Exception("'comp' must be a correlator or a list of correlators.") - 805 - 806 if plateau: - 807 if isinstance(plateau, Obs): - 808 if auto_gamma: - 809 plateau.gamma_method() - 810 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 811 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 812 else: - 813 raise Exception("'plateau' must be an Obs") - 814 - 815 if references: - 816 if isinstance(references, list): - 817 for ref in references: - 818 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 819 else: - 820 raise Exception("'references' must be a list of floating pint values.") - 821 - 822 if self.prange: - 823 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 824 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 825 - 826 if fit_res: - 827 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 828 ax1.plot(x_samples, - 829 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 830 ls='-', marker=',', lw=2) - 831 - 832 ax1.set_xlabel(r'$x_0 / a$') - 833 if ylabel: - 834 ax1.set_ylabel(ylabel) - 835 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 836 - 837 handles, labels = ax1.get_legend_handles_labels() - 838 if labels: - 839 ax1.legend() - 840 plt.draw() - 841 - 842 if save: - 843 if isinstance(save, str): - 844 fig.savefig(save) - 845 else: - 846 raise Exception("'save' has to be a string.") + 761 title : string + 762 Optional title of the figure. + 763 """ + 764 if self.N != 1: + 765 raise Exception("Correlator must be projected before plotting") + 766 + 767 if auto_gamma: + 768 self.gamma_method() + 769 + 770 if x_range is None: + 771 x_range = [0, self.T - 1] + 772 + 773 fig = plt.figure() + 774 ax1 = fig.add_subplot(111) + 775 + 776 x, y, y_err = self.plottable() + 777 if hide_sigma: + 778 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 779 else: + 780 hide_from = None + 781 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 782 if logscale: + 783 ax1.set_yscale('log') + 784 else: + 785 if y_range is None: + 786 try: + 787 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 788 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 789 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 790 except Exception: + 791 pass + 792 else: + 793 ax1.set_ylim(y_range) + 794 if comp: + 795 if isinstance(comp, (Corr, list)): + 796 for corr in comp if isinstance(comp, list) else [comp]: + 797 if auto_gamma: + 798 corr.gamma_method() + 799 x, y, y_err = corr.plottable() + 800 if hide_sigma: + 801 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 802 else: + 803 hide_from = None + 804 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 805 else: + 806 raise Exception("'comp' must be a correlator or a list of correlators.") + 807 + 808 if plateau: + 809 if isinstance(plateau, Obs): + 810 if auto_gamma: + 811 plateau.gamma_method() + 812 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 813 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 814 else: + 815 raise Exception("'plateau' must be an Obs") + 816 + 817 if references: + 818 if isinstance(references, list): + 819 for ref in references: + 820 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 821 else: + 822 raise Exception("'references' must be a list of floating pint values.") + 823 + 824 if self.prange: + 825 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 826 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') + 827 + 828 if fit_res: + 829 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 830 ax1.plot(x_samples, + 831 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 832 ls='-', marker=',', lw=2) + 833 + 834 ax1.set_xlabel(r'$x_0 / a$') + 835 if ylabel: + 836 ax1.set_ylabel(ylabel) + 837 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 838 + 839 handles, labels = ax1.get_legend_handles_labels() + 840 if labels: + 841 ax1.legend() + 842 + 843 if title: + 844 plt.title(title) + 845 + 846 plt.draw() 847 - 848 def spaghetti_plot(self, logscale=True): - 849 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 850 - 851 Parameters - 852 ---------- - 853 logscale : bool - 854 Determines whether the scale of the y-axis is logarithmic or standard. - 855 """ - 856 if self.N != 1: - 857 raise Exception("Correlator needs to be projected first.") - 858 - 859 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) - 860 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 861 - 862 for name in mc_names: - 863 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 848 if save: + 849 if isinstance(save, str): + 850 fig.savefig(save) + 851 else: + 852 raise Exception("'save' has to be a string.") + 853 + 854 def spaghetti_plot(self, logscale=True): + 855 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 856 + 857 Parameters + 858 ---------- + 859 logscale : bool + 860 Determines whether the scale of the y-axis is logarithmic or standard. + 861 """ + 862 if self.N != 1: + 863 raise Exception("Correlator needs to be projected first.") 864 - 865 fig = plt.figure() - 866 ax = fig.add_subplot(111) - 867 for dat in data: - 868 ax.plot(x0_vals, dat, ls='-', marker='') - 869 - 870 if logscale is True: - 871 ax.set_yscale('log') - 872 - 873 ax.set_xlabel(r'$x_0 / a$') - 874 plt.title(name) - 875 plt.draw() - 876 - 877 def dump(self, filename, datatype="json.gz", **kwargs): - 878 """Dumps the Corr into a file of chosen type - 879 Parameters - 880 ---------- - 881 filename : str - 882 Name of the file to be saved. - 883 datatype : str - 884 Format of the exported file. Supported formats include - 885 "json.gz" and "pickle" - 886 path : str - 887 specifies a custom path for the file (default '.') - 888 """ - 889 if datatype == "json.gz": - 890 from .input.json import dump_to_json - 891 if 'path' in kwargs: - 892 file_name = kwargs.get('path') + '/' + filename - 893 else: - 894 file_name = filename - 895 dump_to_json(self, file_name) - 896 elif datatype == "pickle": - 897 dump_object(self, filename, **kwargs) - 898 else: - 899 raise Exception("Unknown datatype " + str(datatype)) - 900 - 901 def print(self, print_range=None): - 902 print(self.__repr__(print_range)) - 903 - 904 def __repr__(self, print_range=None): - 905 if print_range is None: - 906 print_range = [0, None] - 907 - 908 content_string = "" - 909 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here - 910 - 911 if self.tag is not None: - 912 content_string += "Description: " + self.tag + "\n" - 913 if self.N != 1: - 914 return content_string - 915 - 916 if print_range[1]: - 917 print_range[1] += 1 - 918 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 919 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 920 if sub_corr is None: - 921 content_string += str(i + print_range[0]) + '\n' - 922 else: - 923 content_string += str(i + print_range[0]) - 924 for element in sub_corr: - 925 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 926 content_string += '\n' - 927 return content_string - 928 - 929 def __str__(self): - 930 return self.__repr__() - 931 - 932 # We define the basic operations, that can be performed with correlators. - 933 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 934 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 935 # One could try and tell Obs to check if the y in __mul__ is a Corr and - 936 - 937 def __add__(self, y): - 938 if isinstance(y, Corr): - 939 if ((self.N != y.N) or (self.T != y.T)): - 940 raise Exception("Addition of Corrs with different shape") - 941 newcontent = [] - 942 for t in range(self.T): - 943 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 944 newcontent.append(None) - 945 else: - 946 newcontent.append(self.content[t] + y.content[t]) - 947 return Corr(newcontent) - 948 - 949 elif isinstance(y, (Obs, int, float, CObs)): - 950 newcontent = [] - 951 for t in range(self.T): - 952 if _check_for_none(self, self.content[t]): - 953 newcontent.append(None) - 954 else: - 955 newcontent.append(self.content[t] + y) - 956 return Corr(newcontent, prange=self.prange) - 957 elif isinstance(y, np.ndarray): - 958 if y.shape == (self.T,): - 959 return Corr(list((np.array(self.content).T + y).T)) - 960 else: - 961 raise ValueError("operands could not be broadcast together") - 962 else: - 963 raise TypeError("Corr + wrong type") - 964 - 965 def __mul__(self, y): - 966 if isinstance(y, Corr): - 967 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 968 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") - 969 newcontent = [] - 970 for t in range(self.T): - 971 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 972 newcontent.append(None) - 973 else: - 974 newcontent.append(self.content[t] * y.content[t]) - 975 return Corr(newcontent) - 976 - 977 elif isinstance(y, (Obs, int, float, CObs)): - 978 newcontent = [] - 979 for t in range(self.T): - 980 if _check_for_none(self, self.content[t]): - 981 newcontent.append(None) - 982 else: - 983 newcontent.append(self.content[t] * y) - 984 return Corr(newcontent, prange=self.prange) - 985 elif isinstance(y, np.ndarray): - 986 if y.shape == (self.T,): - 987 return Corr(list((np.array(self.content).T * y).T)) - 988 else: - 989 raise ValueError("operands could not be broadcast together") - 990 else: - 991 raise TypeError("Corr * wrong type") - 992 - 993 def __truediv__(self, y): - 994 if isinstance(y, Corr): - 995 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 996 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") - 997 newcontent = [] - 998 for t in range(self.T): - 999 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1000 newcontent.append(None) -1001 else: -1002 newcontent.append(self.content[t] / y.content[t]) -1003 for t in range(self.T): -1004 if _check_for_none(self, newcontent[t]): -1005 continue -1006 if np.isnan(np.sum(newcontent[t]).value): -1007 newcontent[t] = None -1008 -1009 if all([item is None for item in newcontent]): -1010 raise Exception("Division returns completely undefined correlator") -1011 return Corr(newcontent) -1012 -1013 elif isinstance(y, (Obs, CObs)): -1014 if isinstance(y, Obs): -1015 if y.value == 0: -1016 raise Exception('Division by zero will return undefined correlator') -1017 if isinstance(y, CObs): -1018 if y.is_zero(): -1019 raise Exception('Division by zero will return undefined correlator') -1020 -1021 newcontent = [] -1022 for t in range(self.T): -1023 if _check_for_none(self, self.content[t]): -1024 newcontent.append(None) -1025 else: -1026 newcontent.append(self.content[t] / y) -1027 return Corr(newcontent, prange=self.prange) -1028 -1029 elif isinstance(y, (int, float)): -1030 if y == 0: -1031 raise Exception('Division by zero will return undefined correlator') -1032 newcontent = [] -1033 for t in range(self.T): -1034 if _check_for_none(self, self.content[t]): -1035 newcontent.append(None) -1036 else: -1037 newcontent.append(self.content[t] / y) -1038 return Corr(newcontent, prange=self.prange) -1039 elif isinstance(y, np.ndarray): -1040 if y.shape == (self.T,): -1041 return Corr(list((np.array(self.content).T / y).T)) -1042 else: -1043 raise ValueError("operands could not be broadcast together") -1044 else: -1045 raise TypeError('Corr / wrong type') -1046 -1047 def __neg__(self): -1048 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1049 return Corr(newcontent, prange=self.prange) -1050 -1051 def __sub__(self, y): -1052 return self + (-y) -1053 -1054 def __pow__(self, y): -1055 if isinstance(y, (Obs, int, float, CObs)): -1056 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1057 return Corr(newcontent, prange=self.prange) -1058 else: -1059 raise TypeError('Type of exponent not supported') -1060 -1061 def __abs__(self): -1062 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1063 return Corr(newcontent, prange=self.prange) -1064 -1065 # The numpy functions: -1066 def sqrt(self): -1067 return self ** 0.5 -1068 -1069 def log(self): -1070 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1071 return Corr(newcontent, prange=self.prange) -1072 -1073 def exp(self): -1074 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1075 return Corr(newcontent, prange=self.prange) -1076 -1077 def _apply_func_to_corr(self, func): -1078 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1079 for t in range(self.T): -1080 if _check_for_none(self, newcontent[t]): -1081 continue -1082 if np.isnan(np.sum(newcontent[t]).value): -1083 newcontent[t] = None -1084 if all([item is None for item in newcontent]): -1085 raise Exception('Operation returns undefined correlator') -1086 return Corr(newcontent) -1087 -1088 def sin(self): -1089 return self._apply_func_to_corr(np.sin) -1090 -1091 def cos(self): -1092 return self._apply_func_to_corr(np.cos) + 865 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) + 866 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 867 + 868 for name in mc_names: + 869 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 870 + 871 fig = plt.figure() + 872 ax = fig.add_subplot(111) + 873 for dat in data: + 874 ax.plot(x0_vals, dat, ls='-', marker='') + 875 + 876 if logscale is True: + 877 ax.set_yscale('log') + 878 + 879 ax.set_xlabel(r'$x_0 / a$') + 880 plt.title(name) + 881 plt.draw() + 882 + 883 def dump(self, filename, datatype="json.gz", **kwargs): + 884 """Dumps the Corr into a file of chosen type + 885 Parameters + 886 ---------- + 887 filename : str + 888 Name of the file to be saved. + 889 datatype : str + 890 Format of the exported file. Supported formats include + 891 "json.gz" and "pickle" + 892 path : str + 893 specifies a custom path for the file (default '.') + 894 """ + 895 if datatype == "json.gz": + 896 from .input.json import dump_to_json + 897 if 'path' in kwargs: + 898 file_name = kwargs.get('path') + '/' + filename + 899 else: + 900 file_name = filename + 901 dump_to_json(self, file_name) + 902 elif datatype == "pickle": + 903 dump_object(self, filename, **kwargs) + 904 else: + 905 raise Exception("Unknown datatype " + str(datatype)) + 906 + 907 def print(self, print_range=None): + 908 print(self.__repr__(print_range)) + 909 + 910 def __repr__(self, print_range=None): + 911 if print_range is None: + 912 print_range = [0, None] + 913 + 914 content_string = "" + 915 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here + 916 + 917 if self.tag is not None: + 918 content_string += "Description: " + self.tag + "\n" + 919 if self.N != 1: + 920 return content_string + 921 + 922 if print_range[1]: + 923 print_range[1] += 1 + 924 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 925 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 926 if sub_corr is None: + 927 content_string += str(i + print_range[0]) + '\n' + 928 else: + 929 content_string += str(i + print_range[0]) + 930 for element in sub_corr: + 931 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 932 content_string += '\n' + 933 return content_string + 934 + 935 def __str__(self): + 936 return self.__repr__() + 937 + 938 # We define the basic operations, that can be performed with correlators. + 939 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. + 940 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. + 941 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 942 + 943 def __add__(self, y): + 944 if isinstance(y, Corr): + 945 if ((self.N != y.N) or (self.T != y.T)): + 946 raise Exception("Addition of Corrs with different shape") + 947 newcontent = [] + 948 for t in range(self.T): + 949 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): + 950 newcontent.append(None) + 951 else: + 952 newcontent.append(self.content[t] + y.content[t]) + 953 return Corr(newcontent) + 954 + 955 elif isinstance(y, (Obs, int, float, CObs)): + 956 newcontent = [] + 957 for t in range(self.T): + 958 if _check_for_none(self, self.content[t]): + 959 newcontent.append(None) + 960 else: + 961 newcontent.append(self.content[t] + y) + 962 return Corr(newcontent, prange=self.prange) + 963 elif isinstance(y, np.ndarray): + 964 if y.shape == (self.T,): + 965 return Corr(list((np.array(self.content).T + y).T)) + 966 else: + 967 raise ValueError("operands could not be broadcast together") + 968 else: + 969 raise TypeError("Corr + wrong type") + 970 + 971 def __mul__(self, y): + 972 if isinstance(y, Corr): + 973 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): + 974 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") + 975 newcontent = [] + 976 for t in range(self.T): + 977 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): + 978 newcontent.append(None) + 979 else: + 980 newcontent.append(self.content[t] * y.content[t]) + 981 return Corr(newcontent) + 982 + 983 elif isinstance(y, (Obs, int, float, CObs)): + 984 newcontent = [] + 985 for t in range(self.T): + 986 if _check_for_none(self, self.content[t]): + 987 newcontent.append(None) + 988 else: + 989 newcontent.append(self.content[t] * y) + 990 return Corr(newcontent, prange=self.prange) + 991 elif isinstance(y, np.ndarray): + 992 if y.shape == (self.T,): + 993 return Corr(list((np.array(self.content).T * y).T)) + 994 else: + 995 raise ValueError("operands could not be broadcast together") + 996 else: + 997 raise TypeError("Corr * wrong type") + 998 + 999 def __truediv__(self, y): +1000 if isinstance(y, Corr): +1001 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1002 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1003 newcontent = [] +1004 for t in range(self.T): +1005 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1006 newcontent.append(None) +1007 else: +1008 newcontent.append(self.content[t] / y.content[t]) +1009 for t in range(self.T): +1010 if _check_for_none(self, newcontent[t]): +1011 continue +1012 if np.isnan(np.sum(newcontent[t]).value): +1013 newcontent[t] = None +1014 +1015 if all([item is None for item in newcontent]): +1016 raise Exception("Division returns completely undefined correlator") +1017 return Corr(newcontent) +1018 +1019 elif isinstance(y, (Obs, CObs)): +1020 if isinstance(y, Obs): +1021 if y.value == 0: +1022 raise Exception('Division by zero will return undefined correlator') +1023 if isinstance(y, CObs): +1024 if y.is_zero(): +1025 raise Exception('Division by zero will return undefined correlator') +1026 +1027 newcontent = [] +1028 for t in range(self.T): +1029 if _check_for_none(self, self.content[t]): +1030 newcontent.append(None) +1031 else: +1032 newcontent.append(self.content[t] / y) +1033 return Corr(newcontent, prange=self.prange) +1034 +1035 elif isinstance(y, (int, float)): +1036 if y == 0: +1037 raise Exception('Division by zero will return undefined correlator') +1038 newcontent = [] +1039 for t in range(self.T): +1040 if _check_for_none(self, self.content[t]): +1041 newcontent.append(None) +1042 else: +1043 newcontent.append(self.content[t] / y) +1044 return Corr(newcontent, prange=self.prange) +1045 elif isinstance(y, np.ndarray): +1046 if y.shape == (self.T,): +1047 return Corr(list((np.array(self.content).T / y).T)) +1048 else: +1049 raise ValueError("operands could not be broadcast together") +1050 else: +1051 raise TypeError('Corr / wrong type') +1052 +1053 def __neg__(self): +1054 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1055 return Corr(newcontent, prange=self.prange) +1056 +1057 def __sub__(self, y): +1058 return self + (-y) +1059 +1060 def __pow__(self, y): +1061 if isinstance(y, (Obs, int, float, CObs)): +1062 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1063 return Corr(newcontent, prange=self.prange) +1064 else: +1065 raise TypeError('Type of exponent not supported') +1066 +1067 def __abs__(self): +1068 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1069 return Corr(newcontent, prange=self.prange) +1070 +1071 # The numpy functions: +1072 def sqrt(self): +1073 return self ** 0.5 +1074 +1075 def log(self): +1076 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1077 return Corr(newcontent, prange=self.prange) +1078 +1079 def exp(self): +1080 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1081 return Corr(newcontent, prange=self.prange) +1082 +1083 def _apply_func_to_corr(self, func): +1084 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1085 for t in range(self.T): +1086 if _check_for_none(self, newcontent[t]): +1087 continue +1088 if np.isnan(np.sum(newcontent[t]).value): +1089 newcontent[t] = None +1090 if all([item is None for item in newcontent]): +1091 raise Exception('Operation returns undefined correlator') +1092 return Corr(newcontent) 1093 -1094 def tan(self): -1095 return self._apply_func_to_corr(np.tan) +1094 def sin(self): +1095 return self._apply_func_to_corr(np.sin) 1096 -1097 def sinh(self): -1098 return self._apply_func_to_corr(np.sinh) +1097 def cos(self): +1098 return self._apply_func_to_corr(np.cos) 1099 -1100 def cosh(self): -1101 return self._apply_func_to_corr(np.cosh) +1100 def tan(self): +1101 return self._apply_func_to_corr(np.tan) 1102 -1103 def tanh(self): -1104 return self._apply_func_to_corr(np.tanh) +1103 def sinh(self): +1104 return self._apply_func_to_corr(np.sinh) 1105 -1106 def arcsin(self): -1107 return self._apply_func_to_corr(np.arcsin) +1106 def cosh(self): +1107 return self._apply_func_to_corr(np.cosh) 1108 -1109 def arccos(self): -1110 return self._apply_func_to_corr(np.arccos) +1109 def tanh(self): +1110 return self._apply_func_to_corr(np.tanh) 1111 -1112 def arctan(self): -1113 return self._apply_func_to_corr(np.arctan) +1112 def arcsin(self): +1113 return self._apply_func_to_corr(np.arcsin) 1114 -1115 def arcsinh(self): -1116 return self._apply_func_to_corr(np.arcsinh) +1115 def arccos(self): +1116 return self._apply_func_to_corr(np.arccos) 1117 -1118 def arccosh(self): -1119 return self._apply_func_to_corr(np.arccosh) +1118 def arctan(self): +1119 return self._apply_func_to_corr(np.arctan) 1120 -1121 def arctanh(self): -1122 return self._apply_func_to_corr(np.arctanh) +1121 def arcsinh(self): +1122 return self._apply_func_to_corr(np.arcsinh) 1123 -1124 # Right hand side operations (require tweak in main module to work) -1125 def __radd__(self, y): -1126 return self + y -1127 -1128 def __rsub__(self, y): -1129 return -self + y -1130 -1131 def __rmul__(self, y): -1132 return self * y +1124 def arccosh(self): +1125 return self._apply_func_to_corr(np.arccosh) +1126 +1127 def arctanh(self): +1128 return self._apply_func_to_corr(np.arctanh) +1129 +1130 # Right hand side operations (require tweak in main module to work) +1131 def __radd__(self, y): +1132 return self + y 1133 -1134 def __rtruediv__(self, y): -1135 return (self / y) ** (-1) +1134 def __rsub__(self, y): +1135 return -self + y 1136 -1137 @property -1138 def real(self): -1139 def return_real(obs_OR_cobs): -1140 if isinstance(obs_OR_cobs, CObs): -1141 return obs_OR_cobs.real -1142 else: -1143 return obs_OR_cobs -1144 -1145 return self._apply_func_to_corr(return_real) -1146 -1147 @property -1148 def imag(self): -1149 def return_imag(obs_OR_cobs): -1150 if isinstance(obs_OR_cobs, CObs): -1151 return obs_OR_cobs.imag -1152 else: -1153 return obs_OR_cobs * 0 # So it stays the right type -1154 -1155 return self._apply_func_to_corr(return_imag) -1156 -1157 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1158 r''' Project large correlation matrix to lowest states -1159 -1160 This method can be used to reduce the size of an (N x N) correlation matrix -1161 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1162 is still small. -1163 -1164 Parameters -1165 ---------- -1166 Ntrunc: int -1167 Rank of the target matrix. -1168 tproj: int -1169 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1170 The default value is 3. -1171 t0proj: int -1172 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1173 discouraged for O(a) improved theories, since the correctness of the procedure -1174 cannot be granted in this case. The default value is 2. -1175 basematrix : Corr -1176 Correlation matrix that is used to determine the eigenvectors of the -1177 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1178 is is not specified. -1179 -1180 Notes -1181 ----- -1182 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1183 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1184 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1185 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1186 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1187 correlation matrix and to remove some noise that is added by irrelevant operators. -1188 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1189 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1190 ''' -1191 -1192 if self.N == 1: -1193 raise Exception('Method cannot be applied to one-dimensional correlators.') -1194 if basematrix is None: -1195 basematrix = self -1196 if Ntrunc >= basematrix.N: -1197 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1198 if basematrix.N != self.N: -1199 raise Exception('basematrix and targetmatrix have to be of the same size.') -1200 -1201 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1202 -1203 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1204 rmat = [] -1205 for t in range(basematrix.T): -1206 for i in range(Ntrunc): -1207 for j in range(Ntrunc): -1208 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1209 rmat.append(np.copy(tmpmat)) -1210 -1211 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1212 return Corr(newcontent) +1137 def __rmul__(self, y): +1138 return self * y +1139 +1140 def __rtruediv__(self, y): +1141 return (self / y) ** (-1) +1142 +1143 @property +1144 def real(self): +1145 def return_real(obs_OR_cobs): +1146 if isinstance(obs_OR_cobs, CObs): +1147 return obs_OR_cobs.real +1148 else: +1149 return obs_OR_cobs +1150 +1151 return self._apply_func_to_corr(return_real) +1152 +1153 @property +1154 def imag(self): +1155 def return_imag(obs_OR_cobs): +1156 if isinstance(obs_OR_cobs, CObs): +1157 return obs_OR_cobs.imag +1158 else: +1159 return obs_OR_cobs * 0 # So it stays the right type +1160 +1161 return self._apply_func_to_corr(return_imag) +1162 +1163 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1164 r''' Project large correlation matrix to lowest states +1165 +1166 This method can be used to reduce the size of an (N x N) correlation matrix +1167 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1168 is still small. +1169 +1170 Parameters +1171 ---------- +1172 Ntrunc: int +1173 Rank of the target matrix. +1174 tproj: int +1175 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1176 The default value is 3. +1177 t0proj: int +1178 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1179 discouraged for O(a) improved theories, since the correctness of the procedure +1180 cannot be granted in this case. The default value is 2. +1181 basematrix : Corr +1182 Correlation matrix that is used to determine the eigenvectors of the +1183 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1184 is is not specified. +1185 +1186 Notes +1187 ----- +1188 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1189 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1190 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1191 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1192 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1193 correlation matrix and to remove some noise that is added by irrelevant operators. +1194 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1195 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1196 ''' +1197 +1198 if self.N == 1: +1199 raise Exception('Method cannot be applied to one-dimensional correlators.') +1200 if basematrix is None: +1201 basematrix = self +1202 if Ntrunc >= basematrix.N: +1203 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1204 if basematrix.N != self.N: +1205 raise Exception('basematrix and targetmatrix have to be of the same size.') +1206 +1207 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1208 +1209 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1210 rmat = [] +1211 for t in range(basematrix.T): +1212 for i in range(Ntrunc): +1213 for j in range(Ntrunc): +1214 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1215 rmat.append(np.copy(tmpmat)) +1216 +1217 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1218 return Corr(newcontent) @@ -3997,124 +4009,130 @@ apply gamma_method with default parameters to the Corr. Defaults to None
def - show( self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None) + show( self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None)
- 
735    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None):
+            
735    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
 736        """Plots the correlator using the tag of the correlator as label if available.
 737
 738        Parameters
 739        ----------
 740        x_range : list
-741            list of two values, determining the range of the x-axis e.g. [4, 8]
+741            list of two values, determining the range of the x-axis e.g. [4, 8].
 742        comp : Corr or list of Corr
 743            Correlator or list of correlators which are plotted for comparison.
 744            The tags of these correlators are used as labels if available.
 745        logscale : bool
-746            Sets y-axis to logscale
+746            Sets y-axis to logscale.
 747        plateau : Obs
-748            Plateau value to be visualized in the figure
+748            Plateau value to be visualized in the figure.
 749        fit_res : Fit_result
-750            Fit_result object to be visualized
+750            Fit_result object to be visualized.
 751        ylabel : str
-752            Label for the y-axis
+752            Label for the y-axis.
 753        save : str
-754            path to file in which the figure should be saved
+754            path to file in which the figure should be saved.
 755        auto_gamma : bool
 756            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
 757        hide_sigma : float
 758            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
 759        references : list
 760            List of floating point values that are displayed as horizontal lines for reference.
-761        """
-762        if self.N != 1:
-763            raise Exception("Correlator must be projected before plotting")
-764
-765        if auto_gamma:
-766            self.gamma_method()
-767
-768        if x_range is None:
-769            x_range = [0, self.T - 1]
-770
-771        fig = plt.figure()
-772        ax1 = fig.add_subplot(111)
-773
-774        x, y, y_err = self.plottable()
-775        if hide_sigma:
-776            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-777        else:
-778            hide_from = None
-779        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
-780        if logscale:
-781            ax1.set_yscale('log')
-782        else:
-783            if y_range is None:
-784                try:
-785                    y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
-786                    y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
-787                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
-788                except Exception:
-789                    pass
-790            else:
-791                ax1.set_ylim(y_range)
-792        if comp:
-793            if isinstance(comp, (Corr, list)):
-794                for corr in comp if isinstance(comp, list) else [comp]:
-795                    if auto_gamma:
-796                        corr.gamma_method()
-797                    x, y, y_err = corr.plottable()
-798                    if hide_sigma:
-799                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-800                    else:
-801                        hide_from = None
-802                    plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
-803            else:
-804                raise Exception("'comp' must be a correlator or a list of correlators.")
-805
-806        if plateau:
-807            if isinstance(plateau, Obs):
-808                if auto_gamma:
-809                    plateau.gamma_method()
-810                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
-811                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
-812            else:
-813                raise Exception("'plateau' must be an Obs")
-814
-815        if references:
-816            if isinstance(references, list):
-817                for ref in references:
-818                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
-819            else:
-820                raise Exception("'references' must be a list of floating pint values.")
-821
-822        if self.prange:
-823            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
-824            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
-825
-826        if fit_res:
-827            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
-828            ax1.plot(x_samples,
-829                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
-830                     ls='-', marker=',', lw=2)
-831
-832        ax1.set_xlabel(r'$x_0 / a$')
-833        if ylabel:
-834            ax1.set_ylabel(ylabel)
-835        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
-836
-837        handles, labels = ax1.get_legend_handles_labels()
-838        if labels:
-839            ax1.legend()
-840        plt.draw()
-841
-842        if save:
-843            if isinstance(save, str):
-844                fig.savefig(save)
-845            else:
-846                raise Exception("'save' has to be a string.")
+761        title : string
+762            Optional title of the figure.
+763        """
+764        if self.N != 1:
+765            raise Exception("Correlator must be projected before plotting")
+766
+767        if auto_gamma:
+768            self.gamma_method()
+769
+770        if x_range is None:
+771            x_range = [0, self.T - 1]
+772
+773        fig = plt.figure()
+774        ax1 = fig.add_subplot(111)
+775
+776        x, y, y_err = self.plottable()
+777        if hide_sigma:
+778            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+779        else:
+780            hide_from = None
+781        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
+782        if logscale:
+783            ax1.set_yscale('log')
+784        else:
+785            if y_range is None:
+786                try:
+787                    y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+788                    y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+789                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
+790                except Exception:
+791                    pass
+792            else:
+793                ax1.set_ylim(y_range)
+794        if comp:
+795            if isinstance(comp, (Corr, list)):
+796                for corr in comp if isinstance(comp, list) else [comp]:
+797                    if auto_gamma:
+798                        corr.gamma_method()
+799                    x, y, y_err = corr.plottable()
+800                    if hide_sigma:
+801                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+802                    else:
+803                        hide_from = None
+804                    plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
+805            else:
+806                raise Exception("'comp' must be a correlator or a list of correlators.")
+807
+808        if plateau:
+809            if isinstance(plateau, Obs):
+810                if auto_gamma:
+811                    plateau.gamma_method()
+812                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
+813                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+814            else:
+815                raise Exception("'plateau' must be an Obs")
+816
+817        if references:
+818            if isinstance(references, list):
+819                for ref in references:
+820                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
+821            else:
+822                raise Exception("'references' must be a list of floating pint values.")
+823
+824        if self.prange:
+825            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
+826            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
+827
+828        if fit_res:
+829            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
+830            ax1.plot(x_samples,
+831                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
+832                     ls='-', marker=',', lw=2)
+833
+834        ax1.set_xlabel(r'$x_0 / a$')
+835        if ylabel:
+836            ax1.set_ylabel(ylabel)
+837        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
+838
+839        handles, labels = ax1.get_legend_handles_labels()
+840        if labels:
+841            ax1.legend()
+842
+843        if title:
+844            plt.title(title)
+845
+846        plt.draw()
+847
+848        if save:
+849            if isinstance(save, str):
+850                fig.savefig(save)
+851            else:
+852                raise Exception("'save' has to be a string.")
 

 
 
@@ -4124,26 +4142,28 @@ apply gamma_method with default parameters to the Corr. Defaults to None
 
 
    
 
  • x_range (list):
-list of two values, determining the range of the x-axis e.g. [4, 8]
    • 
+list of two values, determining the range of the x-axis e.g. [4, 8].
 
  • comp (Corr or list of Corr):
 Correlator or list of correlators which are plotted for comparison.
 The tags of these correlators are used as labels if available.
    • 
 
  • logscale (bool):
-Sets y-axis to logscale
    • 
+Sets y-axis to logscale.
 
  • plateau (Obs):
-Plateau value to be visualized in the figure
    • 
+Plateau value to be visualized in the figure.
 
  • fit_res (Fit_result):
-Fit_result object to be visualized
    • 
+Fit_result object to be visualized.
 
  • ylabel (str):
-Label for the y-axis
    • 
+Label for the y-axis.
 
  • save (str):
-path to file in which the figure should be saved
    • 
+path to file in which the figure should be saved.
 
  • auto_gamma (bool):
 Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
    • 
 
  • hide_sigma (float):
 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
    • 
 
  • references (list):
 List of floating point values that are displayed as horizontal lines for reference.
    • 
+
  • title (string):
+Optional title of the figure.
    •
@@ -4160,34 +4180,34 @@ List of floating point values that are displayed as horizontal lines for referen - 
848    def spaghetti_plot(self, logscale=True):
-849        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-850
-851        Parameters
-852        ----------
-853        logscale : bool
-854            Determines whether the scale of the y-axis is logarithmic or standard.
-855        """
-856        if self.N != 1:
-857            raise Exception("Correlator needs to be projected first.")
-858
-859        mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist]))
-860        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
-861
-862        for name in mc_names:
-863            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+            
854    def spaghetti_plot(self, logscale=True):
+855        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+856
+857        Parameters
+858        ----------
+859        logscale : bool
+860            Determines whether the scale of the y-axis is logarithmic or standard.
+861        """
+862        if self.N != 1:
+863            raise Exception("Correlator needs to be projected first.")
 864
-865            fig = plt.figure()
-866            ax = fig.add_subplot(111)
-867            for dat in data:
-868                ax.plot(x0_vals, dat, ls='-', marker='')
-869
-870            if logscale is True:
-871                ax.set_yscale('log')
-872
-873            ax.set_xlabel(r'$x_0 / a$')
-874            plt.title(name)
-875            plt.draw()
+865        mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist]))
+866        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+867
+868        for name in mc_names:
+869            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+870
+871            fig = plt.figure()
+872            ax = fig.add_subplot(111)
+873            for dat in data:
+874                ax.plot(x0_vals, dat, ls='-', marker='')
+875
+876            if logscale is True:
+877                ax.set_yscale('log')
+878
+879            ax.set_xlabel(r'$x_0 / a$')
+880            plt.title(name)
+881            plt.draw()
 

 
 
@@ -4214,29 +4234,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.
- 
877    def dump(self, filename, datatype="json.gz", **kwargs):
-878        """Dumps the Corr into a file of chosen type
-879        Parameters
-880        ----------
-881        filename : str
-882            Name of the file to be saved.
-883        datatype : str
-884            Format of the exported file. Supported formats include
-885            "json.gz" and "pickle"
-886        path : str
-887            specifies a custom path for the file (default '.')
-888        """
-889        if datatype == "json.gz":
-890            from .input.json import dump_to_json
-891            if 'path' in kwargs:
-892                file_name = kwargs.get('path') + '/' + filename
-893            else:
-894                file_name = filename
-895            dump_to_json(self, file_name)
-896        elif datatype == "pickle":
-897            dump_object(self, filename, **kwargs)
-898        else:
-899            raise Exception("Unknown datatype " + str(datatype))
+            
883    def dump(self, filename, datatype="json.gz", **kwargs):
+884        """Dumps the Corr into a file of chosen type
+885        Parameters
+886        ----------
+887        filename : str
+888            Name of the file to be saved.
+889        datatype : str
+890            Format of the exported file. Supported formats include
+891            "json.gz" and "pickle"
+892        path : str
+893            specifies a custom path for the file (default '.')
+894        """
+895        if datatype == "json.gz":
+896            from .input.json import dump_to_json
+897            if 'path' in kwargs:
+898                file_name = kwargs.get('path') + '/' + filename
+899            else:
+900                file_name = filename
+901            dump_to_json(self, file_name)
+902        elif datatype == "pickle":
+903            dump_object(self, filename, **kwargs)
+904        else:
+905            raise Exception("Unknown datatype " + str(datatype))
 

 
 
@@ -4268,8 +4288,8 @@ specifies a custom path for the file (default '.')
- 
901    def print(self, print_range=None):
-902        print(self.__repr__(print_range))
+            
907    def print(self, print_range=None):
+908        print(self.__repr__(print_range))
 

 
 
@@ -4287,8 +4307,8 @@ specifies a custom path for the file (default '.')
- 
1066    def sqrt(self):
-1067        return self ** 0.5
+            
1072    def sqrt(self):
+1073        return self ** 0.5
 

 
 
@@ -4306,9 +4326,9 @@ specifies a custom path for the file (default '.')
- 
1069    def log(self):
-1070        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1071        return Corr(newcontent, prange=self.prange)
+            
1075    def log(self):
+1076        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1077        return Corr(newcontent, prange=self.prange)
 

 
 
@@ -4326,9 +4346,9 @@ specifies a custom path for the file (default '.')
- 
1073    def exp(self):
-1074        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1075        return Corr(newcontent, prange=self.prange)
+            
1079    def exp(self):
+1080        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1081        return Corr(newcontent, prange=self.prange)
 

 
 
@@ -4346,8 +4366,8 @@ specifies a custom path for the file (default '.')
- 
1088    def sin(self):
-1089        return self._apply_func_to_corr(np.sin)
+            
1094    def sin(self):
+1095        return self._apply_func_to_corr(np.sin)
 

 
 
@@ -4365,8 +4385,8 @@ specifies a custom path for the file (default '.')
- 
1091    def cos(self):
-1092        return self._apply_func_to_corr(np.cos)
+            
1097    def cos(self):
+1098        return self._apply_func_to_corr(np.cos)
 

 
 
@@ -4384,8 +4404,8 @@ specifies a custom path for the file (default '.')
- 
1094    def tan(self):
-1095        return self._apply_func_to_corr(np.tan)
+            
1100    def tan(self):
+1101        return self._apply_func_to_corr(np.tan)
 

 
 
@@ -4403,8 +4423,8 @@ specifies a custom path for the file (default '.')
- 
1097    def sinh(self):
-1098        return self._apply_func_to_corr(np.sinh)
+            
1103    def sinh(self):
+1104        return self._apply_func_to_corr(np.sinh)
 

 
 
@@ -4422,8 +4442,8 @@ specifies a custom path for the file (default '.')
- 
1100    def cosh(self):
-1101        return self._apply_func_to_corr(np.cosh)
+            
1106    def cosh(self):
+1107        return self._apply_func_to_corr(np.cosh)
 

 
 
@@ -4441,8 +4461,8 @@ specifies a custom path for the file (default '.')
- 
1103    def tanh(self):
-1104        return self._apply_func_to_corr(np.tanh)
+            
1109    def tanh(self):
+1110        return self._apply_func_to_corr(np.tanh)
 

 
 
@@ -4460,8 +4480,8 @@ specifies a custom path for the file (default '.')
- 
1106    def arcsin(self):
-1107        return self._apply_func_to_corr(np.arcsin)
+            
1112    def arcsin(self):
+1113        return self._apply_func_to_corr(np.arcsin)
 

 
 
@@ -4479,8 +4499,8 @@ specifies a custom path for the file (default '.')
- 
1109    def arccos(self):
-1110        return self._apply_func_to_corr(np.arccos)
+            
1115    def arccos(self):
+1116        return self._apply_func_to_corr(np.arccos)
 

 
 
@@ -4498,8 +4518,8 @@ specifies a custom path for the file (default '.')
- 
1112    def arctan(self):
-1113        return self._apply_func_to_corr(np.arctan)
+            
1118    def arctan(self):
+1119        return self._apply_func_to_corr(np.arctan)
 

 
 
@@ -4517,8 +4537,8 @@ specifies a custom path for the file (default '.')
- 
1115    def arcsinh(self):
-1116        return self._apply_func_to_corr(np.arcsinh)
+            
1121    def arcsinh(self):
+1122        return self._apply_func_to_corr(np.arcsinh)
 

 
 
@@ -4536,8 +4556,8 @@ specifies a custom path for the file (default '.')
- 
1118    def arccosh(self):
-1119        return self._apply_func_to_corr(np.arccosh)
+            
1124    def arccosh(self):
+1125        return self._apply_func_to_corr(np.arccosh)
 

 
 
@@ -4555,8 +4575,8 @@ specifies a custom path for the file (default '.')
- 
1121    def arctanh(self):
-1122        return self._apply_func_to_corr(np.arctanh)
+            
1127    def arctanh(self):
+1128        return self._apply_func_to_corr(np.arctanh)
 

 
 
@@ -4596,62 +4616,62 @@ specifies a custom path for the file (default '.')
- 
1157    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1158        r''' Project large correlation matrix to lowest states
-1159
-1160        This method can be used to reduce the size of an (N x N) correlation matrix
-1161        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1162        is still small.
-1163
-1164        Parameters
-1165        ----------
-1166        Ntrunc: int
-1167            Rank of the target matrix.
-1168        tproj: int
-1169            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1170            The default value is 3.
-1171        t0proj: int
-1172            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1173            discouraged for O(a) improved theories, since the correctness of the procedure
-1174            cannot be granted in this case. The default value is 2.
-1175        basematrix : Corr
-1176            Correlation matrix that is used to determine the eigenvectors of the
-1177            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1178            is is not specified.
-1179
-1180        Notes
-1181        -----
-1182        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1183        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1184        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1185        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1186        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1187        correlation matrix and to remove some noise that is added by irrelevant operators.
-1188        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1189        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1190        '''
-1191
-1192        if self.N == 1:
-1193            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1194        if basematrix is None:
-1195            basematrix = self
-1196        if Ntrunc >= basematrix.N:
-1197            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1198        if basematrix.N != self.N:
-1199            raise Exception('basematrix and targetmatrix have to be of the same size.')
-1200
-1201        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1202
-1203        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1204        rmat = []
-1205        for t in range(basematrix.T):
-1206            for i in range(Ntrunc):
-1207                for j in range(Ntrunc):
-1208                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1209            rmat.append(np.copy(tmpmat))
-1210
-1211        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1212        return Corr(newcontent)
+            
1163    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1164        r''' Project large correlation matrix to lowest states
+1165
+1166        This method can be used to reduce the size of an (N x N) correlation matrix
+1167        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1168        is still small.
+1169
+1170        Parameters
+1171        ----------
+1172        Ntrunc: int
+1173            Rank of the target matrix.
+1174        tproj: int
+1175            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1176            The default value is 3.
+1177        t0proj: int
+1178            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1179            discouraged for O(a) improved theories, since the correctness of the procedure
+1180            cannot be granted in this case. The default value is 2.
+1181        basematrix : Corr
+1182            Correlation matrix that is used to determine the eigenvectors of the
+1183            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1184            is is not specified.
+1185
+1186        Notes
+1187        -----
+1188        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1189        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1190        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1191        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1192        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1193        correlation matrix and to remove some noise that is added by irrelevant operators.
+1194        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1195        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1196        '''
+1197
+1198        if self.N == 1:
+1199            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1200        if basematrix is None:
+1201            basematrix = self
+1202        if Ntrunc >= basematrix.N:
+1203            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1204        if basematrix.N != self.N:
+1205            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1206
+1207        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1208
+1209        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1210        rmat = []
+1211        for t in range(basematrix.T):
+1212            for i in range(Ntrunc):
+1213                for j in range(Ntrunc):
+1214                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1215            rmat.append(np.copy(tmpmat))
+1216
+1217        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1218        return Corr(newcontent)
 

 
 
diff --git a/docs/search.js b/docs/search.js
index 5e3d7409..c543f081 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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configuration"),this.buildDefaultConfig(n)}},t.Configuration.prototype.buildDefaultConfig=function(e){this.reset(),e.forEach(function(e){this.config[e]={boost:1,bool:"OR",expand:!1}},this)},t.Configuration.prototype.buildUserConfig=function(e,n){var i="OR",o=!1;if(this.reset(),"bool"in e&&(i=e.bool||i),"expand"in e&&(o=e.expand||o),"fields"in e)for(var r in e.fields)if(n.indexOf(r)>-1){var s=e.fields[r],u=o;void 0!=s.expand&&(u=s.expand),this.config[r]={boost:s.boost||0===s.boost?s.boost:1,bool:s.bool||i,expand:u}}else t.utils.warn("field name in user configuration not found in index instance fields");else this.addAllFields2UserConfig(i,o,n)},t.Configuration.prototype.addAllFields2UserConfig=function(e,t,n){n.forEach(function(n){this.config[n]={boost:1,bool:e,expand:t}},this)},t.Configuration.prototype.get=function(){return 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:
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    \n
  • automatic differentiation for exact liner 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.
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  • 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\".
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There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
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Basic example
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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
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The Obs class
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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.
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import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
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Error propagation
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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.
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The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
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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
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Error estimation
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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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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
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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.
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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
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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_tauint.
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If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize 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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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
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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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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
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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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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
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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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pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
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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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# 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
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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.
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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.
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For the full API see pyerrors.obs.Obs.
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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
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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
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In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
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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
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The individual entries of a correlator can be accessed via slicing
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print(my_corr[3])\n> 0.3227(33)\n
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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.
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my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
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pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
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  • 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.
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  • 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.
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  • 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.
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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).
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For the full API see pyerrors.correlators.Corr.
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Complex valued observables
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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.
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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
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Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
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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
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The Covobs class
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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.
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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.
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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
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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.
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Correlated auxiliary data is defined similarly to above, e.g., via
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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
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where RAP now is a list of two Obs that contains the two correlated parameters.
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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
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o.covobs[k].grad\n
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Error propagation in iterative algorithms
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pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
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Least squares fits
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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.
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Fit functions have to be of the following form
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import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
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It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
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Fits can then be performed via
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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
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where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
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Data stored in Corr objects can be fitted directly using the Corr.fit method.
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my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
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this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
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For fit functions with multiple independent variables the fit function can be of the form
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def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
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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.
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Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
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Total least squares fits
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pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.
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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:
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    \n
  • inv for the matrix inverse.
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  • cholseky for the Cholesky decomposition.
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  • det for the matrix determinant.
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  • eigh for eigenvalues and eigenvectors of hermitean matrices.
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  • eig for eigenvalues of general matrices.
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  • pinv for the Moore-Penrose pseudoinverse.
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  • svd for the singular-value-decomposition.
    • \n
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For the full API see pyerrors.linalg.
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Export data
\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:
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    \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
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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
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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.
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json.gz format specification
\n\n
The first entries of the file provide optional auxiliary information:
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    \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\n
Citing
\n\n
If you use pyerrors for research that leads to a publication please consider citing:
\n\n
    \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.\nand
    • \n
  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.\nwhere applicable.
    • \n
\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "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 GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "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
    • \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 indentified for this correlator.
    • \n
\n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "function", "doc": "
Anti-symmetrize the correlator around x0=0.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "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", "type": "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
C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\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.
      • \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
    • \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
\n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "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')", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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
  • partity (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", "type": "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, 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", "type": "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: symmetric, improved, default: symmetric
    • \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", "type": "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 periodicitiy 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-periodicitiy 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)
    • \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", "type": "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", "type": "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", "type": "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", "type": "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
  • 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
\n", "signature": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "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", "type": "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", "type": "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", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "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.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "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": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "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", "type": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
Rank-3 epsilon tensor
\n\n
Based on https://codegolf.stackexchange.com/a/160375
\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", "type": "function", "doc": "
Rank-4 epsilon tensor
\n\n
Extension of https://codegolf.stackexchange.com/a/160375
\n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "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
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "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", "type": "function", "doc": "
Performs a non-linear fit to y = func(x).
\n\n
Parameters
\n\n
    \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
    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
    For multiple x values func can be of the form
    \n\n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • priors (list, optional):\npriors has to be a 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
  • 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).\nAt the moment this option only works for prior==None and when no method is given.
    • \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
\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", "type": "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
    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
    For multiple x values func can be of the form
    \n\n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\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
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy
\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", "type": "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", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
\n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "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", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "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", "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", "type": "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", "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", "type": "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", "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", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "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", "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", "type": "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", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "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", "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", "type": "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
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
    • \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", "signature": "(content, noempty=False, 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", "type": "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
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in 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 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", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "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", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "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", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "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 source and sink.\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", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "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", "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", "type": "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
>>> 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
Second mode:
\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", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
\n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "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", "type": "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", "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", "type": "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", "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", "type": "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", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "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", "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", "type": "function", "doc": "
Export a list of Obs or structures containing Obs to 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
  • 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", "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", "type": "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", "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", "type": "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", "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", "type": "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", "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", "type": "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", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
Read pbp format from given folder structure. Returns a list of length nrw
\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", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "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", "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", "type": "function", "doc": "
Extract t0 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 - 0.3\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
  • 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", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "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 /\ncycles. 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
  • 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", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "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", "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", "type": "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 /\ncycles. 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", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
Read sfcf c format from given folder structure.
\n\n
Parameters
\n\n
    \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
  • 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
  • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
    • \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 of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
Utilities for the input
\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "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", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "function", "doc": "
Determinant of Obs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "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", "type": "function", "doc": "
Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "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", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "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", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
Load object from pickle file.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "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", "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", "type": "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", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "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", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "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__", "type": "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": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
\n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "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", "type": "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.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "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", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
\n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "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", "type": "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", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "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", "type": "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.
    • \n
\n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "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", "type": "function", "doc": "
Calculates the error covariance matrix of a set of observables.
\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.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "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.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "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", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "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:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • Obs: Obs valued root of the function.
    • \n
\n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 7922}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 108}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 94}, "pyerrors.correlators.Corr.reweighted": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.gamma_method": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 13}, "pyerrors.correlators.Corr.projected": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 64}, "pyerrors.correlators.Corr.item": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 53}, "pyerrors.correlators.Corr.plottable": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 31}, "pyerrors.correlators.Corr.symmetric": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 9}, "pyerrors.correlators.Corr.anti_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.matrix_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.GEVP": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 9, "bases": 0, "doc": 324}, "pyerrors.correlators.Corr.Eigenvalue": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 59}, "pyerrors.correlators.Corr.Hankel": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 6, "bases": 0, "doc": 67}, "pyerrors.correlators.Corr.roll": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 26}, "pyerrors.correlators.Corr.reverse": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 9}, "pyerrors.correlators.Corr.thin": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 7, "bases": 0, "doc": 43}, "pyerrors.correlators.Corr.correlate": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 53}, "pyerrors.correlators.Corr.reweight": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 79}, "pyerrors.correlators.Corr.T_symmetry": {"qualname": 3, "fullname": 5, "annotation": 0, 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What is pyerrors?
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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:
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  • automatic differentiation for exact liner error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
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  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
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  • coherent error propagation for data from different Markov chains.
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  • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
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  • 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
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More detailed examples can found in the GitHub repository \"badge\".
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There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
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Basic example
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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
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The Obs class
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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.
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import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
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Error propagation
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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.
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The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
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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
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Error estimation
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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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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
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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.
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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
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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_tauint.
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If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize 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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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
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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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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
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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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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
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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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pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
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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.
\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
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
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
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
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
The individual entries of a correlator can be accessed via slicing
\n\n
print(my_corr[3])\n> 0.3227(33)\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
my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\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
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
Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
\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
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
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
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
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
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
o.covobs[k].grad\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 sqaures 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
import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\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
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
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
my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\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
def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\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.
\n\n
Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options 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 orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence 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
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
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
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\n
Citing
\n\n
If you use pyerrors for research that leads to a publication please consider citing:
\n\n
    \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.\nand
    • \n
  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.\nwhere applicable.
    • \n
\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "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 GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "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
    • \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 indentified for this correlator.
    • \n
\n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "function", "doc": "
Anti-symmetrize the correlator around x0=0.
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "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", "type": "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
C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\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.
      • \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
    • \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
\n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "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')", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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
  • partity (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", "type": "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, 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", "type": "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: symmetric, improved, default: symmetric
    • \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", "type": "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 periodicitiy 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-periodicitiy 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)
    • \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", "type": "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", "type": "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", "type": "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", "type": "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
  • 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": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None,\n    title=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "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", "type": "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", "type": "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", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "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.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "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": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "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", "type": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
Rank-3 epsilon tensor
\n\n
Based on https://codegolf.stackexchange.com/a/160375
\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", "type": "function", "doc": "
Rank-4 epsilon tensor
\n\n
Extension of https://codegolf.stackexchange.com/a/160375
\n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "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
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "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", "type": "function", "doc": "
Performs a non-linear fit to y = func(x).
\n\n
Parameters
\n\n
    \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
    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
    For multiple x values func can be of the form
    \n\n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • priors (list, optional):\npriors has to be a 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
  • 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).\nAt the moment this option only works for prior==None and when no method is given.
    • \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
\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", "type": "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
    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
    For multiple x values func can be of the form
    \n\n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\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
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy
\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", "type": "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", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
\n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "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", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "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", "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", "type": "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", "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", "type": "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", "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", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "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", "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", "type": "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", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "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", "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", "type": "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
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
    • \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", "signature": "(content, noempty=False, 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", "type": "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
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in 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 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", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "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", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "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", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "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 source and sink.\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", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "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", "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", "type": "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
>>> 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
Second mode:
\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", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
\n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "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", "type": "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", "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", "type": "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", "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", "type": "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", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "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", "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", "type": "function", "doc": "
Export a list of Obs or structures containing Obs to 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
  • 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", "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", "type": "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", "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", "type": "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", "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", "type": "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", "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", "type": "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", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
Read pbp format from given folder structure. Returns a list of length nrw
\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", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "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", "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", "type": "function", "doc": "
Extract t0 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 - 0.3\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
  • 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", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "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 /\ncycles. 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
  • 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", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "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", "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", "type": "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 /\ncycles. 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", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
Read sfcf c format from given folder structure.
\n\n
Parameters
\n\n
    \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
  • 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
  • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
    • \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 of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
Utilities for the input
\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "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", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "function", "doc": "
Determinant of Obs valued matrices.
\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "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", "type": "function", "doc": "
Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "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", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "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", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
Load object from pickle file.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "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", "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", "type": "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", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "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", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "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__", "type": "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": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "variable", "doc": "
\n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
\n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "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", "type": "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.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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", "type": "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.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "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", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
\n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "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", "type": "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", "type": "function", "doc": "
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "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", "type": "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.
    • \n
\n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "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", "type": "function", "doc": "
Calculates the error covariance matrix of a set of observables.
\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.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "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.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "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", "type": "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", "type": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "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:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • Obs: Obs valued root of the function.
    • \n
\n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
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     // mirrored in build-search-index.js (part 1)
     // Also split on html tags. this is a cheap heuristic, but good enough.