diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index a38c0060..44c317f2 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -731,7 +731,7 @@ 523 ---------- 524 variant : str 525 decides which definition of the finite differences derivative is used. - 526 Available choice: symmetric, forward, backward, improved, default: symmetric + 526 Available choice: symmetric, forward, backward, improved, log, default: symmetric 527 """ 528 if self.N != 1: 529 raise Exception("deriv only implemented for one-dimensional correlators.") @@ -775,720 +775,757 @@ 567 if (all([x is None for x in newcontent])): 568 raise Exception('Derivative is undefined at all timeslices') 569 return Corr(newcontent, padding=[2, 2]) - 570 else: - 571 raise Exception("Unknown variant.") - 572 - 573 def second_deriv(self, variant="symmetric"): - 574 """Return the second derivative of the correlator with respect to x0. - 575 - 576 Parameters - 577 ---------- - 578 variant : str - 579 decides which definition of the finite differences derivative is used. - 580 Available choice: symmetric, improved, default: symmetric - 581 """ - 582 if self.N != 1: - 583 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 584 if variant == "symmetric": - 585 newcontent = [] - 586 for t in range(1, self.T - 1): - 587 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 588 newcontent.append(None) - 589 else: - 590 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 591 if (all([x is None for x in newcontent])): - 592 raise Exception("Derivative is undefined at all timeslices") - 593 return Corr(newcontent, padding=[1, 1]) - 594 elif variant == "improved": - 595 newcontent = [] - 596 for t in range(2, self.T - 2): - 597 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): - 598 newcontent.append(None) - 599 else: - 600 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) - 601 if (all([x is None for x in newcontent])): - 602 raise Exception("Derivative is undefined at all timeslices") - 603 return Corr(newcontent, padding=[2, 2]) - 604 else: - 605 raise Exception("Unknown variant.") - 606 - 607 def m_eff(self, variant='log', guess=1.0): - 608 """Returns the effective mass of the correlator as correlator object - 609 - 610 Parameters - 611 ---------- - 612 variant : str - 613 log : uses the standard effective mass log(C(t) / C(t+1)) - 614 cosh, 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. - 615 sinh : 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. - 616 See, e.g., arXiv:1205.5380 - 617 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 618 guess : float - 619 guess for the root finder, only relevant for the root variant - 620 """ - 621 if self.N != 1: - 622 raise Exception('Correlator must be projected before getting m_eff') - 623 if variant == 'log': - 624 newcontent = [] - 625 for t in range(self.T - 1): - 626 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 627 newcontent.append(None) - 628 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 629 newcontent.append(None) - 630 else: - 631 newcontent.append(self.content[t] / self.content[t + 1]) - 632 if (all([x is None for x in newcontent])): - 633 raise Exception('m_eff is undefined at all timeslices') - 634 - 635 return np.log(Corr(newcontent, padding=[0, 1])) - 636 - 637 elif variant in ['periodic', 'cosh', 'sinh']: - 638 if variant in ['periodic', 'cosh']: - 639 func = anp.cosh - 640 else: - 641 func = anp.sinh - 642 - 643 def root_function(x, d): - 644 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 645 - 646 newcontent = [] - 647 for t in range(self.T - 1): - 648 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 649 newcontent.append(None) - 650 # Fill the two timeslices in the middle of the lattice with their predecessors - 651 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 652 newcontent.append(newcontent[-1]) - 653 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 654 newcontent.append(None) - 655 else: - 656 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 657 if (all([x is None for x in newcontent])): - 658 raise Exception('m_eff is undefined at all timeslices') + 570 elif variant == 'log': + 571 newcontent = [] + 572 for t in range(self.T): + 573 if (self.content[t] is None) or (self.content[t] <= 0): + 574 newcontent.append(None) + 575 else: + 576 newcontent.append(np.log(self.content[t])) + 577 if (all([x is None for x in newcontent])): + 578 raise Exception("Log is undefined at all timeslices") + 579 logcorr = Corr(newcontent) + 580 return self * logcorr.deriv('symmetric') + 581 else: + 582 raise Exception("Unknown variant.") + 583 + 584 def second_deriv(self, variant="symmetric"): + 585 """Return the second derivative of the correlator with respect to x0. + 586 + 587 Parameters + 588 ---------- + 589 variant : str + 590 decides which definition of the finite differences derivative is used. + 591 Available choice: symmetric, improved, log, default: symmetric + 592 """ + 593 if self.N != 1: + 594 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 595 if variant == "symmetric": + 596 newcontent = [] + 597 for t in range(1, self.T - 1): + 598 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 599 newcontent.append(None) + 600 else: + 601 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 602 if (all([x is None for x in newcontent])): + 603 raise Exception("Derivative is undefined at all timeslices") + 604 return Corr(newcontent, padding=[1, 1]) + 605 elif variant == "improved": + 606 newcontent = [] + 607 for t in range(2, self.T - 2): + 608 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 609 newcontent.append(None) + 610 else: + 611 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) + 612 if (all([x is None for x in newcontent])): + 613 raise Exception("Derivative is undefined at all timeslices") + 614 return Corr(newcontent, padding=[2, 2]) + 615 elif variant == 'log': + 616 newcontent = [] + 617 for t in range(self.T): + 618 if (self.content[t] is None) or (self.content[t] <= 0): + 619 newcontent.append(None) + 620 else: + 621 newcontent.append(np.log(self.content[t])) + 622 if (all([x is None for x in newcontent])): + 623 raise Exception("Log is undefined at all timeslices") + 624 logcorr = Corr(newcontent) + 625 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) + 626 else: + 627 raise Exception("Unknown variant.") + 628 + 629 def m_eff(self, variant='log', guess=1.0): + 630 """Returns the effective mass of the correlator as correlator object + 631 + 632 Parameters + 633 ---------- + 634 variant : str + 635 log : uses the standard effective mass log(C(t) / C(t+1)) + 636 cosh, 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. + 637 sinh : 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. + 638 See, e.g., arXiv:1205.5380 + 639 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 640 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 + 641 guess : float + 642 guess for the root finder, only relevant for the root variant + 643 """ + 644 if self.N != 1: + 645 raise Exception('Correlator must be projected before getting m_eff') + 646 if variant == 'log': + 647 newcontent = [] + 648 for t in range(self.T - 1): + 649 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 650 newcontent.append(None) + 651 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 652 newcontent.append(None) + 653 else: + 654 newcontent.append(self.content[t] / self.content[t + 1]) + 655 if (all([x is None for x in newcontent])): + 656 raise Exception('m_eff is undefined at all timeslices') + 657 + 658 return np.log(Corr(newcontent, padding=[0, 1])) 659 - 660 return Corr(newcontent, padding=[0, 1]) - 661 - 662 elif variant == 'arccosh': - 663 newcontent = [] - 664 for t in range(1, self.T - 1): - 665 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): + 660 elif variant == 'logsym': + 661 newcontent = [] + 662 for t in range(1, self.T - 1): + 663 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 664 newcontent.append(None) + 665 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: 666 newcontent.append(None) 667 else: - 668 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 668 newcontent.append(self.content[t - 1] / self.content[t + 1]) 669 if (all([x is None for x in newcontent])): - 670 raise Exception("m_eff is undefined at all timeslices") - 671 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 672 - 673 else: - 674 raise Exception('Unknown variant.') - 675 - 676 def fit(self, function, fitrange=None, silent=False, **kwargs): - 677 r'''Fits function to the data - 678 - 679 Parameters - 680 ---------- - 681 function : obj - 682 function to fit to the data. See fits.least_squares for details. - 683 fitrange : list - 684 Two element list containing the timeslices on which the fit is supposed to start and stop. - 685 Caution: This range is inclusive as opposed to standard python indexing. - 686 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 687 If not specified, self.prange or all timeslices are used. - 688 silent : bool - 689 Decides whether output is printed to the standard output. - 690 ''' - 691 if self.N != 1: - 692 raise Exception("Correlator must be projected before fitting") - 693 - 694 if fitrange is None: - 695 if self.prange: - 696 fitrange = self.prange - 697 else: - 698 fitrange = [0, self.T - 1] - 699 else: - 700 if not isinstance(fitrange, list): - 701 raise Exception("fitrange has to be a list with two elements") - 702 if len(fitrange) != 2: - 703 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 704 - 705 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 706 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 707 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 708 return result + 670 raise Exception('m_eff is undefined at all timeslices') + 671 + 672 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 673 + 674 elif variant in ['periodic', 'cosh', 'sinh']: + 675 if variant in ['periodic', 'cosh']: + 676 func = anp.cosh + 677 else: + 678 func = anp.sinh + 679 + 680 def root_function(x, d): + 681 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 682 + 683 newcontent = [] + 684 for t in range(self.T - 1): + 685 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 686 newcontent.append(None) + 687 # Fill the two timeslices in the middle of the lattice with their predecessors + 688 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 689 newcontent.append(newcontent[-1]) + 690 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 691 newcontent.append(None) + 692 else: + 693 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) + 694 if (all([x is None for x in newcontent])): + 695 raise Exception('m_eff is undefined at all timeslices') + 696 + 697 return Corr(newcontent, padding=[0, 1]) + 698 + 699 elif variant == 'arccosh': + 700 newcontent = [] + 701 for t in range(1, self.T - 1): + 702 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): + 703 newcontent.append(None) + 704 else: + 705 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 706 if (all([x is None for x in newcontent])): + 707 raise Exception("m_eff is undefined at all timeslices") + 708 return np.arccosh(Corr(newcontent, padding=[1, 1])) 709 - 710 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 711 """ Extract a plateau value from a Corr object + 710 else: + 711 raise Exception('Unknown variant.') 712 - 713 Parameters - 714 ---------- - 715 plateau_range : list - 716 list with two entries, indicating the first and the last timeslice - 717 of the plateau region. - 718 method : str - 719 method to extract the plateau. - 720 'fit' fits a constant to the plateau region - 721 'avg', 'average' or 'mean' just average over the given timeslices. - 722 auto_gamma : bool - 723 apply gamma_method with default parameters to the Corr. Defaults to None - 724 """ - 725 if not plateau_range: - 726 if self.prange: - 727 plateau_range = self.prange - 728 else: - 729 raise Exception("no plateau range provided") - 730 if self.N != 1: - 731 raise Exception("Correlator must be projected before getting a plateau.") - 732 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 733 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 734 if auto_gamma: - 735 self.gamma_method() - 736 if method == "fit": - 737 def const_func(a, t): - 738 return a[0] - 739 return self.fit(const_func, plateau_range)[0] - 740 elif method in ["avg", "average", "mean"]: - 741 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 742 return returnvalue - 743 - 744 else: - 745 raise Exception("Unsupported plateau method: " + method) + 713 def fit(self, function, fitrange=None, silent=False, **kwargs): + 714 r'''Fits function to the data + 715 + 716 Parameters + 717 ---------- + 718 function : obj + 719 function to fit to the data. See fits.least_squares for details. + 720 fitrange : list + 721 Two element list containing the timeslices on which the fit is supposed to start and stop. + 722 Caution: This range is inclusive as opposed to standard python indexing. + 723 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 724 If not specified, self.prange or all timeslices are used. + 725 silent : bool + 726 Decides whether output is printed to the standard output. + 727 ''' + 728 if self.N != 1: + 729 raise Exception("Correlator must be projected before fitting") + 730 + 731 if fitrange is None: + 732 if self.prange: + 733 fitrange = self.prange + 734 else: + 735 fitrange = [0, self.T - 1] + 736 else: + 737 if not isinstance(fitrange, list): + 738 raise Exception("fitrange has to be a list with two elements") + 739 if len(fitrange) != 2: + 740 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 741 + 742 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 743 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 744 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 745 return result 746 - 747 def set_prange(self, prange): - 748 """Sets the attribute prange of the Corr object.""" - 749 if not len(prange) == 2: - 750 raise Exception("prange must be a list or array with two values") - 751 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 752 raise Exception("Start and end point must be integers") - 753 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 754 raise Exception("Start and end point must define a range in the interval 0,T") - 755 - 756 self.prange = prange - 757 return - 758 - 759 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): - 760 """Plots the correlator using the tag of the correlator as label if available. - 761 - 762 Parameters - 763 ---------- - 764 x_range : list - 765 list of two values, determining the range of the x-axis e.g. [4, 8]. - 766 comp : Corr or list of Corr - 767 Correlator or list of correlators which are plotted for comparison. - 768 The tags of these correlators are used as labels if available. - 769 logscale : bool - 770 Sets y-axis to logscale. - 771 plateau : Obs - 772 Plateau value to be visualized in the figure. - 773 fit_res : Fit_result - 774 Fit_result object to be visualized. - 775 ylabel : str - 776 Label for the y-axis. - 777 save : str - 778 path to file in which the figure should be saved. - 779 auto_gamma : bool - 780 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 781 hide_sigma : float - 782 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 783 references : list - 784 List of floating point values that are displayed as horizontal lines for reference. - 785 title : string - 786 Optional title of the figure. - 787 """ - 788 if self.N != 1: - 789 raise Exception("Correlator must be projected before plotting") - 790 - 791 if auto_gamma: - 792 self.gamma_method() - 793 - 794 if x_range is None: - 795 x_range = [0, self.T - 1] - 796 - 797 fig = plt.figure() - 798 ax1 = fig.add_subplot(111) - 799 - 800 x, y, y_err = self.plottable() - 801 if hide_sigma: - 802 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 803 else: - 804 hide_from = None - 805 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 806 if logscale: - 807 ax1.set_yscale('log') - 808 else: - 809 if y_range is None: - 810 try: - 811 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)]) - 812 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)]) - 813 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 814 except Exception: - 815 pass - 816 else: - 817 ax1.set_ylim(y_range) - 818 if comp: - 819 if isinstance(comp, (Corr, list)): - 820 for corr in comp if isinstance(comp, list) else [comp]: - 821 if auto_gamma: - 822 corr.gamma_method() - 823 x, y, y_err = corr.plottable() - 824 if hide_sigma: - 825 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 826 else: - 827 hide_from = None - 828 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 829 else: - 830 raise Exception("'comp' must be a correlator or a list of correlators.") - 831 - 832 if plateau: - 833 if isinstance(plateau, Obs): - 834 if auto_gamma: - 835 plateau.gamma_method() - 836 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 837 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 838 else: - 839 raise Exception("'plateau' must be an Obs") - 840 - 841 if references: - 842 if isinstance(references, list): - 843 for ref in references: - 844 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 845 else: - 846 raise Exception("'references' must be a list of floating pint values.") - 847 - 848 if self.prange: - 849 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 850 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 851 - 852 if fit_res: - 853 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 854 ax1.plot(x_samples, - 855 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 856 ls='-', marker=',', lw=2) - 857 - 858 ax1.set_xlabel(r'$x_0 / a$') - 859 if ylabel: - 860 ax1.set_ylabel(ylabel) - 861 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 862 - 863 handles, labels = ax1.get_legend_handles_labels() - 864 if labels: - 865 ax1.legend() - 866 - 867 if title: - 868 plt.title(title) - 869 - 870 plt.draw() - 871 - 872 if save: - 873 if isinstance(save, str): - 874 fig.savefig(save, bbox_inches='tight') + 747 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 748 """ Extract a plateau value from a Corr object + 749 + 750 Parameters + 751 ---------- + 752 plateau_range : list + 753 list with two entries, indicating the first and the last timeslice + 754 of the plateau region. + 755 method : str + 756 method to extract the plateau. + 757 'fit' fits a constant to the plateau region + 758 'avg', 'average' or 'mean' just average over the given timeslices. + 759 auto_gamma : bool + 760 apply gamma_method with default parameters to the Corr. Defaults to None + 761 """ + 762 if not plateau_range: + 763 if self.prange: + 764 plateau_range = self.prange + 765 else: + 766 raise Exception("no plateau range provided") + 767 if self.N != 1: + 768 raise Exception("Correlator must be projected before getting a plateau.") + 769 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 770 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 771 if auto_gamma: + 772 self.gamma_method() + 773 if method == "fit": + 774 def const_func(a, t): + 775 return a[0] + 776 return self.fit(const_func, plateau_range)[0] + 777 elif method in ["avg", "average", "mean"]: + 778 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 779 return returnvalue + 780 + 781 else: + 782 raise Exception("Unsupported plateau method: " + method) + 783 + 784 def set_prange(self, prange): + 785 """Sets the attribute prange of the Corr object.""" + 786 if not len(prange) == 2: + 787 raise Exception("prange must be a list or array with two values") + 788 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 789 raise Exception("Start and end point must be integers") + 790 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 791 raise Exception("Start and end point must define a range in the interval 0,T") + 792 + 793 self.prange = prange + 794 return + 795 + 796 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): + 797 """Plots the correlator using the tag of the correlator as label if available. + 798 + 799 Parameters + 800 ---------- + 801 x_range : list + 802 list of two values, determining the range of the x-axis e.g. [4, 8]. + 803 comp : Corr or list of Corr + 804 Correlator or list of correlators which are plotted for comparison. + 805 The tags of these correlators are used as labels if available. + 806 logscale : bool + 807 Sets y-axis to logscale. + 808 plateau : Obs + 809 Plateau value to be visualized in the figure. + 810 fit_res : Fit_result + 811 Fit_result object to be visualized. + 812 ylabel : str + 813 Label for the y-axis. + 814 save : str + 815 path to file in which the figure should be saved. + 816 auto_gamma : bool + 817 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 818 hide_sigma : float + 819 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 820 references : list + 821 List of floating point values that are displayed as horizontal lines for reference. + 822 title : string + 823 Optional title of the figure. + 824 """ + 825 if self.N != 1: + 826 raise Exception("Correlator must be projected before plotting") + 827 + 828 if auto_gamma: + 829 self.gamma_method() + 830 + 831 if x_range is None: + 832 x_range = [0, self.T - 1] + 833 + 834 fig = plt.figure() + 835 ax1 = fig.add_subplot(111) + 836 + 837 x, y, y_err = self.plottable() + 838 if hide_sigma: + 839 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 840 else: + 841 hide_from = None + 842 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 843 if logscale: + 844 ax1.set_yscale('log') + 845 else: + 846 if y_range is None: + 847 try: + 848 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)]) + 849 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)]) + 850 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 851 except Exception: + 852 pass + 853 else: + 854 ax1.set_ylim(y_range) + 855 if comp: + 856 if isinstance(comp, (Corr, list)): + 857 for corr in comp if isinstance(comp, list) else [comp]: + 858 if auto_gamma: + 859 corr.gamma_method() + 860 x, y, y_err = corr.plottable() + 861 if hide_sigma: + 862 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 863 else: + 864 hide_from = None + 865 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 866 else: + 867 raise Exception("'comp' must be a correlator or a list of correlators.") + 868 + 869 if plateau: + 870 if isinstance(plateau, Obs): + 871 if auto_gamma: + 872 plateau.gamma_method() + 873 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 874 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') 875 else: - 876 raise Exception("'save' has to be a string.") + 876 raise Exception("'plateau' must be an Obs") 877 - 878 def spaghetti_plot(self, logscale=True): - 879 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 880 - 881 Parameters - 882 ---------- - 883 logscale : bool - 884 Determines whether the scale of the y-axis is logarithmic or standard. - 885 """ - 886 if self.N != 1: - 887 raise Exception("Correlator needs to be projected first.") + 878 if references: + 879 if isinstance(references, list): + 880 for ref in references: + 881 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 882 else: + 883 raise Exception("'references' must be a list of floating pint values.") + 884 + 885 if self.prange: + 886 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 887 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') 888 - 889 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])) - 890 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 891 - 892 for name in mc_names: - 893 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 889 if fit_res: + 890 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 891 ax1.plot(x_samples, + 892 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 893 ls='-', marker=',', lw=2) 894 - 895 fig = plt.figure() - 896 ax = fig.add_subplot(111) - 897 for dat in data: - 898 ax.plot(x0_vals, dat, ls='-', marker='') + 895 ax1.set_xlabel(r'$x_0 / a$') + 896 if ylabel: + 897 ax1.set_ylabel(ylabel) + 898 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) 899 - 900 if logscale is True: - 901 ax.set_yscale('log') - 902 - 903 ax.set_xlabel(r'$x_0 / a$') - 904 plt.title(name) - 905 plt.draw() + 900 handles, labels = ax1.get_legend_handles_labels() + 901 if labels: + 902 ax1.legend() + 903 + 904 if title: + 905 plt.title(title) 906 - 907 def dump(self, filename, datatype="json.gz", **kwargs): - 908 """Dumps the Corr into a file of chosen type - 909 Parameters - 910 ---------- - 911 filename : str - 912 Name of the file to be saved. - 913 datatype : str - 914 Format of the exported file. Supported formats include - 915 "json.gz" and "pickle" - 916 path : str - 917 specifies a custom path for the file (default '.') - 918 """ - 919 if datatype == "json.gz": - 920 from .input.json import dump_to_json - 921 if 'path' in kwargs: - 922 file_name = kwargs.get('path') + '/' + filename - 923 else: - 924 file_name = filename - 925 dump_to_json(self, file_name) - 926 elif datatype == "pickle": - 927 dump_object(self, filename, **kwargs) - 928 else: - 929 raise Exception("Unknown datatype " + str(datatype)) - 930 - 931 def print(self, print_range=None): - 932 print(self.__repr__(print_range)) - 933 - 934 def __repr__(self, print_range=None): - 935 if print_range is None: - 936 print_range = [0, None] - 937 - 938 content_string = "" - 939 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 - 940 - 941 if self.tag is not None: - 942 content_string += "Description: " + self.tag + "\n" - 943 if self.N != 1: - 944 return content_string - 945 - 946 if print_range[1]: - 947 print_range[1] += 1 - 948 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 949 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 950 if sub_corr is None: - 951 content_string += str(i + print_range[0]) + '\n' - 952 else: - 953 content_string += str(i + print_range[0]) - 954 for element in sub_corr: - 955 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 956 content_string += '\n' - 957 return content_string - 958 - 959 def __str__(self): - 960 return self.__repr__() - 961 - 962 # We define the basic operations, that can be performed with correlators. - 963 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 964 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 965 # One could try and tell Obs to check if the y in __mul__ is a Corr and - 966 - 967 def __add__(self, y): - 968 if isinstance(y, Corr): - 969 if ((self.N != y.N) or (self.T != y.T)): - 970 raise Exception("Addition of Corrs with different shape") - 971 newcontent = [] - 972 for t in range(self.T): - 973 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 974 newcontent.append(None) - 975 else: - 976 newcontent.append(self.content[t] + y.content[t]) - 977 return Corr(newcontent) - 978 - 979 elif isinstance(y, (Obs, int, float, CObs)): - 980 newcontent = [] - 981 for t in range(self.T): - 982 if _check_for_none(self, self.content[t]): - 983 newcontent.append(None) - 984 else: - 985 newcontent.append(self.content[t] + y) - 986 return Corr(newcontent, prange=self.prange) - 987 elif isinstance(y, np.ndarray): - 988 if y.shape == (self.T,): - 989 return Corr(list((np.array(self.content).T + y).T)) - 990 else: - 991 raise ValueError("operands could not be broadcast together") - 992 else: - 993 raise TypeError("Corr + wrong type") - 994 - 995 def __mul__(self, y): - 996 if isinstance(y, Corr): - 997 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 998 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") - 999 newcontent = [] -1000 for t in range(self.T): -1001 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1002 newcontent.append(None) -1003 else: -1004 newcontent.append(self.content[t] * y.content[t]) -1005 return Corr(newcontent) -1006 -1007 elif isinstance(y, (Obs, int, float, CObs)): + 907 plt.draw() + 908 + 909 if save: + 910 if isinstance(save, str): + 911 fig.savefig(save, bbox_inches='tight') + 912 else: + 913 raise Exception("'save' has to be a string.") + 914 + 915 def spaghetti_plot(self, logscale=True): + 916 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 917 + 918 Parameters + 919 ---------- + 920 logscale : bool + 921 Determines whether the scale of the y-axis is logarithmic or standard. + 922 """ + 923 if self.N != 1: + 924 raise Exception("Correlator needs to be projected first.") + 925 + 926 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])) + 927 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 928 + 929 for name in mc_names: + 930 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 931 + 932 fig = plt.figure() + 933 ax = fig.add_subplot(111) + 934 for dat in data: + 935 ax.plot(x0_vals, dat, ls='-', marker='') + 936 + 937 if logscale is True: + 938 ax.set_yscale('log') + 939 + 940 ax.set_xlabel(r'$x_0 / a$') + 941 plt.title(name) + 942 plt.draw() + 943 + 944 def dump(self, filename, datatype="json.gz", **kwargs): + 945 """Dumps the Corr into a file of chosen type + 946 Parameters + 947 ---------- + 948 filename : str + 949 Name of the file to be saved. + 950 datatype : str + 951 Format of the exported file. Supported formats include + 952 "json.gz" and "pickle" + 953 path : str + 954 specifies a custom path for the file (default '.') + 955 """ + 956 if datatype == "json.gz": + 957 from .input.json import dump_to_json + 958 if 'path' in kwargs: + 959 file_name = kwargs.get('path') + '/' + filename + 960 else: + 961 file_name = filename + 962 dump_to_json(self, file_name) + 963 elif datatype == "pickle": + 964 dump_object(self, filename, **kwargs) + 965 else: + 966 raise Exception("Unknown datatype " + str(datatype)) + 967 + 968 def print(self, print_range=None): + 969 print(self.__repr__(print_range)) + 970 + 971 def __repr__(self, print_range=None): + 972 if print_range is None: + 973 print_range = [0, None] + 974 + 975 content_string = "" + 976 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 + 977 + 978 if self.tag is not None: + 979 content_string += "Description: " + self.tag + "\n" + 980 if self.N != 1: + 981 return content_string + 982 + 983 if print_range[1]: + 984 print_range[1] += 1 + 985 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 986 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 987 if sub_corr is None: + 988 content_string += str(i + print_range[0]) + '\n' + 989 else: + 990 content_string += str(i + print_range[0]) + 991 for element in sub_corr: + 992 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 993 content_string += '\n' + 994 return content_string + 995 + 996 def __str__(self): + 997 return self.__repr__() + 998 + 999 # We define the basic operations, that can be performed with correlators. +1000 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. +1001 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. +1002 # One could try and tell Obs to check if the y in __mul__ is a Corr and +1003 +1004 def __add__(self, y): +1005 if isinstance(y, Corr): +1006 if ((self.N != y.N) or (self.T != y.T)): +1007 raise Exception("Addition of Corrs with different shape") 1008 newcontent = [] 1009 for t in range(self.T): -1010 if _check_for_none(self, self.content[t]): +1010 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1011 newcontent.append(None) 1012 else: -1013 newcontent.append(self.content[t] * y) -1014 return Corr(newcontent, prange=self.prange) -1015 elif isinstance(y, np.ndarray): -1016 if y.shape == (self.T,): -1017 return Corr(list((np.array(self.content).T * y).T)) -1018 else: -1019 raise ValueError("operands could not be broadcast together") -1020 else: -1021 raise TypeError("Corr * wrong type") -1022 -1023 def __truediv__(self, y): -1024 if isinstance(y, Corr): -1025 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1026 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1027 newcontent = [] -1028 for t in range(self.T): -1029 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1030 newcontent.append(None) -1031 else: -1032 newcontent.append(self.content[t] / y.content[t]) -1033 for t in range(self.T): -1034 if _check_for_none(self, newcontent[t]): -1035 continue -1036 if np.isnan(np.sum(newcontent[t]).value): -1037 newcontent[t] = None -1038 -1039 if all([item is None for item in newcontent]): -1040 raise Exception("Division returns completely undefined correlator") -1041 return Corr(newcontent) -1042 -1043 elif isinstance(y, (Obs, CObs)): -1044 if isinstance(y, Obs): -1045 if y.value == 0: -1046 raise Exception('Division by zero will return undefined correlator') -1047 if isinstance(y, CObs): -1048 if y.is_zero(): -1049 raise Exception('Division by zero will return undefined correlator') -1050 -1051 newcontent = [] -1052 for t in range(self.T): -1053 if _check_for_none(self, self.content[t]): -1054 newcontent.append(None) -1055 else: -1056 newcontent.append(self.content[t] / y) -1057 return Corr(newcontent, prange=self.prange) -1058 -1059 elif isinstance(y, (int, float)): -1060 if y == 0: -1061 raise Exception('Division by zero will return undefined correlator') -1062 newcontent = [] -1063 for t in range(self.T): -1064 if _check_for_none(self, self.content[t]): -1065 newcontent.append(None) -1066 else: -1067 newcontent.append(self.content[t] / y) -1068 return Corr(newcontent, prange=self.prange) -1069 elif isinstance(y, np.ndarray): -1070 if y.shape == (self.T,): -1071 return Corr(list((np.array(self.content).T / y).T)) -1072 else: -1073 raise ValueError("operands could not be broadcast together") -1074 else: -1075 raise TypeError('Corr / wrong type') -1076 -1077 def __neg__(self): -1078 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1079 return Corr(newcontent, prange=self.prange) -1080 -1081 def __sub__(self, y): -1082 return self + (-y) -1083 -1084 def __pow__(self, y): -1085 if isinstance(y, (Obs, int, float, CObs)): -1086 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1087 return Corr(newcontent, prange=self.prange) -1088 else: -1089 raise TypeError('Type of exponent not supported') -1090 -1091 def __abs__(self): -1092 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1093 return Corr(newcontent, prange=self.prange) -1094 -1095 # The numpy functions: -1096 def sqrt(self): -1097 return self ** 0.5 -1098 -1099 def log(self): -1100 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1101 return Corr(newcontent, prange=self.prange) -1102 -1103 def exp(self): -1104 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1105 return Corr(newcontent, prange=self.prange) -1106 -1107 def _apply_func_to_corr(self, func): -1108 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1109 for t in range(self.T): -1110 if _check_for_none(self, newcontent[t]): -1111 continue -1112 if np.isnan(np.sum(newcontent[t]).value): -1113 newcontent[t] = None -1114 if all([item is None for item in newcontent]): -1115 raise Exception('Operation returns undefined correlator') -1116 return Corr(newcontent) +1013 newcontent.append(self.content[t] + y.content[t]) +1014 return Corr(newcontent) +1015 +1016 elif isinstance(y, (Obs, int, float, CObs)): +1017 newcontent = [] +1018 for t in range(self.T): +1019 if _check_for_none(self, self.content[t]): +1020 newcontent.append(None) +1021 else: +1022 newcontent.append(self.content[t] + y) +1023 return Corr(newcontent, prange=self.prange) +1024 elif isinstance(y, np.ndarray): +1025 if y.shape == (self.T,): +1026 return Corr(list((np.array(self.content).T + y).T)) +1027 else: +1028 raise ValueError("operands could not be broadcast together") +1029 else: +1030 raise TypeError("Corr + wrong type") +1031 +1032 def __mul__(self, y): +1033 if isinstance(y, Corr): +1034 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1035 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1036 newcontent = [] +1037 for t in range(self.T): +1038 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1039 newcontent.append(None) +1040 else: +1041 newcontent.append(self.content[t] * y.content[t]) +1042 return Corr(newcontent) +1043 +1044 elif isinstance(y, (Obs, int, float, CObs)): +1045 newcontent = [] +1046 for t in range(self.T): +1047 if _check_for_none(self, self.content[t]): +1048 newcontent.append(None) +1049 else: +1050 newcontent.append(self.content[t] * y) +1051 return Corr(newcontent, prange=self.prange) +1052 elif isinstance(y, np.ndarray): +1053 if y.shape == (self.T,): +1054 return Corr(list((np.array(self.content).T * y).T)) +1055 else: +1056 raise ValueError("operands could not be broadcast together") +1057 else: +1058 raise TypeError("Corr * wrong type") +1059 +1060 def __truediv__(self, y): +1061 if isinstance(y, Corr): +1062 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1063 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1064 newcontent = [] +1065 for t in range(self.T): +1066 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1067 newcontent.append(None) +1068 else: +1069 newcontent.append(self.content[t] / y.content[t]) +1070 for t in range(self.T): +1071 if _check_for_none(self, newcontent[t]): +1072 continue +1073 if np.isnan(np.sum(newcontent[t]).value): +1074 newcontent[t] = None +1075 +1076 if all([item is None for item in newcontent]): +1077 raise Exception("Division returns completely undefined correlator") +1078 return Corr(newcontent) +1079 +1080 elif isinstance(y, (Obs, CObs)): +1081 if isinstance(y, Obs): +1082 if y.value == 0: +1083 raise Exception('Division by zero will return undefined correlator') +1084 if isinstance(y, CObs): +1085 if y.is_zero(): +1086 raise Exception('Division by zero will return undefined correlator') +1087 +1088 newcontent = [] +1089 for t in range(self.T): +1090 if _check_for_none(self, self.content[t]): +1091 newcontent.append(None) +1092 else: +1093 newcontent.append(self.content[t] / y) +1094 return Corr(newcontent, prange=self.prange) +1095 +1096 elif isinstance(y, (int, float)): +1097 if y == 0: +1098 raise Exception('Division by zero will return undefined correlator') +1099 newcontent = [] +1100 for t in range(self.T): +1101 if _check_for_none(self, self.content[t]): +1102 newcontent.append(None) +1103 else: +1104 newcontent.append(self.content[t] / y) +1105 return Corr(newcontent, prange=self.prange) +1106 elif isinstance(y, np.ndarray): +1107 if y.shape == (self.T,): +1108 return Corr(list((np.array(self.content).T / y).T)) +1109 else: +1110 raise ValueError("operands could not be broadcast together") +1111 else: +1112 raise TypeError('Corr / wrong type') +1113 +1114 def __neg__(self): +1115 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1116 return Corr(newcontent, prange=self.prange) 1117 -1118 def sin(self): -1119 return self._apply_func_to_corr(np.sin) +1118 def __sub__(self, y): +1119 return self + (-y) 1120 -1121 def cos(self): -1122 return self._apply_func_to_corr(np.cos) -1123 -1124 def tan(self): -1125 return self._apply_func_to_corr(np.tan) -1126 -1127 def sinh(self): -1128 return self._apply_func_to_corr(np.sinh) -1129 -1130 def cosh(self): -1131 return self._apply_func_to_corr(np.cosh) -1132 -1133 def tanh(self): -1134 return self._apply_func_to_corr(np.tanh) +1121 def __pow__(self, y): +1122 if isinstance(y, (Obs, int, float, CObs)): +1123 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1124 return Corr(newcontent, prange=self.prange) +1125 else: +1126 raise TypeError('Type of exponent not supported') +1127 +1128 def __abs__(self): +1129 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1130 return Corr(newcontent, prange=self.prange) +1131 +1132 # The numpy functions: +1133 def sqrt(self): +1134 return self ** 0.5 1135 -1136 def arcsin(self): -1137 return self._apply_func_to_corr(np.arcsin) -1138 -1139 def arccos(self): -1140 return self._apply_func_to_corr(np.arccos) -1141 -1142 def arctan(self): -1143 return self._apply_func_to_corr(np.arctan) -1144 -1145 def arcsinh(self): -1146 return self._apply_func_to_corr(np.arcsinh) -1147 -1148 def arccosh(self): -1149 return self._apply_func_to_corr(np.arccosh) -1150 -1151 def arctanh(self): -1152 return self._apply_func_to_corr(np.arctanh) -1153 -1154 # Right hand side operations (require tweak in main module to work) -1155 def __radd__(self, y): -1156 return self + y +1136 def log(self): +1137 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1138 return Corr(newcontent, prange=self.prange) +1139 +1140 def exp(self): +1141 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1142 return Corr(newcontent, prange=self.prange) +1143 +1144 def _apply_func_to_corr(self, func): +1145 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1146 for t in range(self.T): +1147 if _check_for_none(self, newcontent[t]): +1148 continue +1149 if np.isnan(np.sum(newcontent[t]).value): +1150 newcontent[t] = None +1151 if all([item is None for item in newcontent]): +1152 raise Exception('Operation returns undefined correlator') +1153 return Corr(newcontent) +1154 +1155 def sin(self): +1156 return self._apply_func_to_corr(np.sin) 1157 -1158 def __rsub__(self, y): -1159 return -self + y +1158 def cos(self): +1159 return self._apply_func_to_corr(np.cos) 1160 -1161 def __rmul__(self, y): -1162 return self * y +1161 def tan(self): +1162 return self._apply_func_to_corr(np.tan) 1163 -1164 def __rtruediv__(self, y): -1165 return (self / y) ** (-1) +1164 def sinh(self): +1165 return self._apply_func_to_corr(np.sinh) 1166 -1167 @property -1168 def real(self): -1169 def return_real(obs_OR_cobs): -1170 if isinstance(obs_OR_cobs, CObs): -1171 return obs_OR_cobs.real -1172 else: -1173 return obs_OR_cobs -1174 -1175 return self._apply_func_to_corr(return_real) -1176 -1177 @property -1178 def imag(self): -1179 def return_imag(obs_OR_cobs): -1180 if isinstance(obs_OR_cobs, CObs): -1181 return obs_OR_cobs.imag -1182 else: -1183 return obs_OR_cobs * 0 # So it stays the right type +1167 def cosh(self): +1168 return self._apply_func_to_corr(np.cosh) +1169 +1170 def tanh(self): +1171 return self._apply_func_to_corr(np.tanh) +1172 +1173 def arcsin(self): +1174 return self._apply_func_to_corr(np.arcsin) +1175 +1176 def arccos(self): +1177 return self._apply_func_to_corr(np.arccos) +1178 +1179 def arctan(self): +1180 return self._apply_func_to_corr(np.arctan) +1181 +1182 def arcsinh(self): +1183 return self._apply_func_to_corr(np.arcsinh) 1184 -1185 return self._apply_func_to_corr(return_imag) -1186 -1187 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1188 r''' Project large correlation matrix to lowest states -1189 -1190 This method can be used to reduce the size of an (N x N) correlation matrix -1191 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1192 is still small. -1193 -1194 Parameters -1195 ---------- -1196 Ntrunc: int -1197 Rank of the target matrix. -1198 tproj: int -1199 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1200 The default value is 3. -1201 t0proj: int -1202 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1203 discouraged for O(a) improved theories, since the correctness of the procedure -1204 cannot be granted in this case. The default value is 2. -1205 basematrix : Corr -1206 Correlation matrix that is used to determine the eigenvectors of the -1207 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1208 is is not specified. -1209 -1210 Notes -1211 ----- -1212 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1213 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1214 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1215 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1216 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1217 correlation matrix and to remove some noise that is added by irrelevant operators. -1218 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1219 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1220 ''' +1185 def arccosh(self): +1186 return self._apply_func_to_corr(np.arccosh) +1187 +1188 def arctanh(self): +1189 return self._apply_func_to_corr(np.arctanh) +1190 +1191 # Right hand side operations (require tweak in main module to work) +1192 def __radd__(self, y): +1193 return self + y +1194 +1195 def __rsub__(self, y): +1196 return -self + y +1197 +1198 def __rmul__(self, y): +1199 return self * y +1200 +1201 def __rtruediv__(self, y): +1202 return (self / y) ** (-1) +1203 +1204 @property +1205 def real(self): +1206 def return_real(obs_OR_cobs): +1207 if isinstance(obs_OR_cobs, CObs): +1208 return obs_OR_cobs.real +1209 else: +1210 return obs_OR_cobs +1211 +1212 return self._apply_func_to_corr(return_real) +1213 +1214 @property +1215 def imag(self): +1216 def return_imag(obs_OR_cobs): +1217 if isinstance(obs_OR_cobs, CObs): +1218 return obs_OR_cobs.imag +1219 else: +1220 return obs_OR_cobs * 0 # So it stays the right type 1221 -1222 if self.N == 1: -1223 raise Exception('Method cannot be applied to one-dimensional correlators.') -1224 if basematrix is None: -1225 basematrix = self -1226 if Ntrunc >= basematrix.N: -1227 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1228 if basematrix.N != self.N: -1229 raise Exception('basematrix and targetmatrix have to be of the same size.') +1222 return self._apply_func_to_corr(return_imag) +1223 +1224 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1225 r''' Project large correlation matrix to lowest states +1226 +1227 This method can be used to reduce the size of an (N x N) correlation matrix +1228 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1229 is still small. 1230 -1231 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1232 -1233 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1234 rmat = [] -1235 for t in range(basematrix.T): -1236 for i in range(Ntrunc): -1237 for j in range(Ntrunc): -1238 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1239 rmat.append(np.copy(tmpmat)) -1240 -1241 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1242 return Corr(newcontent) -1243 -1244 -1245def _sort_vectors(vec_set, ts): -1246 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" -1247 reference_sorting = np.array(vec_set[ts]) -1248 N = reference_sorting.shape[0] -1249 sorted_vec_set = [] -1250 for t in range(len(vec_set)): -1251 if vec_set[t] is None: -1252 sorted_vec_set.append(None) -1253 elif not t == ts: -1254 perms = [list(o) for o in permutations([i for i in range(N)], N)] -1255 best_score = 0 -1256 for perm in perms: -1257 current_score = 1 -1258 for k in range(N): -1259 new_sorting = reference_sorting.copy() -1260 new_sorting[perm[k], :] = vec_set[t][k] -1261 current_score *= abs(np.linalg.det(new_sorting)) -1262 if current_score > best_score: -1263 best_score = current_score -1264 best_perm = perm -1265 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) -1266 else: -1267 sorted_vec_set.append(vec_set[t]) -1268 -1269 return sorted_vec_set -1270 -1271 -1272def _check_for_none(corr, entry): -1273 """Checks if entry for correlator corr is None""" -1274 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 -1275 -1276 -1277def _GEVP_solver(Gt, G0): -1278 """Helper function for solving the GEVP and sorting the eigenvectors. -1279 -1280 The helper function assumes that both provided matrices are symmetric and -1281 only processes the lower triangular part of both matrices. In case the matrices -1282 are not symmetric the upper triangular parts are effectively discarded.""" -1283 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] +1231 Parameters +1232 ---------- +1233 Ntrunc: int +1234 Rank of the target matrix. +1235 tproj: int +1236 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1237 The default value is 3. +1238 t0proj: int +1239 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1240 discouraged for O(a) improved theories, since the correctness of the procedure +1241 cannot be granted in this case. The default value is 2. +1242 basematrix : Corr +1243 Correlation matrix that is used to determine the eigenvectors of the +1244 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1245 is is not specified. +1246 +1247 Notes +1248 ----- +1249 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1250 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1251 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1252 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1253 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1254 correlation matrix and to remove some noise that is added by irrelevant operators. +1255 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1256 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1257 ''' +1258 +1259 if self.N == 1: +1260 raise Exception('Method cannot be applied to one-dimensional correlators.') +1261 if basematrix is None: +1262 basematrix = self +1263 if Ntrunc >= basematrix.N: +1264 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1265 if basematrix.N != self.N: +1266 raise Exception('basematrix and targetmatrix have to be of the same size.') +1267 +1268 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1269 +1270 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1271 rmat = [] +1272 for t in range(basematrix.T): +1273 for i in range(Ntrunc): +1274 for j in range(Ntrunc): +1275 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1276 rmat.append(np.copy(tmpmat)) +1277 +1278 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1279 return Corr(newcontent) +1280 +1281 +1282def _sort_vectors(vec_set, ts): +1283 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" +1284 reference_sorting = np.array(vec_set[ts]) +1285 N = reference_sorting.shape[0] +1286 sorted_vec_set = [] +1287 for t in range(len(vec_set)): +1288 if vec_set[t] is None: +1289 sorted_vec_set.append(None) +1290 elif not t == ts: +1291 perms = [list(o) for o in permutations([i for i in range(N)], N)] +1292 best_score = 0 +1293 for perm in perms: +1294 current_score = 1 +1295 for k in range(N): +1296 new_sorting = reference_sorting.copy() +1297 new_sorting[perm[k], :] = vec_set[t][k] +1298 current_score *= abs(np.linalg.det(new_sorting)) +1299 if current_score > best_score: +1300 best_score = current_score +1301 best_perm = perm +1302 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) +1303 else: +1304 sorted_vec_set.append(vec_set[t]) +1305 +1306 return sorted_vec_set +1307 +1308 +1309def _check_for_none(corr, entry): +1310 """Checks if entry for correlator corr is None""" +1311 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1312 +1313 +1314def _GEVP_solver(Gt, G0): +1315 """Helper function for solving the GEVP and sorting the eigenvectors. +1316 +1317 The helper function assumes that both provided matrices are symmetric and +1318 only processes the lower triangular part of both matrices. In case the matrices +1319 are not symmetric the upper triangular parts are effectively discarded.""" +1320 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] @@ -2017,7 +2054,7 @@ 524 ---------- 525 variant : str 526 decides which definition of the finite differences derivative is used. - 527 Available choice: symmetric, forward, backward, improved, default: symmetric + 527 Available choice: symmetric, forward, backward, improved, log, default: symmetric 528 """ 529 if self.N != 1: 530 raise Exception("deriv only implemented for one-dimensional correlators.") @@ -2061,679 +2098,716 @@ 568 if (all([x is None for x in newcontent])): 569 raise Exception('Derivative is undefined at all timeslices') 570 return Corr(newcontent, padding=[2, 2]) - 571 else: - 572 raise Exception("Unknown variant.") - 573 - 574 def second_deriv(self, variant="symmetric"): - 575 """Return the second derivative of the correlator with respect to x0. - 576 - 577 Parameters - 578 ---------- - 579 variant : str - 580 decides which definition of the finite differences derivative is used. - 581 Available choice: symmetric, improved, default: symmetric - 582 """ - 583 if self.N != 1: - 584 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 585 if variant == "symmetric": - 586 newcontent = [] - 587 for t in range(1, self.T - 1): - 588 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 589 newcontent.append(None) - 590 else: - 591 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 592 if (all([x is None for x in newcontent])): - 593 raise Exception("Derivative is undefined at all timeslices") - 594 return Corr(newcontent, padding=[1, 1]) - 595 elif variant == "improved": - 596 newcontent = [] - 597 for t in range(2, self.T - 2): - 598 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): - 599 newcontent.append(None) - 600 else: - 601 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) - 602 if (all([x is None for x in newcontent])): - 603 raise Exception("Derivative is undefined at all timeslices") - 604 return Corr(newcontent, padding=[2, 2]) - 605 else: - 606 raise Exception("Unknown variant.") - 607 - 608 def m_eff(self, variant='log', guess=1.0): - 609 """Returns the effective mass of the correlator as correlator object - 610 - 611 Parameters - 612 ---------- - 613 variant : str - 614 log : uses the standard effective mass log(C(t) / C(t+1)) - 615 cosh, 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. - 616 sinh : 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. - 617 See, e.g., arXiv:1205.5380 - 618 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 619 guess : float - 620 guess for the root finder, only relevant for the root variant - 621 """ - 622 if self.N != 1: - 623 raise Exception('Correlator must be projected before getting m_eff') - 624 if variant == 'log': - 625 newcontent = [] - 626 for t in range(self.T - 1): - 627 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 628 newcontent.append(None) - 629 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 630 newcontent.append(None) - 631 else: - 632 newcontent.append(self.content[t] / self.content[t + 1]) - 633 if (all([x is None for x in newcontent])): - 634 raise Exception('m_eff is undefined at all timeslices') - 635 - 636 return np.log(Corr(newcontent, padding=[0, 1])) - 637 - 638 elif variant in ['periodic', 'cosh', 'sinh']: - 639 if variant in ['periodic', 'cosh']: - 640 func = anp.cosh - 641 else: - 642 func = anp.sinh - 643 - 644 def root_function(x, d): - 645 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 646 - 647 newcontent = [] - 648 for t in range(self.T - 1): - 649 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 650 newcontent.append(None) - 651 # Fill the two timeslices in the middle of the lattice with their predecessors - 652 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 653 newcontent.append(newcontent[-1]) - 654 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 655 newcontent.append(None) - 656 else: - 657 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 658 if (all([x is None for x in newcontent])): - 659 raise Exception('m_eff is undefined at all timeslices') + 571 elif variant == 'log': + 572 newcontent = [] + 573 for t in range(self.T): + 574 if (self.content[t] is None) or (self.content[t] <= 0): + 575 newcontent.append(None) + 576 else: + 577 newcontent.append(np.log(self.content[t])) + 578 if (all([x is None for x in newcontent])): + 579 raise Exception("Log is undefined at all timeslices") + 580 logcorr = Corr(newcontent) + 581 return self * logcorr.deriv('symmetric') + 582 else: + 583 raise Exception("Unknown variant.") + 584 + 585 def second_deriv(self, variant="symmetric"): + 586 """Return the second derivative of the correlator with respect to x0. + 587 + 588 Parameters + 589 ---------- + 590 variant : str + 591 decides which definition of the finite differences derivative is used. + 592 Available choice: symmetric, improved, log, default: symmetric + 593 """ + 594 if self.N != 1: + 595 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 596 if variant == "symmetric": + 597 newcontent = [] + 598 for t in range(1, self.T - 1): + 599 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 600 newcontent.append(None) + 601 else: + 602 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 603 if (all([x is None for x in newcontent])): + 604 raise Exception("Derivative is undefined at all timeslices") + 605 return Corr(newcontent, padding=[1, 1]) + 606 elif variant == "improved": + 607 newcontent = [] + 608 for t in range(2, self.T - 2): + 609 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 610 newcontent.append(None) + 611 else: + 612 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) + 613 if (all([x is None for x in newcontent])): + 614 raise Exception("Derivative is undefined at all timeslices") + 615 return Corr(newcontent, padding=[2, 2]) + 616 elif variant == 'log': + 617 newcontent = [] + 618 for t in range(self.T): + 619 if (self.content[t] is None) or (self.content[t] <= 0): + 620 newcontent.append(None) + 621 else: + 622 newcontent.append(np.log(self.content[t])) + 623 if (all([x is None for x in newcontent])): + 624 raise Exception("Log is undefined at all timeslices") + 625 logcorr = Corr(newcontent) + 626 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) + 627 else: + 628 raise Exception("Unknown variant.") + 629 + 630 def m_eff(self, variant='log', guess=1.0): + 631 """Returns the effective mass of the correlator as correlator object + 632 + 633 Parameters + 634 ---------- + 635 variant : str + 636 log : uses the standard effective mass log(C(t) / C(t+1)) + 637 cosh, 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. + 638 sinh : 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. + 639 See, e.g., arXiv:1205.5380 + 640 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 641 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 + 642 guess : float + 643 guess for the root finder, only relevant for the root variant + 644 """ + 645 if self.N != 1: + 646 raise Exception('Correlator must be projected before getting m_eff') + 647 if variant == 'log': + 648 newcontent = [] + 649 for t in range(self.T - 1): + 650 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 651 newcontent.append(None) + 652 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 653 newcontent.append(None) + 654 else: + 655 newcontent.append(self.content[t] / self.content[t + 1]) + 656 if (all([x is None for x in newcontent])): + 657 raise Exception('m_eff is undefined at all timeslices') + 658 + 659 return np.log(Corr(newcontent, padding=[0, 1])) 660 - 661 return Corr(newcontent, padding=[0, 1]) - 662 - 663 elif variant == 'arccosh': - 664 newcontent = [] - 665 for t in range(1, self.T - 1): - 666 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): + 661 elif variant == 'logsym': + 662 newcontent = [] + 663 for t in range(1, self.T - 1): + 664 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 665 newcontent.append(None) + 666 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: 667 newcontent.append(None) 668 else: - 669 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 669 newcontent.append(self.content[t - 1] / self.content[t + 1]) 670 if (all([x is None for x in newcontent])): - 671 raise Exception("m_eff is undefined at all timeslices") - 672 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 673 - 674 else: - 675 raise Exception('Unknown variant.') - 676 - 677 def fit(self, function, fitrange=None, silent=False, **kwargs): - 678 r'''Fits function to the data - 679 - 680 Parameters - 681 ---------- - 682 function : obj - 683 function to fit to the data. See fits.least_squares for details. - 684 fitrange : list - 685 Two element list containing the timeslices on which the fit is supposed to start and stop. - 686 Caution: This range is inclusive as opposed to standard python indexing. - 687 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 688 If not specified, self.prange or all timeslices are used. - 689 silent : bool - 690 Decides whether output is printed to the standard output. - 691 ''' - 692 if self.N != 1: - 693 raise Exception("Correlator must be projected before fitting") - 694 - 695 if fitrange is None: - 696 if self.prange: - 697 fitrange = self.prange - 698 else: - 699 fitrange = [0, self.T - 1] - 700 else: - 701 if not isinstance(fitrange, list): - 702 raise Exception("fitrange has to be a list with two elements") - 703 if len(fitrange) != 2: - 704 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 705 - 706 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 707 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 708 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 709 return result + 671 raise Exception('m_eff is undefined at all timeslices') + 672 + 673 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 674 + 675 elif variant in ['periodic', 'cosh', 'sinh']: + 676 if variant in ['periodic', 'cosh']: + 677 func = anp.cosh + 678 else: + 679 func = anp.sinh + 680 + 681 def root_function(x, d): + 682 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 683 + 684 newcontent = [] + 685 for t in range(self.T - 1): + 686 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 687 newcontent.append(None) + 688 # Fill the two timeslices in the middle of the lattice with their predecessors + 689 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 690 newcontent.append(newcontent[-1]) + 691 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 692 newcontent.append(None) + 693 else: + 694 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) + 695 if (all([x is None for x in newcontent])): + 696 raise Exception('m_eff is undefined at all timeslices') + 697 + 698 return Corr(newcontent, padding=[0, 1]) + 699 + 700 elif variant == 'arccosh': + 701 newcontent = [] + 702 for t in range(1, self.T - 1): + 703 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): + 704 newcontent.append(None) + 705 else: + 706 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 707 if (all([x is None for x in newcontent])): + 708 raise Exception("m_eff is undefined at all timeslices") + 709 return np.arccosh(Corr(newcontent, padding=[1, 1])) 710 - 711 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 712 """ Extract a plateau value from a Corr object + 711 else: + 712 raise Exception('Unknown variant.') 713 - 714 Parameters - 715 ---------- - 716 plateau_range : list - 717 list with two entries, indicating the first and the last timeslice - 718 of the plateau region. - 719 method : str - 720 method to extract the plateau. - 721 'fit' fits a constant to the plateau region - 722 'avg', 'average' or 'mean' just average over the given timeslices. - 723 auto_gamma : bool - 724 apply gamma_method with default parameters to the Corr. Defaults to None - 725 """ - 726 if not plateau_range: - 727 if self.prange: - 728 plateau_range = self.prange - 729 else: - 730 raise Exception("no plateau range provided") - 731 if self.N != 1: - 732 raise Exception("Correlator must be projected before getting a plateau.") - 733 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 734 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 735 if auto_gamma: - 736 self.gamma_method() - 737 if method == "fit": - 738 def const_func(a, t): - 739 return a[0] - 740 return self.fit(const_func, plateau_range)[0] - 741 elif method in ["avg", "average", "mean"]: - 742 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 743 return returnvalue - 744 - 745 else: - 746 raise Exception("Unsupported plateau method: " + method) + 714 def fit(self, function, fitrange=None, silent=False, **kwargs): + 715 r'''Fits function to the data + 716 + 717 Parameters + 718 ---------- + 719 function : obj + 720 function to fit to the data. See fits.least_squares for details. + 721 fitrange : list + 722 Two element list containing the timeslices on which the fit is supposed to start and stop. + 723 Caution: This range is inclusive as opposed to standard python indexing. + 724 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 725 If not specified, self.prange or all timeslices are used. + 726 silent : bool + 727 Decides whether output is printed to the standard output. + 728 ''' + 729 if self.N != 1: + 730 raise Exception("Correlator must be projected before fitting") + 731 + 732 if fitrange is None: + 733 if self.prange: + 734 fitrange = self.prange + 735 else: + 736 fitrange = [0, self.T - 1] + 737 else: + 738 if not isinstance(fitrange, list): + 739 raise Exception("fitrange has to be a list with two elements") + 740 if len(fitrange) != 2: + 741 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 742 + 743 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 744 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 745 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 746 return result 747 - 748 def set_prange(self, prange): - 749 """Sets the attribute prange of the Corr object.""" - 750 if not len(prange) == 2: - 751 raise Exception("prange must be a list or array with two values") - 752 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 753 raise Exception("Start and end point must be integers") - 754 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 755 raise Exception("Start and end point must define a range in the interval 0,T") - 756 - 757 self.prange = prange - 758 return - 759 - 760 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): - 761 """Plots the correlator using the tag of the correlator as label if available. - 762 - 763 Parameters - 764 ---------- - 765 x_range : list - 766 list of two values, determining the range of the x-axis e.g. [4, 8]. - 767 comp : Corr or list of Corr - 768 Correlator or list of correlators which are plotted for comparison. - 769 The tags of these correlators are used as labels if available. - 770 logscale : bool - 771 Sets y-axis to logscale. - 772 plateau : Obs - 773 Plateau value to be visualized in the figure. - 774 fit_res : Fit_result - 775 Fit_result object to be visualized. - 776 ylabel : str - 777 Label for the y-axis. - 778 save : str - 779 path to file in which the figure should be saved. - 780 auto_gamma : bool - 781 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 782 hide_sigma : float - 783 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 784 references : list - 785 List of floating point values that are displayed as horizontal lines for reference. - 786 title : string - 787 Optional title of the figure. - 788 """ - 789 if self.N != 1: - 790 raise Exception("Correlator must be projected before plotting") - 791 - 792 if auto_gamma: - 793 self.gamma_method() - 794 - 795 if x_range is None: - 796 x_range = [0, self.T - 1] - 797 - 798 fig = plt.figure() - 799 ax1 = fig.add_subplot(111) - 800 - 801 x, y, y_err = self.plottable() - 802 if hide_sigma: - 803 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 804 else: - 805 hide_from = None - 806 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 807 if logscale: - 808 ax1.set_yscale('log') - 809 else: - 810 if y_range is None: - 811 try: - 812 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)]) - 813 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)]) - 814 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 815 except Exception: - 816 pass - 817 else: - 818 ax1.set_ylim(y_range) - 819 if comp: - 820 if isinstance(comp, (Corr, list)): - 821 for corr in comp if isinstance(comp, list) else [comp]: - 822 if auto_gamma: - 823 corr.gamma_method() - 824 x, y, y_err = corr.plottable() - 825 if hide_sigma: - 826 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 827 else: - 828 hide_from = None - 829 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 830 else: - 831 raise Exception("'comp' must be a correlator or a list of correlators.") - 832 - 833 if plateau: - 834 if isinstance(plateau, Obs): - 835 if auto_gamma: - 836 plateau.gamma_method() - 837 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 838 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 839 else: - 840 raise Exception("'plateau' must be an Obs") - 841 - 842 if references: - 843 if isinstance(references, list): - 844 for ref in references: - 845 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 846 else: - 847 raise Exception("'references' must be a list of floating pint values.") - 848 - 849 if self.prange: - 850 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 851 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 852 - 853 if fit_res: - 854 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 855 ax1.plot(x_samples, - 856 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 857 ls='-', marker=',', lw=2) - 858 - 859 ax1.set_xlabel(r'$x_0 / a$') - 860 if ylabel: - 861 ax1.set_ylabel(ylabel) - 862 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 863 - 864 handles, labels = ax1.get_legend_handles_labels() - 865 if labels: - 866 ax1.legend() - 867 - 868 if title: - 869 plt.title(title) - 870 - 871 plt.draw() - 872 - 873 if save: - 874 if isinstance(save, str): - 875 fig.savefig(save, bbox_inches='tight') + 748 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 749 """ Extract a plateau value from a Corr object + 750 + 751 Parameters + 752 ---------- + 753 plateau_range : list + 754 list with two entries, indicating the first and the last timeslice + 755 of the plateau region. + 756 method : str + 757 method to extract the plateau. + 758 'fit' fits a constant to the plateau region + 759 'avg', 'average' or 'mean' just average over the given timeslices. + 760 auto_gamma : bool + 761 apply gamma_method with default parameters to the Corr. Defaults to None + 762 """ + 763 if not plateau_range: + 764 if self.prange: + 765 plateau_range = self.prange + 766 else: + 767 raise Exception("no plateau range provided") + 768 if self.N != 1: + 769 raise Exception("Correlator must be projected before getting a plateau.") + 770 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 771 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 772 if auto_gamma: + 773 self.gamma_method() + 774 if method == "fit": + 775 def const_func(a, t): + 776 return a[0] + 777 return self.fit(const_func, plateau_range)[0] + 778 elif method in ["avg", "average", "mean"]: + 779 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 780 return returnvalue + 781 + 782 else: + 783 raise Exception("Unsupported plateau method: " + method) + 784 + 785 def set_prange(self, prange): + 786 """Sets the attribute prange of the Corr object.""" + 787 if not len(prange) == 2: + 788 raise Exception("prange must be a list or array with two values") + 789 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 790 raise Exception("Start and end point must be integers") + 791 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 792 raise Exception("Start and end point must define a range in the interval 0,T") + 793 + 794 self.prange = prange + 795 return + 796 + 797 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): + 798 """Plots the correlator using the tag of the correlator as label if available. + 799 + 800 Parameters + 801 ---------- + 802 x_range : list + 803 list of two values, determining the range of the x-axis e.g. [4, 8]. + 804 comp : Corr or list of Corr + 805 Correlator or list of correlators which are plotted for comparison. + 806 The tags of these correlators are used as labels if available. + 807 logscale : bool + 808 Sets y-axis to logscale. + 809 plateau : Obs + 810 Plateau value to be visualized in the figure. + 811 fit_res : Fit_result + 812 Fit_result object to be visualized. + 813 ylabel : str + 814 Label for the y-axis. + 815 save : str + 816 path to file in which the figure should be saved. + 817 auto_gamma : bool + 818 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 819 hide_sigma : float + 820 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 821 references : list + 822 List of floating point values that are displayed as horizontal lines for reference. + 823 title : string + 824 Optional title of the figure. + 825 """ + 826 if self.N != 1: + 827 raise Exception("Correlator must be projected before plotting") + 828 + 829 if auto_gamma: + 830 self.gamma_method() + 831 + 832 if x_range is None: + 833 x_range = [0, self.T - 1] + 834 + 835 fig = plt.figure() + 836 ax1 = fig.add_subplot(111) + 837 + 838 x, y, y_err = self.plottable() + 839 if hide_sigma: + 840 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 841 else: + 842 hide_from = None + 843 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 844 if logscale: + 845 ax1.set_yscale('log') + 846 else: + 847 if y_range is None: + 848 try: + 849 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)]) + 850 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)]) + 851 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 852 except Exception: + 853 pass + 854 else: + 855 ax1.set_ylim(y_range) + 856 if comp: + 857 if isinstance(comp, (Corr, list)): + 858 for corr in comp if isinstance(comp, list) else [comp]: + 859 if auto_gamma: + 860 corr.gamma_method() + 861 x, y, y_err = corr.plottable() + 862 if hide_sigma: + 863 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 864 else: + 865 hide_from = None + 866 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 867 else: + 868 raise Exception("'comp' must be a correlator or a list of correlators.") + 869 + 870 if plateau: + 871 if isinstance(plateau, Obs): + 872 if auto_gamma: + 873 plateau.gamma_method() + 874 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 875 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') 876 else: - 877 raise Exception("'save' has to be a string.") + 877 raise Exception("'plateau' must be an Obs") 878 - 879 def spaghetti_plot(self, logscale=True): - 880 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 881 - 882 Parameters - 883 ---------- - 884 logscale : bool - 885 Determines whether the scale of the y-axis is logarithmic or standard. - 886 """ - 887 if self.N != 1: - 888 raise Exception("Correlator needs to be projected first.") + 879 if references: + 880 if isinstance(references, list): + 881 for ref in references: + 882 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 883 else: + 884 raise Exception("'references' must be a list of floating pint values.") + 885 + 886 if self.prange: + 887 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 888 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') 889 - 890 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])) - 891 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 892 - 893 for name in mc_names: - 894 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 890 if fit_res: + 891 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 892 ax1.plot(x_samples, + 893 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 894 ls='-', marker=',', lw=2) 895 - 896 fig = plt.figure() - 897 ax = fig.add_subplot(111) - 898 for dat in data: - 899 ax.plot(x0_vals, dat, ls='-', marker='') + 896 ax1.set_xlabel(r'$x_0 / a$') + 897 if ylabel: + 898 ax1.set_ylabel(ylabel) + 899 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) 900 - 901 if logscale is True: - 902 ax.set_yscale('log') - 903 - 904 ax.set_xlabel(r'$x_0 / a$') - 905 plt.title(name) - 906 plt.draw() + 901 handles, labels = ax1.get_legend_handles_labels() + 902 if labels: + 903 ax1.legend() + 904 + 905 if title: + 906 plt.title(title) 907 - 908 def dump(self, filename, datatype="json.gz", **kwargs): - 909 """Dumps the Corr into a file of chosen type - 910 Parameters - 911 ---------- - 912 filename : str - 913 Name of the file to be saved. - 914 datatype : str - 915 Format of the exported file. Supported formats include - 916 "json.gz" and "pickle" - 917 path : str - 918 specifies a custom path for the file (default '.') - 919 """ - 920 if datatype == "json.gz": - 921 from .input.json import dump_to_json - 922 if 'path' in kwargs: - 923 file_name = kwargs.get('path') + '/' + filename - 924 else: - 925 file_name = filename - 926 dump_to_json(self, file_name) - 927 elif datatype == "pickle": - 928 dump_object(self, filename, **kwargs) - 929 else: - 930 raise Exception("Unknown datatype " + str(datatype)) - 931 - 932 def print(self, print_range=None): - 933 print(self.__repr__(print_range)) - 934 - 935 def __repr__(self, print_range=None): - 936 if print_range is None: - 937 print_range = [0, None] - 938 - 939 content_string = "" - 940 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 - 941 - 942 if self.tag is not None: - 943 content_string += "Description: " + self.tag + "\n" - 944 if self.N != 1: - 945 return content_string - 946 - 947 if print_range[1]: - 948 print_range[1] += 1 - 949 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 950 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 951 if sub_corr is None: - 952 content_string += str(i + print_range[0]) + '\n' - 953 else: - 954 content_string += str(i + print_range[0]) - 955 for element in sub_corr: - 956 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 957 content_string += '\n' - 958 return content_string - 959 - 960 def __str__(self): - 961 return self.__repr__() - 962 - 963 # We define the basic operations, that can be performed with correlators. - 964 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 965 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 966 # One could try and tell Obs to check if the y in __mul__ is a Corr and - 967 - 968 def __add__(self, y): - 969 if isinstance(y, Corr): - 970 if ((self.N != y.N) or (self.T != y.T)): - 971 raise Exception("Addition of Corrs with different shape") - 972 newcontent = [] - 973 for t in range(self.T): - 974 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 975 newcontent.append(None) - 976 else: - 977 newcontent.append(self.content[t] + y.content[t]) - 978 return Corr(newcontent) - 979 - 980 elif isinstance(y, (Obs, int, float, CObs)): - 981 newcontent = [] - 982 for t in range(self.T): - 983 if _check_for_none(self, self.content[t]): - 984 newcontent.append(None) - 985 else: - 986 newcontent.append(self.content[t] + y) - 987 return Corr(newcontent, prange=self.prange) - 988 elif isinstance(y, np.ndarray): - 989 if y.shape == (self.T,): - 990 return Corr(list((np.array(self.content).T + y).T)) - 991 else: - 992 raise ValueError("operands could not be broadcast together") - 993 else: - 994 raise TypeError("Corr + wrong type") - 995 - 996 def __mul__(self, y): - 997 if isinstance(y, Corr): - 998 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 999 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1000 newcontent = [] -1001 for t in range(self.T): -1002 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1003 newcontent.append(None) -1004 else: -1005 newcontent.append(self.content[t] * y.content[t]) -1006 return Corr(newcontent) -1007 -1008 elif isinstance(y, (Obs, int, float, CObs)): + 908 plt.draw() + 909 + 910 if save: + 911 if isinstance(save, str): + 912 fig.savefig(save, bbox_inches='tight') + 913 else: + 914 raise Exception("'save' has to be a string.") + 915 + 916 def spaghetti_plot(self, logscale=True): + 917 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 918 + 919 Parameters + 920 ---------- + 921 logscale : bool + 922 Determines whether the scale of the y-axis is logarithmic or standard. + 923 """ + 924 if self.N != 1: + 925 raise Exception("Correlator needs to be projected first.") + 926 + 927 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])) + 928 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 929 + 930 for name in mc_names: + 931 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 932 + 933 fig = plt.figure() + 934 ax = fig.add_subplot(111) + 935 for dat in data: + 936 ax.plot(x0_vals, dat, ls='-', marker='') + 937 + 938 if logscale is True: + 939 ax.set_yscale('log') + 940 + 941 ax.set_xlabel(r'$x_0 / a$') + 942 plt.title(name) + 943 plt.draw() + 944 + 945 def dump(self, filename, datatype="json.gz", **kwargs): + 946 """Dumps the Corr into a file of chosen type + 947 Parameters + 948 ---------- + 949 filename : str + 950 Name of the file to be saved. + 951 datatype : str + 952 Format of the exported file. Supported formats include + 953 "json.gz" and "pickle" + 954 path : str + 955 specifies a custom path for the file (default '.') + 956 """ + 957 if datatype == "json.gz": + 958 from .input.json import dump_to_json + 959 if 'path' in kwargs: + 960 file_name = kwargs.get('path') + '/' + filename + 961 else: + 962 file_name = filename + 963 dump_to_json(self, file_name) + 964 elif datatype == "pickle": + 965 dump_object(self, filename, **kwargs) + 966 else: + 967 raise Exception("Unknown datatype " + str(datatype)) + 968 + 969 def print(self, print_range=None): + 970 print(self.__repr__(print_range)) + 971 + 972 def __repr__(self, print_range=None): + 973 if print_range is None: + 974 print_range = [0, None] + 975 + 976 content_string = "" + 977 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 + 978 + 979 if self.tag is not None: + 980 content_string += "Description: " + self.tag + "\n" + 981 if self.N != 1: + 982 return content_string + 983 + 984 if print_range[1]: + 985 print_range[1] += 1 + 986 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 987 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 988 if sub_corr is None: + 989 content_string += str(i + print_range[0]) + '\n' + 990 else: + 991 content_string += str(i + print_range[0]) + 992 for element in sub_corr: + 993 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 994 content_string += '\n' + 995 return content_string + 996 + 997 def __str__(self): + 998 return self.__repr__() + 999 +1000 # We define the basic operations, that can be performed with correlators. +1001 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. +1002 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. +1003 # One could try and tell Obs to check if the y in __mul__ is a Corr and +1004 +1005 def __add__(self, y): +1006 if isinstance(y, Corr): +1007 if ((self.N != y.N) or (self.T != y.T)): +1008 raise Exception("Addition of Corrs with different shape") 1009 newcontent = [] 1010 for t in range(self.T): -1011 if _check_for_none(self, self.content[t]): +1011 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1012 newcontent.append(None) 1013 else: -1014 newcontent.append(self.content[t] * y) -1015 return Corr(newcontent, prange=self.prange) -1016 elif isinstance(y, np.ndarray): -1017 if y.shape == (self.T,): -1018 return Corr(list((np.array(self.content).T * y).T)) -1019 else: -1020 raise ValueError("operands could not be broadcast together") -1021 else: -1022 raise TypeError("Corr * wrong type") -1023 -1024 def __truediv__(self, y): -1025 if isinstance(y, Corr): -1026 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1027 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1028 newcontent = [] -1029 for t in range(self.T): -1030 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1031 newcontent.append(None) -1032 else: -1033 newcontent.append(self.content[t] / y.content[t]) -1034 for t in range(self.T): -1035 if _check_for_none(self, newcontent[t]): -1036 continue -1037 if np.isnan(np.sum(newcontent[t]).value): -1038 newcontent[t] = None -1039 -1040 if all([item is None for item in newcontent]): -1041 raise Exception("Division returns completely undefined correlator") -1042 return Corr(newcontent) -1043 -1044 elif isinstance(y, (Obs, CObs)): -1045 if isinstance(y, Obs): -1046 if y.value == 0: -1047 raise Exception('Division by zero will return undefined correlator') -1048 if isinstance(y, CObs): -1049 if y.is_zero(): -1050 raise Exception('Division by zero will return undefined correlator') -1051 -1052 newcontent = [] -1053 for t in range(self.T): -1054 if _check_for_none(self, self.content[t]): -1055 newcontent.append(None) -1056 else: -1057 newcontent.append(self.content[t] / y) -1058 return Corr(newcontent, prange=self.prange) -1059 -1060 elif isinstance(y, (int, float)): -1061 if y == 0: -1062 raise Exception('Division by zero will return undefined correlator') -1063 newcontent = [] -1064 for t in range(self.T): -1065 if _check_for_none(self, self.content[t]): -1066 newcontent.append(None) -1067 else: -1068 newcontent.append(self.content[t] / y) -1069 return Corr(newcontent, prange=self.prange) -1070 elif isinstance(y, np.ndarray): -1071 if y.shape == (self.T,): -1072 return Corr(list((np.array(self.content).T / y).T)) -1073 else: -1074 raise ValueError("operands could not be broadcast together") -1075 else: -1076 raise TypeError('Corr / wrong type') -1077 -1078 def __neg__(self): -1079 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1080 return Corr(newcontent, prange=self.prange) -1081 -1082 def __sub__(self, y): -1083 return self + (-y) -1084 -1085 def __pow__(self, y): -1086 if isinstance(y, (Obs, int, float, CObs)): -1087 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1088 return Corr(newcontent, prange=self.prange) -1089 else: -1090 raise TypeError('Type of exponent not supported') -1091 -1092 def __abs__(self): -1093 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1094 return Corr(newcontent, prange=self.prange) -1095 -1096 # The numpy functions: -1097 def sqrt(self): -1098 return self ** 0.5 -1099 -1100 def log(self): -1101 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1102 return Corr(newcontent, prange=self.prange) -1103 -1104 def exp(self): -1105 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1106 return Corr(newcontent, prange=self.prange) -1107 -1108 def _apply_func_to_corr(self, func): -1109 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1110 for t in range(self.T): -1111 if _check_for_none(self, newcontent[t]): -1112 continue -1113 if np.isnan(np.sum(newcontent[t]).value): -1114 newcontent[t] = None -1115 if all([item is None for item in newcontent]): -1116 raise Exception('Operation returns undefined correlator') -1117 return Corr(newcontent) +1014 newcontent.append(self.content[t] + y.content[t]) +1015 return Corr(newcontent) +1016 +1017 elif isinstance(y, (Obs, int, float, CObs)): +1018 newcontent = [] +1019 for t in range(self.T): +1020 if _check_for_none(self, self.content[t]): +1021 newcontent.append(None) +1022 else: +1023 newcontent.append(self.content[t] + y) +1024 return Corr(newcontent, prange=self.prange) +1025 elif isinstance(y, np.ndarray): +1026 if y.shape == (self.T,): +1027 return Corr(list((np.array(self.content).T + y).T)) +1028 else: +1029 raise ValueError("operands could not be broadcast together") +1030 else: +1031 raise TypeError("Corr + wrong type") +1032 +1033 def __mul__(self, y): +1034 if isinstance(y, Corr): +1035 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1036 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1037 newcontent = [] +1038 for t in range(self.T): +1039 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1040 newcontent.append(None) +1041 else: +1042 newcontent.append(self.content[t] * y.content[t]) +1043 return Corr(newcontent) +1044 +1045 elif isinstance(y, (Obs, int, float, CObs)): +1046 newcontent = [] +1047 for t in range(self.T): +1048 if _check_for_none(self, self.content[t]): +1049 newcontent.append(None) +1050 else: +1051 newcontent.append(self.content[t] * y) +1052 return Corr(newcontent, prange=self.prange) +1053 elif isinstance(y, np.ndarray): +1054 if y.shape == (self.T,): +1055 return Corr(list((np.array(self.content).T * y).T)) +1056 else: +1057 raise ValueError("operands could not be broadcast together") +1058 else: +1059 raise TypeError("Corr * wrong type") +1060 +1061 def __truediv__(self, y): +1062 if isinstance(y, Corr): +1063 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1064 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1065 newcontent = [] +1066 for t in range(self.T): +1067 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1068 newcontent.append(None) +1069 else: +1070 newcontent.append(self.content[t] / y.content[t]) +1071 for t in range(self.T): +1072 if _check_for_none(self, newcontent[t]): +1073 continue +1074 if np.isnan(np.sum(newcontent[t]).value): +1075 newcontent[t] = None +1076 +1077 if all([item is None for item in newcontent]): +1078 raise Exception("Division returns completely undefined correlator") +1079 return Corr(newcontent) +1080 +1081 elif isinstance(y, (Obs, CObs)): +1082 if isinstance(y, Obs): +1083 if y.value == 0: +1084 raise Exception('Division by zero will return undefined correlator') +1085 if isinstance(y, CObs): +1086 if y.is_zero(): +1087 raise Exception('Division by zero will return undefined correlator') +1088 +1089 newcontent = [] +1090 for t in range(self.T): +1091 if _check_for_none(self, self.content[t]): +1092 newcontent.append(None) +1093 else: +1094 newcontent.append(self.content[t] / y) +1095 return Corr(newcontent, prange=self.prange) +1096 +1097 elif isinstance(y, (int, float)): +1098 if y == 0: +1099 raise Exception('Division by zero will return undefined correlator') +1100 newcontent = [] +1101 for t in range(self.T): +1102 if _check_for_none(self, self.content[t]): +1103 newcontent.append(None) +1104 else: +1105 newcontent.append(self.content[t] / y) +1106 return Corr(newcontent, prange=self.prange) +1107 elif isinstance(y, np.ndarray): +1108 if y.shape == (self.T,): +1109 return Corr(list((np.array(self.content).T / y).T)) +1110 else: +1111 raise ValueError("operands could not be broadcast together") +1112 else: +1113 raise TypeError('Corr / wrong type') +1114 +1115 def __neg__(self): +1116 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1117 return Corr(newcontent, prange=self.prange) 1118 -1119 def sin(self): -1120 return self._apply_func_to_corr(np.sin) +1119 def __sub__(self, y): +1120 return self + (-y) 1121 -1122 def cos(self): -1123 return self._apply_func_to_corr(np.cos) -1124 -1125 def tan(self): -1126 return self._apply_func_to_corr(np.tan) -1127 -1128 def sinh(self): -1129 return self._apply_func_to_corr(np.sinh) -1130 -1131 def cosh(self): -1132 return self._apply_func_to_corr(np.cosh) -1133 -1134 def tanh(self): -1135 return self._apply_func_to_corr(np.tanh) +1122 def __pow__(self, y): +1123 if isinstance(y, (Obs, int, float, CObs)): +1124 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1125 return Corr(newcontent, prange=self.prange) +1126 else: +1127 raise TypeError('Type of exponent not supported') +1128 +1129 def __abs__(self): +1130 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1131 return Corr(newcontent, prange=self.prange) +1132 +1133 # The numpy functions: +1134 def sqrt(self): +1135 return self ** 0.5 1136 -1137 def arcsin(self): -1138 return self._apply_func_to_corr(np.arcsin) -1139 -1140 def arccos(self): -1141 return self._apply_func_to_corr(np.arccos) -1142 -1143 def arctan(self): -1144 return self._apply_func_to_corr(np.arctan) -1145 -1146 def arcsinh(self): -1147 return self._apply_func_to_corr(np.arcsinh) -1148 -1149 def arccosh(self): -1150 return self._apply_func_to_corr(np.arccosh) -1151 -1152 def arctanh(self): -1153 return self._apply_func_to_corr(np.arctanh) -1154 -1155 # Right hand side operations (require tweak in main module to work) -1156 def __radd__(self, y): -1157 return self + y +1137 def log(self): +1138 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1139 return Corr(newcontent, prange=self.prange) +1140 +1141 def exp(self): +1142 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1143 return Corr(newcontent, prange=self.prange) +1144 +1145 def _apply_func_to_corr(self, func): +1146 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1147 for t in range(self.T): +1148 if _check_for_none(self, newcontent[t]): +1149 continue +1150 if np.isnan(np.sum(newcontent[t]).value): +1151 newcontent[t] = None +1152 if all([item is None for item in newcontent]): +1153 raise Exception('Operation returns undefined correlator') +1154 return Corr(newcontent) +1155 +1156 def sin(self): +1157 return self._apply_func_to_corr(np.sin) 1158 -1159 def __rsub__(self, y): -1160 return -self + y +1159 def cos(self): +1160 return self._apply_func_to_corr(np.cos) 1161 -1162 def __rmul__(self, y): -1163 return self * y +1162 def tan(self): +1163 return self._apply_func_to_corr(np.tan) 1164 -1165 def __rtruediv__(self, y): -1166 return (self / y) ** (-1) +1165 def sinh(self): +1166 return self._apply_func_to_corr(np.sinh) 1167 -1168 @property -1169 def real(self): -1170 def return_real(obs_OR_cobs): -1171 if isinstance(obs_OR_cobs, CObs): -1172 return obs_OR_cobs.real -1173 else: -1174 return obs_OR_cobs -1175 -1176 return self._apply_func_to_corr(return_real) -1177 -1178 @property -1179 def imag(self): -1180 def return_imag(obs_OR_cobs): -1181 if isinstance(obs_OR_cobs, CObs): -1182 return obs_OR_cobs.imag -1183 else: -1184 return obs_OR_cobs * 0 # So it stays the right type +1168 def cosh(self): +1169 return self._apply_func_to_corr(np.cosh) +1170 +1171 def tanh(self): +1172 return self._apply_func_to_corr(np.tanh) +1173 +1174 def arcsin(self): +1175 return self._apply_func_to_corr(np.arcsin) +1176 +1177 def arccos(self): +1178 return self._apply_func_to_corr(np.arccos) +1179 +1180 def arctan(self): +1181 return self._apply_func_to_corr(np.arctan) +1182 +1183 def arcsinh(self): +1184 return self._apply_func_to_corr(np.arcsinh) 1185 -1186 return self._apply_func_to_corr(return_imag) -1187 -1188 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1189 r''' Project large correlation matrix to lowest states -1190 -1191 This method can be used to reduce the size of an (N x N) correlation matrix -1192 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1193 is still small. -1194 -1195 Parameters -1196 ---------- -1197 Ntrunc: int -1198 Rank of the target matrix. -1199 tproj: int -1200 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1201 The default value is 3. -1202 t0proj: int -1203 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1204 discouraged for O(a) improved theories, since the correctness of the procedure -1205 cannot be granted in this case. The default value is 2. -1206 basematrix : Corr -1207 Correlation matrix that is used to determine the eigenvectors of the -1208 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1209 is is not specified. -1210 -1211 Notes -1212 ----- -1213 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1214 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1215 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1216 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1217 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1218 correlation matrix and to remove some noise that is added by irrelevant operators. -1219 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1220 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1221 ''' +1186 def arccosh(self): +1187 return self._apply_func_to_corr(np.arccosh) +1188 +1189 def arctanh(self): +1190 return self._apply_func_to_corr(np.arctanh) +1191 +1192 # Right hand side operations (require tweak in main module to work) +1193 def __radd__(self, y): +1194 return self + y +1195 +1196 def __rsub__(self, y): +1197 return -self + y +1198 +1199 def __rmul__(self, y): +1200 return self * y +1201 +1202 def __rtruediv__(self, y): +1203 return (self / y) ** (-1) +1204 +1205 @property +1206 def real(self): +1207 def return_real(obs_OR_cobs): +1208 if isinstance(obs_OR_cobs, CObs): +1209 return obs_OR_cobs.real +1210 else: +1211 return obs_OR_cobs +1212 +1213 return self._apply_func_to_corr(return_real) +1214 +1215 @property +1216 def imag(self): +1217 def return_imag(obs_OR_cobs): +1218 if isinstance(obs_OR_cobs, CObs): +1219 return obs_OR_cobs.imag +1220 else: +1221 return obs_OR_cobs * 0 # So it stays the right type 1222 -1223 if self.N == 1: -1224 raise Exception('Method cannot be applied to one-dimensional correlators.') -1225 if basematrix is None: -1226 basematrix = self -1227 if Ntrunc >= basematrix.N: -1228 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1229 if basematrix.N != self.N: -1230 raise Exception('basematrix and targetmatrix have to be of the same size.') +1223 return self._apply_func_to_corr(return_imag) +1224 +1225 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1226 r''' Project large correlation matrix to lowest states +1227 +1228 This method can be used to reduce the size of an (N x N) correlation matrix +1229 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1230 is still small. 1231 -1232 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1233 -1234 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1235 rmat = [] -1236 for t in range(basematrix.T): -1237 for i in range(Ntrunc): -1238 for j in range(Ntrunc): -1239 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1240 rmat.append(np.copy(tmpmat)) -1241 -1242 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1243 return Corr(newcontent) +1232 Parameters +1233 ---------- +1234 Ntrunc: int +1235 Rank of the target matrix. +1236 tproj: int +1237 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1238 The default value is 3. +1239 t0proj: int +1240 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1241 discouraged for O(a) improved theories, since the correctness of the procedure +1242 cannot be granted in this case. The default value is 2. +1243 basematrix : Corr +1244 Correlation matrix that is used to determine the eigenvectors of the +1245 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1246 is is not specified. +1247 +1248 Notes +1249 ----- +1250 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1251 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1252 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1253 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1254 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1255 correlation matrix and to remove some noise that is added by irrelevant operators. +1256 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1257 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1258 ''' +1259 +1260 if self.N == 1: +1261 raise Exception('Method cannot be applied to one-dimensional correlators.') +1262 if basematrix is None: +1263 basematrix = self +1264 if Ntrunc >= basematrix.N: +1265 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1266 if basematrix.N != self.N: +1267 raise Exception('basematrix and targetmatrix have to be of the same size.') +1268 +1269 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1270 +1271 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1272 rmat = [] +1273 for t in range(basematrix.T): +1274 for i in range(Ntrunc): +1275 for j in range(Ntrunc): +1276 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1277 rmat.append(np.copy(tmpmat)) +1278 +1279 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1280 return Corr(newcontent) @@ -3695,7 +3769,7 @@ Parity quantum number of the correlator, can be +1 or -1 524 ---------- 525 variant : str 526 decides which definition of the finite differences derivative is used. -527 Available choice: symmetric, forward, backward, improved, default: symmetric +527 Available choice: symmetric, forward, backward, improved, log, default: symmetric 528 """ 529 if self.N != 1: 530 raise Exception("deriv only implemented for one-dimensional correlators.") @@ -3739,8 +3813,19 @@ Parity quantum number of the correlator, can be +1 or -1 568 if (all([x is None for x in newcontent])): 569 raise Exception('Derivative is undefined at all timeslices') 570 return Corr(newcontent, padding=[2, 2]) -571 else: -572 raise Exception("Unknown variant.") +571 elif variant == 'log': +572 newcontent = [] +573 for t in range(self.T): +574 if (self.content[t] is None) or (self.content[t] <= 0): +575 newcontent.append(None) +576 else: +577 newcontent.append(np.log(self.content[t])) +578 if (all([x is None for x in newcontent])): +579 raise Exception("Log is undefined at all timeslices") +580 logcorr = Corr(newcontent) +581 return self * logcorr.deriv('symmetric') +582 else: +583 raise Exception("Unknown variant.") @@ -3751,7 +3836,7 @@ Parity quantum number of the correlator, can be +1 or -1 @@ -3768,39 +3853,50 @@ Available choice: symmetric, forward, backward, improved, default: symmetric - 
574    def second_deriv(self, variant="symmetric"):
-575        """Return the second derivative of the correlator with respect to x0.
-576
-577        Parameters
-578        ----------
-579        variant : str
-580            decides which definition of the finite differences derivative is used.
-581            Available choice: symmetric, improved, default: symmetric
-582        """
-583        if self.N != 1:
-584            raise Exception("second_deriv only implemented for one-dimensional correlators.")
-585        if variant == "symmetric":
-586            newcontent = []
-587            for t in range(1, self.T - 1):
-588                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-589                    newcontent.append(None)
-590                else:
-591                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
-592            if (all([x is None for x in newcontent])):
-593                raise Exception("Derivative is undefined at all timeslices")
-594            return Corr(newcontent, padding=[1, 1])
-595        elif variant == "improved":
-596            newcontent = []
-597            for t in range(2, self.T - 2):
-598                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
-599                    newcontent.append(None)
-600                else:
-601                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
-602            if (all([x is None for x in newcontent])):
-603                raise Exception("Derivative is undefined at all timeslices")
-604            return Corr(newcontent, padding=[2, 2])
-605        else:
-606            raise Exception("Unknown variant.")
+            
585    def second_deriv(self, variant="symmetric"):
+586        """Return the second derivative of the correlator with respect to x0.
+587
+588        Parameters
+589        ----------
+590        variant : str
+591            decides which definition of the finite differences derivative is used.
+592            Available choice: symmetric, improved, log, default: symmetric
+593        """
+594        if self.N != 1:
+595            raise Exception("second_deriv only implemented for one-dimensional correlators.")
+596        if variant == "symmetric":
+597            newcontent = []
+598            for t in range(1, self.T - 1):
+599                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+600                    newcontent.append(None)
+601                else:
+602                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
+603            if (all([x is None for x in newcontent])):
+604                raise Exception("Derivative is undefined at all timeslices")
+605            return Corr(newcontent, padding=[1, 1])
+606        elif variant == "improved":
+607            newcontent = []
+608            for t in range(2, self.T - 2):
+609                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+610                    newcontent.append(None)
+611                else:
+612                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
+613            if (all([x is None for x in newcontent])):
+614                raise Exception("Derivative is undefined at all timeslices")
+615            return Corr(newcontent, padding=[2, 2])
+616        elif variant == 'log':
+617            newcontent = []
+618            for t in range(self.T):
+619                if (self.content[t] is None) or (self.content[t] <= 0):
+620                    newcontent.append(None)
+621                else:
+622                    newcontent.append(np.log(self.content[t]))
+623            if (all([x is None for x in newcontent])):
+624                raise Exception("Log is undefined at all timeslices")
+625            logcorr = Corr(newcontent)
+626            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
+627        else:
+628            raise Exception("Unknown variant.")
 

 
 
@@ -3811,7 +3907,7 @@ Available choice: symmetric, forward, backward, improved, default: symmetric
 
  • variant (str):
 decides which definition of the finite differences derivative is used.
-Available choice: symmetric, improved, default: symmetric
    • 
+Available choice: symmetric, improved, log, default: symmetric
    @@ -3828,74 +3924,89 @@ Available choice: symmetric, improved, default: symmetric - 
    608    def m_eff(self, variant='log', guess=1.0):
-609        """Returns the effective mass of the correlator as correlator object
-610
-611        Parameters
-612        ----------
-613        variant : str
-614            log : uses the standard effective mass log(C(t) / C(t+1))
-615            cosh, 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.
-616            sinh : 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.
-617            See, e.g., arXiv:1205.5380
-618            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
-619        guess : float
-620            guess for the root finder, only relevant for the root variant
-621        """
-622        if self.N != 1:
-623            raise Exception('Correlator must be projected before getting m_eff')
-624        if variant == 'log':
-625            newcontent = []
-626            for t in range(self.T - 1):
-627                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-628                    newcontent.append(None)
-629                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-630                    newcontent.append(None)
-631                else:
-632                    newcontent.append(self.content[t] / self.content[t + 1])
-633            if (all([x is None for x in newcontent])):
-634                raise Exception('m_eff is undefined at all timeslices')
-635
-636            return np.log(Corr(newcontent, padding=[0, 1]))
-637
-638        elif variant in ['periodic', 'cosh', 'sinh']:
-639            if variant in ['periodic', 'cosh']:
-640                func = anp.cosh
-641            else:
-642                func = anp.sinh
-643
-644            def root_function(x, d):
-645                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
-646
-647            newcontent = []
-648            for t in range(self.T - 1):
-649                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
-650                    newcontent.append(None)
-651                # Fill the two timeslices in the middle of the lattice with their predecessors
-652                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
-653                    newcontent.append(newcontent[-1])
-654                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-655                    newcontent.append(None)
-656                else:
-657                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
-658            if (all([x is None for x in newcontent])):
-659                raise Exception('m_eff is undefined at all timeslices')
+            
    630    def m_eff(self, variant='log', guess=1.0):
+631        """Returns the effective mass of the correlator as correlator object
+632
+633        Parameters
+634        ----------
+635        variant : str
+636            log : uses the standard effective mass log(C(t) / C(t+1))
+637            cosh, 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.
+638            sinh : 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.
+639            See, e.g., arXiv:1205.5380
+640            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+641            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
+642        guess : float
+643            guess for the root finder, only relevant for the root variant
+644        """
+645        if self.N != 1:
+646            raise Exception('Correlator must be projected before getting m_eff')
+647        if variant == 'log':
+648            newcontent = []
+649            for t in range(self.T - 1):
+650                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+651                    newcontent.append(None)
+652                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+653                    newcontent.append(None)
+654                else:
+655                    newcontent.append(self.content[t] / self.content[t + 1])
+656            if (all([x is None for x in newcontent])):
+657                raise Exception('m_eff is undefined at all timeslices')
+658
+659            return np.log(Corr(newcontent, padding=[0, 1]))
 660
-661            return Corr(newcontent, padding=[0, 1])
-662
-663        elif variant == 'arccosh':
-664            newcontent = []
-665            for t in range(1, self.T - 1):
-666                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0):
+661        elif variant == 'logsym':
+662            newcontent = []
+663            for t in range(1, self.T - 1):
+664                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+665                    newcontent.append(None)
+666                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
 667                    newcontent.append(None)
 668                else:
-669                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+669                    newcontent.append(self.content[t - 1] / self.content[t + 1])
 670            if (all([x is None for x in newcontent])):
-671                raise Exception("m_eff is undefined at all timeslices")
-672            return np.arccosh(Corr(newcontent, padding=[1, 1]))
-673
-674        else:
-675            raise Exception('Unknown variant.')
+671                raise Exception('m_eff is undefined at all timeslices')
+672
+673            return np.log(Corr(newcontent, padding=[1, 1])) / 2
+674
+675        elif variant in ['periodic', 'cosh', 'sinh']:
+676            if variant in ['periodic', 'cosh']:
+677                func = anp.cosh
+678            else:
+679                func = anp.sinh
+680
+681            def root_function(x, d):
+682                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
+683
+684            newcontent = []
+685            for t in range(self.T - 1):
+686                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+687                    newcontent.append(None)
+688                # Fill the two timeslices in the middle of the lattice with their predecessors
+689                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
+690                    newcontent.append(newcontent[-1])
+691                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+692                    newcontent.append(None)
+693                else:
+694                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
+695            if (all([x is None for x in newcontent])):
+696                raise Exception('m_eff is undefined at all timeslices')
+697
+698            return Corr(newcontent, padding=[0, 1])
+699
+700        elif variant == 'arccosh':
+701            newcontent = []
+702            for t in range(1, self.T - 1):
+703                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0):
+704                    newcontent.append(None)
+705                else:
+706                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+707            if (all([x is None for x in newcontent])):
+708                raise Exception("m_eff is undefined at all timeslices")
+709            return np.arccosh(Corr(newcontent, padding=[1, 1]))
+710
+711        else:
+712            raise Exception('Unknown variant.')
 
    
 
 
@@ -3909,7 +4020,8 @@ log : uses the standard effective mass log(C(t) / C(t+1))
 cosh, 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.
 sinh : 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.
 See, e.g., arXiv:1205.5380
-arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
 
  • guess (float):
 guess for the root finder, only relevant for the root variant
    • 
 
@@ -3928,39 +4040,39 @@ guess for the root finder, only relevant for the root variant
    - 
    677    def fit(self, function, fitrange=None, silent=False, **kwargs):
-678        r'''Fits function to the data
-679
-680        Parameters
-681        ----------
-682        function : obj
-683            function to fit to the data. See fits.least_squares for details.
-684        fitrange : list
-685            Two element list containing the timeslices on which the fit is supposed to start and stop.
-686            Caution: This range is inclusive as opposed to standard python indexing.
-687            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
-688            If not specified, self.prange or all timeslices are used.
-689        silent : bool
-690            Decides whether output is printed to the standard output.
-691        '''
-692        if self.N != 1:
-693            raise Exception("Correlator must be projected before fitting")
-694
-695        if fitrange is None:
-696            if self.prange:
-697                fitrange = self.prange
-698            else:
-699                fitrange = [0, self.T - 1]
-700        else:
-701            if not isinstance(fitrange, list):
-702                raise Exception("fitrange has to be a list with two elements")
-703            if len(fitrange) != 2:
-704                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
-705
-706        xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
-707        ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
-708        result = least_squares(xs, ys, function, silent=silent, **kwargs)
-709        return result
+            
    714    def fit(self, function, fitrange=None, silent=False, **kwargs):
+715        r'''Fits function to the data
+716
+717        Parameters
+718        ----------
+719        function : obj
+720            function to fit to the data. See fits.least_squares for details.
+721        fitrange : list
+722            Two element list containing the timeslices on which the fit is supposed to start and stop.
+723            Caution: This range is inclusive as opposed to standard python indexing.
+724            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
+725            If not specified, self.prange or all timeslices are used.
+726        silent : bool
+727            Decides whether output is printed to the standard output.
+728        '''
+729        if self.N != 1:
+730            raise Exception("Correlator must be projected before fitting")
+731
+732        if fitrange is None:
+733            if self.prange:
+734                fitrange = self.prange
+735            else:
+736                fitrange = [0, self.T - 1]
+737        else:
+738            if not isinstance(fitrange, list):
+739                raise Exception("fitrange has to be a list with two elements")
+740            if len(fitrange) != 2:
+741                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
+742
+743        xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
+744        ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
+745        result = least_squares(xs, ys, function, silent=silent, **kwargs)
+746        return result
 
    
 
 
@@ -3994,42 +4106,42 @@ Decides whether output is printed to the standard output.
    - 
    711    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
-712        """ Extract a plateau value from a Corr object
-713
-714        Parameters
-715        ----------
-716        plateau_range : list
-717            list with two entries, indicating the first and the last timeslice
-718            of the plateau region.
-719        method : str
-720            method to extract the plateau.
-721                'fit' fits a constant to the plateau region
-722                'avg', 'average' or 'mean' just average over the given timeslices.
-723        auto_gamma : bool
-724            apply gamma_method with default parameters to the Corr. Defaults to None
-725        """
-726        if not plateau_range:
-727            if self.prange:
-728                plateau_range = self.prange
-729            else:
-730                raise Exception("no plateau range provided")
-731        if self.N != 1:
-732            raise Exception("Correlator must be projected before getting a plateau.")
-733        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
-734            raise Exception("plateau is undefined at all timeslices in plateaurange.")
-735        if auto_gamma:
-736            self.gamma_method()
-737        if method == "fit":
-738            def const_func(a, t):
-739                return a[0]
-740            return self.fit(const_func, plateau_range)[0]
-741        elif method in ["avg", "average", "mean"]:
-742            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
-743            return returnvalue
-744
-745        else:
-746            raise Exception("Unsupported plateau method: " + method)
+            
    748    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+749        """ Extract a plateau value from a Corr object
+750
+751        Parameters
+752        ----------
+753        plateau_range : list
+754            list with two entries, indicating the first and the last timeslice
+755            of the plateau region.
+756        method : str
+757            method to extract the plateau.
+758                'fit' fits a constant to the plateau region
+759                'avg', 'average' or 'mean' just average over the given timeslices.
+760        auto_gamma : bool
+761            apply gamma_method with default parameters to the Corr. Defaults to None
+762        """
+763        if not plateau_range:
+764            if self.prange:
+765                plateau_range = self.prange
+766            else:
+767                raise Exception("no plateau range provided")
+768        if self.N != 1:
+769            raise Exception("Correlator must be projected before getting a plateau.")
+770        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
+771            raise Exception("plateau is undefined at all timeslices in plateaurange.")
+772        if auto_gamma:
+773            self.gamma_method()
+774        if method == "fit":
+775            def const_func(a, t):
+776                return a[0]
+777            return self.fit(const_func, plateau_range)[0]
+778        elif method in ["avg", "average", "mean"]:
+779            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
+780            return returnvalue
+781
+782        else:
+783            raise Exception("Unsupported plateau method: " + method)
 
    
 
 
@@ -4063,17 +4175,17 @@ apply gamma_method with default parameters to the Corr. Defaults to None
    - 
    748    def set_prange(self, prange):
-749        """Sets the attribute prange of the Corr object."""
-750        if not len(prange) == 2:
-751            raise Exception("prange must be a list or array with two values")
-752        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
-753            raise Exception("Start and end point must be integers")
-754        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
-755            raise Exception("Start and end point must define a range in the interval 0,T")
-756
-757        self.prange = prange
-758        return
+            
    785    def set_prange(self, prange):
+786        """Sets the attribute prange of the Corr object."""
+787        if not len(prange) == 2:
+788            raise Exception("prange must be a list or array with two values")
+789        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
+790            raise Exception("Start and end point must be integers")
+791        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
+792            raise Exception("Start and end point must define a range in the interval 0,T")
+793
+794        self.prange = prange
+795        return
 
    
 
 
@@ -4093,124 +4205,124 @@ apply gamma_method with default parameters to the Corr. Defaults to None
    - 
    760    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):
-761        """Plots the correlator using the tag of the correlator as label if available.
-762
-763        Parameters
-764        ----------
-765        x_range : list
-766            list of two values, determining the range of the x-axis e.g. [4, 8].
-767        comp : Corr or list of Corr
-768            Correlator or list of correlators which are plotted for comparison.
-769            The tags of these correlators are used as labels if available.
-770        logscale : bool
-771            Sets y-axis to logscale.
-772        plateau : Obs
-773            Plateau value to be visualized in the figure.
-774        fit_res : Fit_result
-775            Fit_result object to be visualized.
-776        ylabel : str
-777            Label for the y-axis.
-778        save : str
-779            path to file in which the figure should be saved.
-780        auto_gamma : bool
-781            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
-782        hide_sigma : float
-783            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
-784        references : list
-785            List of floating point values that are displayed as horizontal lines for reference.
-786        title : string
-787            Optional title of the figure.
-788        """
-789        if self.N != 1:
-790            raise Exception("Correlator must be projected before plotting")
-791
-792        if auto_gamma:
-793            self.gamma_method()
-794
-795        if x_range is None:
-796            x_range = [0, self.T - 1]
-797
-798        fig = plt.figure()
-799        ax1 = fig.add_subplot(111)
-800
-801        x, y, y_err = self.plottable()
-802        if hide_sigma:
-803            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-804        else:
-805            hide_from = None
-806        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
-807        if logscale:
-808            ax1.set_yscale('log')
-809        else:
-810            if y_range is None:
-811                try:
-812                    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)])
-813                    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)])
-814                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
-815                except Exception:
-816                    pass
-817            else:
-818                ax1.set_ylim(y_range)
-819        if comp:
-820            if isinstance(comp, (Corr, list)):
-821                for corr in comp if isinstance(comp, list) else [comp]:
-822                    if auto_gamma:
-823                        corr.gamma_method()
-824                    x, y, y_err = corr.plottable()
-825                    if hide_sigma:
-826                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-827                    else:
-828                        hide_from = None
-829                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
-830            else:
-831                raise Exception("'comp' must be a correlator or a list of correlators.")
-832
-833        if plateau:
-834            if isinstance(plateau, Obs):
-835                if auto_gamma:
-836                    plateau.gamma_method()
-837                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
-838                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
-839            else:
-840                raise Exception("'plateau' must be an Obs")
-841
-842        if references:
-843            if isinstance(references, list):
-844                for ref in references:
-845                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
-846            else:
-847                raise Exception("'references' must be a list of floating pint values.")
-848
-849        if self.prange:
-850            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
-851            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
-852
-853        if fit_res:
-854            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
-855            ax1.plot(x_samples,
-856                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
-857                     ls='-', marker=',', lw=2)
-858
-859        ax1.set_xlabel(r'$x_0 / a$')
-860        if ylabel:
-861            ax1.set_ylabel(ylabel)
-862        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
-863
-864        handles, labels = ax1.get_legend_handles_labels()
-865        if labels:
-866            ax1.legend()
-867
-868        if title:
-869            plt.title(title)
-870
-871        plt.draw()
-872
-873        if save:
-874            if isinstance(save, str):
-875                fig.savefig(save, bbox_inches='tight')
+            
    797    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):
+798        """Plots the correlator using the tag of the correlator as label if available.
+799
+800        Parameters
+801        ----------
+802        x_range : list
+803            list of two values, determining the range of the x-axis e.g. [4, 8].
+804        comp : Corr or list of Corr
+805            Correlator or list of correlators which are plotted for comparison.
+806            The tags of these correlators are used as labels if available.
+807        logscale : bool
+808            Sets y-axis to logscale.
+809        plateau : Obs
+810            Plateau value to be visualized in the figure.
+811        fit_res : Fit_result
+812            Fit_result object to be visualized.
+813        ylabel : str
+814            Label for the y-axis.
+815        save : str
+816            path to file in which the figure should be saved.
+817        auto_gamma : bool
+818            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
+819        hide_sigma : float
+820            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
+821        references : list
+822            List of floating point values that are displayed as horizontal lines for reference.
+823        title : string
+824            Optional title of the figure.
+825        """
+826        if self.N != 1:
+827            raise Exception("Correlator must be projected before plotting")
+828
+829        if auto_gamma:
+830            self.gamma_method()
+831
+832        if x_range is None:
+833            x_range = [0, self.T - 1]
+834
+835        fig = plt.figure()
+836        ax1 = fig.add_subplot(111)
+837
+838        x, y, y_err = self.plottable()
+839        if hide_sigma:
+840            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+841        else:
+842            hide_from = None
+843        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
+844        if logscale:
+845            ax1.set_yscale('log')
+846        else:
+847            if y_range is None:
+848                try:
+849                    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)])
+850                    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)])
+851                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
+852                except Exception:
+853                    pass
+854            else:
+855                ax1.set_ylim(y_range)
+856        if comp:
+857            if isinstance(comp, (Corr, list)):
+858                for corr in comp if isinstance(comp, list) else [comp]:
+859                    if auto_gamma:
+860                        corr.gamma_method()
+861                    x, y, y_err = corr.plottable()
+862                    if hide_sigma:
+863                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+864                    else:
+865                        hide_from = None
+866                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
+867            else:
+868                raise Exception("'comp' must be a correlator or a list of correlators.")
+869
+870        if plateau:
+871            if isinstance(plateau, Obs):
+872                if auto_gamma:
+873                    plateau.gamma_method()
+874                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
+875                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
 876            else:
-877                raise Exception("'save' has to be a string.")
+877                raise Exception("'plateau' must be an Obs")
+878
+879        if references:
+880            if isinstance(references, list):
+881                for ref in references:
+882                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
+883            else:
+884                raise Exception("'references' must be a list of floating pint values.")
+885
+886        if self.prange:
+887            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
+888            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
+889
+890        if fit_res:
+891            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
+892            ax1.plot(x_samples,
+893                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
+894                     ls='-', marker=',', lw=2)
+895
+896        ax1.set_xlabel(r'$x_0 / a$')
+897        if ylabel:
+898            ax1.set_ylabel(ylabel)
+899        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
+900
+901        handles, labels = ax1.get_legend_handles_labels()
+902        if labels:
+903            ax1.legend()
+904
+905        if title:
+906            plt.title(title)
+907
+908        plt.draw()
+909
+910        if save:
+911            if isinstance(save, str):
+912                fig.savefig(save, bbox_inches='tight')
+913            else:
+914                raise Exception("'save' has to be a string.")
 
    
 
 
@@ -4258,34 +4370,34 @@ Optional title of the figure.
    - 
    879    def spaghetti_plot(self, logscale=True):
-880        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-881
-882        Parameters
-883        ----------
-884        logscale : bool
-885            Determines whether the scale of the y-axis is logarithmic or standard.
-886        """
-887        if self.N != 1:
-888            raise Exception("Correlator needs to be projected first.")
-889
-890        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]))
-891        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
-892
-893        for name in mc_names:
-894            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
-895
-896            fig = plt.figure()
-897            ax = fig.add_subplot(111)
-898            for dat in data:
-899                ax.plot(x0_vals, dat, ls='-', marker='')
-900
-901            if logscale is True:
-902                ax.set_yscale('log')
-903
-904            ax.set_xlabel(r'$x_0 / a$')
-905            plt.title(name)
-906            plt.draw()
+            
    916    def spaghetti_plot(self, logscale=True):
+917        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+918
+919        Parameters
+920        ----------
+921        logscale : bool
+922            Determines whether the scale of the y-axis is logarithmic or standard.
+923        """
+924        if self.N != 1:
+925            raise Exception("Correlator needs to be projected first.")
+926
+927        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]))
+928        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+929
+930        for name in mc_names:
+931            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+932
+933            fig = plt.figure()
+934            ax = fig.add_subplot(111)
+935            for dat in data:
+936                ax.plot(x0_vals, dat, ls='-', marker='')
+937
+938            if logscale is True:
+939                ax.set_yscale('log')
+940
+941            ax.set_xlabel(r'$x_0 / a$')
+942            plt.title(name)
+943            plt.draw()
 
    
 
 
@@ -4312,29 +4424,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.
    - 
    908    def dump(self, filename, datatype="json.gz", **kwargs):
-909        """Dumps the Corr into a file of chosen type
-910        Parameters
-911        ----------
-912        filename : str
-913            Name of the file to be saved.
-914        datatype : str
-915            Format of the exported file. Supported formats include
-916            "json.gz" and "pickle"
-917        path : str
-918            specifies a custom path for the file (default '.')
-919        """
-920        if datatype == "json.gz":
-921            from .input.json import dump_to_json
-922            if 'path' in kwargs:
-923                file_name = kwargs.get('path') + '/' + filename
-924            else:
-925                file_name = filename
-926            dump_to_json(self, file_name)
-927        elif datatype == "pickle":
-928            dump_object(self, filename, **kwargs)
-929        else:
-930            raise Exception("Unknown datatype " + str(datatype))
+            
    945    def dump(self, filename, datatype="json.gz", **kwargs):
+946        """Dumps the Corr into a file of chosen type
+947        Parameters
+948        ----------
+949        filename : str
+950            Name of the file to be saved.
+951        datatype : str
+952            Format of the exported file. Supported formats include
+953            "json.gz" and "pickle"
+954        path : str
+955            specifies a custom path for the file (default '.')
+956        """
+957        if datatype == "json.gz":
+958            from .input.json import dump_to_json
+959            if 'path' in kwargs:
+960                file_name = kwargs.get('path') + '/' + filename
+961            else:
+962                file_name = filename
+963            dump_to_json(self, file_name)
+964        elif datatype == "pickle":
+965            dump_object(self, filename, **kwargs)
+966        else:
+967            raise Exception("Unknown datatype " + str(datatype))
 
    
 
 
@@ -4366,8 +4478,8 @@ specifies a custom path for the file (default '.')
    - 
    932    def print(self, print_range=None):
-933        print(self.__repr__(print_range))
+            
    969    def print(self, print_range=None):
+970        print(self.__repr__(print_range))
 
    
 
 
@@ -4385,8 +4497,8 @@ specifies a custom path for the file (default '.')
    - 
    1097    def sqrt(self):
-1098        return self ** 0.5
+            
    1134    def sqrt(self):
+1135        return self ** 0.5
 
    
 
 
@@ -4404,9 +4516,9 @@ specifies a custom path for the file (default '.')
    - 
    1100    def log(self):
-1101        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1102        return Corr(newcontent, prange=self.prange)
+            
    1137    def log(self):
+1138        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1139        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4424,9 +4536,9 @@ specifies a custom path for the file (default '.')
    - 
    1104    def exp(self):
-1105        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1106        return Corr(newcontent, prange=self.prange)
+            
    1141    def exp(self):
+1142        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1143        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4444,8 +4556,8 @@ specifies a custom path for the file (default '.')
    - 
    1119    def sin(self):
-1120        return self._apply_func_to_corr(np.sin)
+            
    1156    def sin(self):
+1157        return self._apply_func_to_corr(np.sin)
 
    
 
 
@@ -4463,8 +4575,8 @@ specifies a custom path for the file (default '.')
    - 
    1122    def cos(self):
-1123        return self._apply_func_to_corr(np.cos)
+            
    1159    def cos(self):
+1160        return self._apply_func_to_corr(np.cos)
 
    
 
 
@@ -4482,8 +4594,8 @@ specifies a custom path for the file (default '.')
    - 
    1125    def tan(self):
-1126        return self._apply_func_to_corr(np.tan)
+            
    1162    def tan(self):
+1163        return self._apply_func_to_corr(np.tan)
 
    
 
 
@@ -4501,8 +4613,8 @@ specifies a custom path for the file (default '.')
    - 
    1128    def sinh(self):
-1129        return self._apply_func_to_corr(np.sinh)
+            
    1165    def sinh(self):
+1166        return self._apply_func_to_corr(np.sinh)
 
    
 
 
@@ -4520,8 +4632,8 @@ specifies a custom path for the file (default '.')
    - 
    1131    def cosh(self):
-1132        return self._apply_func_to_corr(np.cosh)
+            
    1168    def cosh(self):
+1169        return self._apply_func_to_corr(np.cosh)
 
    
 
 
@@ -4539,8 +4651,8 @@ specifies a custom path for the file (default '.')
    - 
    1134    def tanh(self):
-1135        return self._apply_func_to_corr(np.tanh)
+            
    1171    def tanh(self):
+1172        return self._apply_func_to_corr(np.tanh)
 
    
 
 
@@ -4558,8 +4670,8 @@ specifies a custom path for the file (default '.')
    - 
    1137    def arcsin(self):
-1138        return self._apply_func_to_corr(np.arcsin)
+            
    1174    def arcsin(self):
+1175        return self._apply_func_to_corr(np.arcsin)
 
    
 
 
@@ -4577,8 +4689,8 @@ specifies a custom path for the file (default '.')
    - 
    1140    def arccos(self):
-1141        return self._apply_func_to_corr(np.arccos)
+            
    1177    def arccos(self):
+1178        return self._apply_func_to_corr(np.arccos)
 
    
 
 
@@ -4596,8 +4708,8 @@ specifies a custom path for the file (default '.')
    - 
    1143    def arctan(self):
-1144        return self._apply_func_to_corr(np.arctan)
+            
    1180    def arctan(self):
+1181        return self._apply_func_to_corr(np.arctan)
 
    
 
 
@@ -4615,8 +4727,8 @@ specifies a custom path for the file (default '.')
    - 
    1146    def arcsinh(self):
-1147        return self._apply_func_to_corr(np.arcsinh)
+            
    1183    def arcsinh(self):
+1184        return self._apply_func_to_corr(np.arcsinh)
 
    
 
 
@@ -4634,8 +4746,8 @@ specifies a custom path for the file (default '.')
    - 
    1149    def arccosh(self):
-1150        return self._apply_func_to_corr(np.arccosh)
+            
    1186    def arccosh(self):
+1187        return self._apply_func_to_corr(np.arccosh)
 
    
 
 
@@ -4653,8 +4765,8 @@ specifies a custom path for the file (default '.')
    - 
    1152    def arctanh(self):
-1153        return self._apply_func_to_corr(np.arctanh)
+            
    1189    def arctanh(self):
+1190        return self._apply_func_to_corr(np.arctanh)
 
    
 
 
@@ -4672,62 +4784,62 @@ specifies a custom path for the file (default '.')
    - 
    1188    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1189        r''' Project large correlation matrix to lowest states
-1190
-1191        This method can be used to reduce the size of an (N x N) correlation matrix
-1192        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1193        is still small.
-1194
-1195        Parameters
-1196        ----------
-1197        Ntrunc: int
-1198            Rank of the target matrix.
-1199        tproj: int
-1200            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1201            The default value is 3.
-1202        t0proj: int
-1203            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1204            discouraged for O(a) improved theories, since the correctness of the procedure
-1205            cannot be granted in this case. The default value is 2.
-1206        basematrix : Corr
-1207            Correlation matrix that is used to determine the eigenvectors of the
-1208            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1209            is is not specified.
-1210
-1211        Notes
-1212        -----
-1213        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1214        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1215        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1216        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1217        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1218        correlation matrix and to remove some noise that is added by irrelevant operators.
-1219        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1220        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1221        '''
-1222
-1223        if self.N == 1:
-1224            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1225        if basematrix is None:
-1226            basematrix = self
-1227        if Ntrunc >= basematrix.N:
-1228            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1229        if basematrix.N != self.N:
-1230            raise Exception('basematrix and targetmatrix have to be of the same size.')
+            
    1225    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1226        r''' Project large correlation matrix to lowest states
+1227
+1228        This method can be used to reduce the size of an (N x N) correlation matrix
+1229        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1230        is still small.
 1231
-1232        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1233
-1234        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1235        rmat = []
-1236        for t in range(basematrix.T):
-1237            for i in range(Ntrunc):
-1238                for j in range(Ntrunc):
-1239                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1240            rmat.append(np.copy(tmpmat))
-1241
-1242        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1243        return Corr(newcontent)
+1232        Parameters
+1233        ----------
+1234        Ntrunc: int
+1235            Rank of the target matrix.
+1236        tproj: int
+1237            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1238            The default value is 3.
+1239        t0proj: int
+1240            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1241            discouraged for O(a) improved theories, since the correctness of the procedure
+1242            cannot be granted in this case. The default value is 2.
+1243        basematrix : Corr
+1244            Correlation matrix that is used to determine the eigenvectors of the
+1245            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1246            is is not specified.
+1247
+1248        Notes
+1249        -----
+1250        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1251        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1252        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1253        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1254        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1255        correlation matrix and to remove some noise that is added by irrelevant operators.
+1256        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1257        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1258        '''
+1259
+1260        if self.N == 1:
+1261            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1262        if basematrix is None:
+1263            basematrix = self
+1264        if Ntrunc >= basematrix.N:
+1265            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1266        if basematrix.N != self.N:
+1267            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1268
+1269        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1270
+1271        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1272        rmat = []
+1273        for t in range(basematrix.T):
+1274            for i in range(Ntrunc):
+1275                for j in range(Ntrunc):
+1276                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1277            rmat.append(np.copy(tmpmat))
+1278
+1279        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1280        return Corr(newcontent)
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index f27433b0..350dfde0 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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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. [arXiv:2209.14371 [hep-lat]].
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \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 difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "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": "(data_input, padding=[0, 0], prange=None)"}, "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.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "type": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \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
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \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": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "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.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": "(mean, cov, name, pos=None, grad=None)"}, "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.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": "()"}, "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
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • 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
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (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
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "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": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "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": "(\tfname,\tnoempty=False,\tfull_output=False,\tgz=True,\tseparator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "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": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "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": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "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
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()"}, "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 /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • 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.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "type": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "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 /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "type": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "type": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "type": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "type": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "type": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "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": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\t**kwargs):", "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": "(samples, names, idl=None, **kwargs)"}, "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.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "type": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "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.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": "(real, imag=0.0)"}, "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. Default False.
      • \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:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • 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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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "type": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. [arXiv:2209.14371 [hep-lat]].
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \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 difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "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": "(data_input, padding=[0, 0], prange=None)"}, "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.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "type": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \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
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \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, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "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, log, 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)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "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": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "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.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": "(mean, cov, name, pos=None, grad=None)"}, "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.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": "()"}, "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
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • 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
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (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
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "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": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "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": "(\tfname,\tnoempty=False,\tfull_output=False,\tgz=True,\tseparator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "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": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "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": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "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
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()"}, "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 /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • 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.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "type": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "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 /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "type": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "type": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "type": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "type": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "type": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "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": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\t**kwargs):", "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": "(samples, names, idl=None, **kwargs)"}, "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.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "type": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "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.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": "(real, imag=0.0)"}, "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. Default False.
      • \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:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • 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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