diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html index 0f8c1039..9e5b2239 100644 --- a/docs/pyerrors/obs.html +++ b/docs/pyerrors/obs.html @@ -882,1000 +882,1008 @@ 570 plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})') 571 plt.draw() 572 - 573 def plot_piechart(self): + 573 def plot_piechart(self, save=None): 574 """Plot piechart which shows the fractional contribution of each - 575 ensemble to the error and returns a dictionary containing the fractions.""" - 576 if not hasattr(self, 'e_dvalue'): - 577 raise Exception('Run the gamma method first.') - 578 if np.isclose(0.0, self._dvalue, atol=1e-15): - 579 raise Exception('Error is 0.0') - 580 labels = self.e_names - 581 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 - 582 fig1, ax1 = plt.subplots() - 583 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) - 584 ax1.axis('equal') - 585 plt.draw() - 586 - 587 return dict(zip(self.e_names, sizes)) - 588 - 589 def dump(self, filename, datatype="json.gz", description="", **kwargs): - 590 """Dump the Obs to a file 'name' of chosen format. - 591 - 592 Parameters - 593 ---------- - 594 filename : str - 595 name of the file to be saved. - 596 datatype : str - 597 Format of the exported file. Supported formats include - 598 "json.gz" and "pickle" - 599 description : str - 600 Description for output file, only relevant for json.gz format. - 601 path : str - 602 specifies a custom path for the file (default '.') - 603 """ - 604 if 'path' in kwargs: - 605 file_name = kwargs.get('path') + '/' + filename - 606 else: - 607 file_name = filename - 608 - 609 if datatype == "json.gz": - 610 from .input.json import dump_to_json - 611 dump_to_json([self], file_name, description=description) - 612 elif datatype == "pickle": - 613 with open(file_name + '.p', 'wb') as fb: - 614 pickle.dump(self, fb) - 615 else: - 616 raise Exception("Unknown datatype " + str(datatype)) - 617 - 618 def export_jackknife(self): - 619 """Export jackknife samples from the Obs - 620 - 621 Returns - 622 ------- - 623 numpy.ndarray - 624 Returns a numpy array of length N + 1 where N is the number of samples - 625 for the given ensemble and replicum. The zeroth entry of the array contains - 626 the mean value of the Obs, entries 1 to N contain the N jackknife samples - 627 derived from the Obs. The current implementation only works for observables - 628 defined on exactly one ensemble and replicum. The derived jackknife samples - 629 should agree with samples from a full jackknife analysis up to O(1/N). - 630 """ - 631 - 632 if len(self.names) != 1: - 633 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") - 634 - 635 name = self.names[0] - 636 full_data = self.deltas[name] + self.r_values[name] - 637 n = full_data.size - 638 mean = self.value - 639 tmp_jacks = np.zeros(n + 1) - 640 tmp_jacks[0] = mean - 641 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) - 642 return tmp_jacks - 643 - 644 def __float__(self): - 645 return float(self.value) - 646 - 647 def __repr__(self): - 648 return 'Obs[' + str(self) + ']' - 649 - 650 def __str__(self): - 651 if self._dvalue == 0.0: - 652 return str(self.value) - 653 fexp = np.floor(np.log10(self._dvalue)) - 654 if fexp < 0.0: - 655 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') - 656 elif fexp == 0.0: - 657 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) - 658 else: - 659 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) - 660 - 661 # Overload comparisons - 662 def __lt__(self, other): - 663 return self.value < other - 664 - 665 def __le__(self, other): - 666 return self.value <= other - 667 - 668 def __gt__(self, other): - 669 return self.value > other - 670 - 671 def __ge__(self, other): - 672 return self.value >= other - 673 - 674 def __eq__(self, other): - 675 return (self - other).is_zero() - 676 - 677 def __ne__(self, other): - 678 return not (self - other).is_zero() - 679 - 680 # Overload math operations - 681 def __add__(self, y): - 682 if isinstance(y, Obs): - 683 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) - 684 else: - 685 if isinstance(y, np.ndarray): - 686 return np.array([self + o for o in y]) - 687 elif y.__class__.__name__ in ['Corr', 'CObs']: - 688 return NotImplemented - 689 else: - 690 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) - 691 - 692 def __radd__(self, y): - 693 return self + y - 694 - 695 def __mul__(self, y): - 696 if isinstance(y, Obs): - 697 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) - 698 else: - 699 if isinstance(y, np.ndarray): - 700 return np.array([self * o for o in y]) - 701 elif isinstance(y, complex): - 702 return CObs(self * y.real, self * y.imag) - 703 elif y.__class__.__name__ in ['Corr', 'CObs']: - 704 return NotImplemented - 705 else: - 706 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) - 707 - 708 def __rmul__(self, y): - 709 return self * y - 710 - 711 def __sub__(self, y): - 712 if isinstance(y, Obs): - 713 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) - 714 else: - 715 if isinstance(y, np.ndarray): - 716 return np.array([self - o for o in y]) - 717 elif y.__class__.__name__ in ['Corr', 'CObs']: - 718 return NotImplemented - 719 else: - 720 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) - 721 - 722 def __rsub__(self, y): - 723 return -1 * (self - y) - 724 - 725 def __pos__(self): - 726 return self - 727 - 728 def __neg__(self): - 729 return -1 * self - 730 - 731 def __truediv__(self, y): - 732 if isinstance(y, Obs): - 733 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) - 734 else: - 735 if isinstance(y, np.ndarray): - 736 return np.array([self / o for o in y]) - 737 elif y.__class__.__name__ in ['Corr', 'CObs']: - 738 return NotImplemented - 739 else: - 740 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) - 741 - 742 def __rtruediv__(self, y): - 743 if isinstance(y, Obs): - 744 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) - 745 else: - 746 if isinstance(y, np.ndarray): - 747 return np.array([o / self for o in y]) - 748 elif y.__class__.__name__ in ['Corr', 'CObs']: - 749 return NotImplemented - 750 else: - 751 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) - 752 - 753 def __pow__(self, y): - 754 if isinstance(y, Obs): - 755 return derived_observable(lambda x: x[0] ** x[1], [self, y]) - 756 else: - 757 return derived_observable(lambda x: x[0] ** y, [self]) - 758 - 759 def __rpow__(self, y): - 760 if isinstance(y, Obs): - 761 return derived_observable(lambda x: x[0] ** x[1], [y, self]) - 762 else: - 763 return derived_observable(lambda x: y ** x[0], [self]) - 764 - 765 def __abs__(self): - 766 return derived_observable(lambda x: anp.abs(x[0]), [self]) - 767 - 768 # Overload numpy functions - 769 def sqrt(self): - 770 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) - 771 - 772 def log(self): - 773 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) - 774 - 775 def exp(self): - 776 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) - 777 - 778 def sin(self): - 779 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) - 780 - 781 def cos(self): - 782 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) - 783 - 784 def tan(self): - 785 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) - 786 - 787 def arcsin(self): - 788 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) - 789 - 790 def arccos(self): - 791 return derived_observable(lambda x: anp.arccos(x[0]), [self]) - 792 - 793 def arctan(self): - 794 return derived_observable(lambda x: anp.arctan(x[0]), [self]) - 795 - 796 def sinh(self): - 797 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) - 798 - 799 def cosh(self): - 800 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) - 801 - 802 def tanh(self): - 803 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) - 804 - 805 def arcsinh(self): - 806 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) - 807 - 808 def arccosh(self): - 809 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) - 810 - 811 def arctanh(self): - 812 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) - 813 - 814 - 815class CObs: - 816 """Class for a complex valued observable.""" - 817 __slots__ = ['_real', '_imag', 'tag'] + 575 ensemble to the error and returns a dictionary containing the fractions. + 576 + 577 Parameters + 578 ---------- + 579 save : str + 580 saves the figure to a file named 'save' if. + 581 """ + 582 if not hasattr(self, 'e_dvalue'): + 583 raise Exception('Run the gamma method first.') + 584 if np.isclose(0.0, self._dvalue, atol=1e-15): + 585 raise Exception('Error is 0.0') + 586 labels = self.e_names + 587 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 + 588 fig1, ax1 = plt.subplots() + 589 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) + 590 ax1.axis('equal') + 591 plt.draw() + 592 if save: + 593 fig1.savefig(save) + 594 + 595 return dict(zip(self.e_names, sizes)) + 596 + 597 def dump(self, filename, datatype="json.gz", description="", **kwargs): + 598 """Dump the Obs to a file 'name' of chosen format. + 599 + 600 Parameters + 601 ---------- + 602 filename : str + 603 name of the file to be saved. + 604 datatype : str + 605 Format of the exported file. Supported formats include + 606 "json.gz" and "pickle" + 607 description : str + 608 Description for output file, only relevant for json.gz format. + 609 path : str + 610 specifies a custom path for the file (default '.') + 611 """ + 612 if 'path' in kwargs: + 613 file_name = kwargs.get('path') + '/' + filename + 614 else: + 615 file_name = filename + 616 + 617 if datatype == "json.gz": + 618 from .input.json import dump_to_json + 619 dump_to_json([self], file_name, description=description) + 620 elif datatype == "pickle": + 621 with open(file_name + '.p', 'wb') as fb: + 622 pickle.dump(self, fb) + 623 else: + 624 raise Exception("Unknown datatype " + str(datatype)) + 625 + 626 def export_jackknife(self): + 627 """Export jackknife samples from the Obs + 628 + 629 Returns + 630 ------- + 631 numpy.ndarray + 632 Returns a numpy array of length N + 1 where N is the number of samples + 633 for the given ensemble and replicum. The zeroth entry of the array contains + 634 the mean value of the Obs, entries 1 to N contain the N jackknife samples + 635 derived from the Obs. The current implementation only works for observables + 636 defined on exactly one ensemble and replicum. The derived jackknife samples + 637 should agree with samples from a full jackknife analysis up to O(1/N). + 638 """ + 639 + 640 if len(self.names) != 1: + 641 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") + 642 + 643 name = self.names[0] + 644 full_data = self.deltas[name] + self.r_values[name] + 645 n = full_data.size + 646 mean = self.value + 647 tmp_jacks = np.zeros(n + 1) + 648 tmp_jacks[0] = mean + 649 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) + 650 return tmp_jacks + 651 + 652 def __float__(self): + 653 return float(self.value) + 654 + 655 def __repr__(self): + 656 return 'Obs[' + str(self) + ']' + 657 + 658 def __str__(self): + 659 if self._dvalue == 0.0: + 660 return str(self.value) + 661 fexp = np.floor(np.log10(self._dvalue)) + 662 if fexp < 0.0: + 663 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') + 664 elif fexp == 0.0: + 665 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) + 666 else: + 667 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) + 668 + 669 # Overload comparisons + 670 def __lt__(self, other): + 671 return self.value < other + 672 + 673 def __le__(self, other): + 674 return self.value <= other + 675 + 676 def __gt__(self, other): + 677 return self.value > other + 678 + 679 def __ge__(self, other): + 680 return self.value >= other + 681 + 682 def __eq__(self, other): + 683 return (self - other).is_zero() + 684 + 685 def __ne__(self, other): + 686 return not (self - other).is_zero() + 687 + 688 # Overload math operations + 689 def __add__(self, y): + 690 if isinstance(y, Obs): + 691 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) + 692 else: + 693 if isinstance(y, np.ndarray): + 694 return np.array([self + o for o in y]) + 695 elif y.__class__.__name__ in ['Corr', 'CObs']: + 696 return NotImplemented + 697 else: + 698 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) + 699 + 700 def __radd__(self, y): + 701 return self + y + 702 + 703 def __mul__(self, y): + 704 if isinstance(y, Obs): + 705 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) + 706 else: + 707 if isinstance(y, np.ndarray): + 708 return np.array([self * o for o in y]) + 709 elif isinstance(y, complex): + 710 return CObs(self * y.real, self * y.imag) + 711 elif y.__class__.__name__ in ['Corr', 'CObs']: + 712 return NotImplemented + 713 else: + 714 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) + 715 + 716 def __rmul__(self, y): + 717 return self * y + 718 + 719 def __sub__(self, y): + 720 if isinstance(y, Obs): + 721 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) + 722 else: + 723 if isinstance(y, np.ndarray): + 724 return np.array([self - o for o in y]) + 725 elif y.__class__.__name__ in ['Corr', 'CObs']: + 726 return NotImplemented + 727 else: + 728 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) + 729 + 730 def __rsub__(self, y): + 731 return -1 * (self - y) + 732 + 733 def __pos__(self): + 734 return self + 735 + 736 def __neg__(self): + 737 return -1 * self + 738 + 739 def __truediv__(self, y): + 740 if isinstance(y, Obs): + 741 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) + 742 else: + 743 if isinstance(y, np.ndarray): + 744 return np.array([self / o for o in y]) + 745 elif y.__class__.__name__ in ['Corr', 'CObs']: + 746 return NotImplemented + 747 else: + 748 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) + 749 + 750 def __rtruediv__(self, y): + 751 if isinstance(y, Obs): + 752 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) + 753 else: + 754 if isinstance(y, np.ndarray): + 755 return np.array([o / self for o in y]) + 756 elif y.__class__.__name__ in ['Corr', 'CObs']: + 757 return NotImplemented + 758 else: + 759 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) + 760 + 761 def __pow__(self, y): + 762 if isinstance(y, Obs): + 763 return derived_observable(lambda x: x[0] ** x[1], [self, y]) + 764 else: + 765 return derived_observable(lambda x: x[0] ** y, [self]) + 766 + 767 def __rpow__(self, y): + 768 if isinstance(y, Obs): + 769 return derived_observable(lambda x: x[0] ** x[1], [y, self]) + 770 else: + 771 return derived_observable(lambda x: y ** x[0], [self]) + 772 + 773 def __abs__(self): + 774 return derived_observable(lambda x: anp.abs(x[0]), [self]) + 775 + 776 # Overload numpy functions + 777 def sqrt(self): + 778 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) + 779 + 780 def log(self): + 781 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) + 782 + 783 def exp(self): + 784 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) + 785 + 786 def sin(self): + 787 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) + 788 + 789 def cos(self): + 790 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) + 791 + 792 def tan(self): + 793 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) + 794 + 795 def arcsin(self): + 796 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) + 797 + 798 def arccos(self): + 799 return derived_observable(lambda x: anp.arccos(x[0]), [self]) + 800 + 801 def arctan(self): + 802 return derived_observable(lambda x: anp.arctan(x[0]), [self]) + 803 + 804 def sinh(self): + 805 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) + 806 + 807 def cosh(self): + 808 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) + 809 + 810 def tanh(self): + 811 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) + 812 + 813 def arcsinh(self): + 814 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) + 815 + 816 def arccosh(self): + 817 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) 818 - 819 def __init__(self, real, imag=0.0): - 820 self._real = real - 821 self._imag = imag - 822 self.tag = None - 823 - 824 @property - 825 def real(self): - 826 return self._real - 827 - 828 @property - 829 def imag(self): - 830 return self._imag + 819 def arctanh(self): + 820 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) + 821 + 822 + 823class CObs: + 824 """Class for a complex valued observable.""" + 825 __slots__ = ['_real', '_imag', 'tag'] + 826 + 827 def __init__(self, real, imag=0.0): + 828 self._real = real + 829 self._imag = imag + 830 self.tag = None 831 - 832 def gamma_method(self, **kwargs): - 833 """Executes the gamma_method for the real and the imaginary part.""" - 834 if isinstance(self.real, Obs): - 835 self.real.gamma_method(**kwargs) - 836 if isinstance(self.imag, Obs): - 837 self.imag.gamma_method(**kwargs) - 838 - 839 def is_zero(self): - 840 """Checks whether both real and imaginary part are zero within machine precision.""" - 841 return self.real == 0.0 and self.imag == 0.0 - 842 - 843 def conjugate(self): - 844 return CObs(self.real, -self.imag) - 845 - 846 def __add__(self, other): - 847 if isinstance(other, np.ndarray): - 848 return other + self - 849 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 850 return CObs(self.real + other.real, - 851 self.imag + other.imag) - 852 else: - 853 return CObs(self.real + other, self.imag) - 854 - 855 def __radd__(self, y): - 856 return self + y - 857 - 858 def __sub__(self, other): - 859 if isinstance(other, np.ndarray): - 860 return -1 * (other - self) - 861 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 862 return CObs(self.real - other.real, self.imag - other.imag) - 863 else: - 864 return CObs(self.real - other, self.imag) + 832 @property + 833 def real(self): + 834 return self._real + 835 + 836 @property + 837 def imag(self): + 838 return self._imag + 839 + 840 def gamma_method(self, **kwargs): + 841 """Executes the gamma_method for the real and the imaginary part.""" + 842 if isinstance(self.real, Obs): + 843 self.real.gamma_method(**kwargs) + 844 if isinstance(self.imag, Obs): + 845 self.imag.gamma_method(**kwargs) + 846 + 847 def is_zero(self): + 848 """Checks whether both real and imaginary part are zero within machine precision.""" + 849 return self.real == 0.0 and self.imag == 0.0 + 850 + 851 def conjugate(self): + 852 return CObs(self.real, -self.imag) + 853 + 854 def __add__(self, other): + 855 if isinstance(other, np.ndarray): + 856 return other + self + 857 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 858 return CObs(self.real + other.real, + 859 self.imag + other.imag) + 860 else: + 861 return CObs(self.real + other, self.imag) + 862 + 863 def __radd__(self, y): + 864 return self + y 865 - 866 def __rsub__(self, other): - 867 return -1 * (self - other) - 868 - 869 def __mul__(self, other): - 870 if isinstance(other, np.ndarray): - 871 return other * self - 872 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 873 if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]): - 874 return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3], - 875 [self.real, other.real, self.imag, other.imag], - 876 man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]), - 877 derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3], - 878 [self.real, other.real, self.imag, other.imag], - 879 man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value])) - 880 elif getattr(other, 'imag', 0) != 0: - 881 return CObs(self.real * other.real - self.imag * other.imag, - 882 self.imag * other.real + self.real * other.imag) - 883 else: - 884 return CObs(self.real * other.real, self.imag * other.real) - 885 else: - 886 return CObs(self.real * other, self.imag * other) - 887 - 888 def __rmul__(self, other): - 889 return self * other - 890 - 891 def __truediv__(self, other): - 892 if isinstance(other, np.ndarray): - 893 return 1 / (other / self) - 894 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 895 r = other.real ** 2 + other.imag ** 2 - 896 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r) - 897 else: - 898 return CObs(self.real / other, self.imag / other) - 899 - 900 def __rtruediv__(self, other): - 901 r = self.real ** 2 + self.imag ** 2 - 902 if hasattr(other, 'real') and hasattr(other, 'imag'): - 903 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r) - 904 else: - 905 return CObs(self.real * other / r, -self.imag * other / r) - 906 - 907 def __abs__(self): - 908 return np.sqrt(self.real**2 + self.imag**2) - 909 - 910 def __pos__(self): - 911 return self - 912 - 913 def __neg__(self): - 914 return -1 * self - 915 - 916 def __eq__(self, other): - 917 return self.real == other.real and self.imag == other.imag - 918 - 919 def __str__(self): - 920 return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)' - 921 - 922 def __repr__(self): - 923 return 'CObs[' + str(self) + ']' - 924 - 925 - 926def _expand_deltas(deltas, idx, shape): - 927 """Expand deltas defined on idx to a regular, contiguous range, where holes are filled by 0. - 928 If idx is of type range, the deltas are not changed + 866 def __sub__(self, other): + 867 if isinstance(other, np.ndarray): + 868 return -1 * (other - self) + 869 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 870 return CObs(self.real - other.real, self.imag - other.imag) + 871 else: + 872 return CObs(self.real - other, self.imag) + 873 + 874 def __rsub__(self, other): + 875 return -1 * (self - other) + 876 + 877 def __mul__(self, other): + 878 if isinstance(other, np.ndarray): + 879 return other * self + 880 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 881 if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]): + 882 return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3], + 883 [self.real, other.real, self.imag, other.imag], + 884 man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]), + 885 derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3], + 886 [self.real, other.real, self.imag, other.imag], + 887 man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value])) + 888 elif getattr(other, 'imag', 0) != 0: + 889 return CObs(self.real * other.real - self.imag * other.imag, + 890 self.imag * other.real + self.real * other.imag) + 891 else: + 892 return CObs(self.real * other.real, self.imag * other.real) + 893 else: + 894 return CObs(self.real * other, self.imag * other) + 895 + 896 def __rmul__(self, other): + 897 return self * other + 898 + 899 def __truediv__(self, other): + 900 if isinstance(other, np.ndarray): + 901 return 1 / (other / self) + 902 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 903 r = other.real ** 2 + other.imag ** 2 + 904 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r) + 905 else: + 906 return CObs(self.real / other, self.imag / other) + 907 + 908 def __rtruediv__(self, other): + 909 r = self.real ** 2 + self.imag ** 2 + 910 if hasattr(other, 'real') and hasattr(other, 'imag'): + 911 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r) + 912 else: + 913 return CObs(self.real * other / r, -self.imag * other / r) + 914 + 915 def __abs__(self): + 916 return np.sqrt(self.real**2 + self.imag**2) + 917 + 918 def __pos__(self): + 919 return self + 920 + 921 def __neg__(self): + 922 return -1 * self + 923 + 924 def __eq__(self, other): + 925 return self.real == other.real and self.imag == other.imag + 926 + 927 def __str__(self): + 928 return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)' 929 - 930 Parameters - 931 ---------- - 932 deltas : list - 933 List of fluctuations - 934 idx : list - 935 List or range of configs on which the deltas are defined, has to be sorted in ascending order. - 936 shape : int - 937 Number of configs in idx. - 938 """ - 939 if isinstance(idx, range): - 940 return deltas - 941 else: - 942 ret = np.zeros(idx[-1] - idx[0] + 1) - 943 for i in range(shape): - 944 ret[idx[i] - idx[0]] = deltas[i] - 945 return ret - 946 - 947 - 948def _merge_idx(idl): - 949 """Returns the union of all lists in idl as sorted list - 950 - 951 Parameters - 952 ---------- - 953 idl : list - 954 List of lists or ranges. - 955 """ - 956 - 957 # Use groupby to efficiently check whether all elements of idl are identical - 958 try: - 959 g = groupby(idl) - 960 if next(g, True) and not next(g, False): - 961 return idl[0] - 962 except Exception: - 963 pass + 930 def __repr__(self): + 931 return 'CObs[' + str(self) + ']' + 932 + 933 + 934def _expand_deltas(deltas, idx, shape): + 935 """Expand deltas defined on idx to a regular, contiguous range, where holes are filled by 0. + 936 If idx is of type range, the deltas are not changed + 937 + 938 Parameters + 939 ---------- + 940 deltas : list + 941 List of fluctuations + 942 idx : list + 943 List or range of configs on which the deltas are defined, has to be sorted in ascending order. + 944 shape : int + 945 Number of configs in idx. + 946 """ + 947 if isinstance(idx, range): + 948 return deltas + 949 else: + 950 ret = np.zeros(idx[-1] - idx[0] + 1) + 951 for i in range(shape): + 952 ret[idx[i] - idx[0]] = deltas[i] + 953 return ret + 954 + 955 + 956def _merge_idx(idl): + 957 """Returns the union of all lists in idl as sorted list + 958 + 959 Parameters + 960 ---------- + 961 idl : list + 962 List of lists or ranges. + 963 """ 964 - 965 if np.all([type(idx) is range for idx in idl]): - 966 if len(set([idx[0] for idx in idl])) == 1: - 967 idstart = min([idx.start for idx in idl]) - 968 idstop = max([idx.stop for idx in idl]) - 969 idstep = min([idx.step for idx in idl]) - 970 return range(idstart, idstop, idstep) - 971 - 972 return sorted(set().union(*idl)) - 973 - 974 - 975def _expand_deltas_for_merge(deltas, idx, shape, new_idx): - 976 """Expand deltas defined on idx to the list of configs that is defined by new_idx. - 977 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest - 978 common divisor of the step sizes is used as new step size. + 965 # Use groupby to efficiently check whether all elements of idl are identical + 966 try: + 967 g = groupby(idl) + 968 if next(g, True) and not next(g, False): + 969 return idl[0] + 970 except Exception: + 971 pass + 972 + 973 if np.all([type(idx) is range for idx in idl]): + 974 if len(set([idx[0] for idx in idl])) == 1: + 975 idstart = min([idx.start for idx in idl]) + 976 idstop = max([idx.stop for idx in idl]) + 977 idstep = min([idx.step for idx in idl]) + 978 return range(idstart, idstop, idstep) 979 - 980 Parameters - 981 ---------- - 982 deltas : list - 983 List of fluctuations - 984 idx : list - 985 List or range of configs on which the deltas are defined. - 986 Has to be a subset of new_idx and has to be sorted in ascending order. - 987 shape : list - 988 Number of configs in idx. - 989 new_idx : list - 990 List of configs that defines the new range, has to be sorted in ascending order. - 991 """ - 992 - 993 if type(idx) is range and type(new_idx) is range: - 994 if idx == new_idx: - 995 return deltas - 996 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) - 997 for i in range(shape): - 998 ret[idx[i] - new_idx[0]] = deltas[i] - 999 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) + 980 return sorted(set().union(*idl)) + 981 + 982 + 983def _expand_deltas_for_merge(deltas, idx, shape, new_idx): + 984 """Expand deltas defined on idx to the list of configs that is defined by new_idx. + 985 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest + 986 common divisor of the step sizes is used as new step size. + 987 + 988 Parameters + 989 ---------- + 990 deltas : list + 991 List of fluctuations + 992 idx : list + 993 List or range of configs on which the deltas are defined. + 994 Has to be a subset of new_idx and has to be sorted in ascending order. + 995 shape : list + 996 Number of configs in idx. + 997 new_idx : list + 998 List of configs that defines the new range, has to be sorted in ascending order. + 999 """ 1000 -1001 -1002def _filter_zeroes(deltas, idx, eps=Obs.filter_eps): -1003 """Filter out all configurations with vanishing fluctuation such that they do not -1004 contribute to the error estimate anymore. Returns the new deltas and -1005 idx according to the filtering. -1006 A fluctuation is considered to be vanishing, if it is smaller than eps times -1007 the mean of the absolute values of all deltas in one list. +1001 if type(idx) is range and type(new_idx) is range: +1002 if idx == new_idx: +1003 return deltas +1004 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) +1005 for i in range(shape): +1006 ret[idx[i] - new_idx[0]] = deltas[i] +1007 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) 1008 -1009 Parameters -1010 ---------- -1011 deltas : list -1012 List of fluctuations -1013 idx : list -1014 List or ranges of configs on which the deltas are defined. -1015 eps : float -1016 Prefactor that enters the filter criterion. -1017 """ -1018 new_deltas = [] -1019 new_idx = [] -1020 maxd = np.mean(np.fabs(deltas)) -1021 for i in range(len(deltas)): -1022 if abs(deltas[i]) > eps * maxd: -1023 new_deltas.append(deltas[i]) -1024 new_idx.append(idx[i]) -1025 if new_idx: -1026 return np.array(new_deltas), new_idx -1027 else: -1028 return deltas, idx -1029 -1030 -1031def derived_observable(func, data, array_mode=False, **kwargs): -1032 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. -1033 -1034 Parameters -1035 ---------- -1036 func : object -1037 arbitrary function of the form func(data, **kwargs). For the -1038 automatic differentiation to work, all numpy functions have to have -1039 the autograd wrapper (use 'import autograd.numpy as anp'). -1040 data : list -1041 list of Obs, e.g. [obs1, obs2, obs3]. -1042 num_grad : bool -1043 if True, numerical derivatives are used instead of autograd -1044 (default False). To control the numerical differentiation the -1045 kwargs of numdifftools.step_generators.MaxStepGenerator -1046 can be used. -1047 man_grad : list -1048 manually supply a list or an array which contains the jacobian -1049 of func. Use cautiously, supplying the wrong derivative will -1050 not be intercepted. -1051 -1052 Notes -1053 ----- -1054 For simple mathematical operations it can be practical to use anonymous -1055 functions. For the ratio of two observables one can e.g. use -1056 -1057 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) -1058 """ +1009 +1010def _filter_zeroes(deltas, idx, eps=Obs.filter_eps): +1011 """Filter out all configurations with vanishing fluctuation such that they do not +1012 contribute to the error estimate anymore. Returns the new deltas and +1013 idx according to the filtering. +1014 A fluctuation is considered to be vanishing, if it is smaller than eps times +1015 the mean of the absolute values of all deltas in one list. +1016 +1017 Parameters +1018 ---------- +1019 deltas : list +1020 List of fluctuations +1021 idx : list +1022 List or ranges of configs on which the deltas are defined. +1023 eps : float +1024 Prefactor that enters the filter criterion. +1025 """ +1026 new_deltas = [] +1027 new_idx = [] +1028 maxd = np.mean(np.fabs(deltas)) +1029 for i in range(len(deltas)): +1030 if abs(deltas[i]) > eps * maxd: +1031 new_deltas.append(deltas[i]) +1032 new_idx.append(idx[i]) +1033 if new_idx: +1034 return np.array(new_deltas), new_idx +1035 else: +1036 return deltas, idx +1037 +1038 +1039def derived_observable(func, data, array_mode=False, **kwargs): +1040 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. +1041 +1042 Parameters +1043 ---------- +1044 func : object +1045 arbitrary function of the form func(data, **kwargs). For the +1046 automatic differentiation to work, all numpy functions have to have +1047 the autograd wrapper (use 'import autograd.numpy as anp'). +1048 data : list +1049 list of Obs, e.g. [obs1, obs2, obs3]. +1050 num_grad : bool +1051 if True, numerical derivatives are used instead of autograd +1052 (default False). To control the numerical differentiation the +1053 kwargs of numdifftools.step_generators.MaxStepGenerator +1054 can be used. +1055 man_grad : list +1056 manually supply a list or an array which contains the jacobian +1057 of func. Use cautiously, supplying the wrong derivative will +1058 not be intercepted. 1059 -1060 data = np.asarray(data) -1061 raveled_data = data.ravel() -1062 -1063 # Workaround for matrix operations containing non Obs data -1064 if not all(isinstance(x, Obs) for x in raveled_data): -1065 for i in range(len(raveled_data)): -1066 if isinstance(raveled_data[i], (int, float)): -1067 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") -1068 -1069 allcov = {} -1070 for o in raveled_data: -1071 for name in o.cov_names: -1072 if name in allcov: -1073 if not np.allclose(allcov[name], o.covobs[name].cov): -1074 raise Exception('Inconsistent covariance matrices for %s!' % (name)) -1075 else: -1076 allcov[name] = o.covobs[name].cov -1077 -1078 n_obs = len(raveled_data) -1079 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) -1080 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) -1081 new_sample_names = sorted(set(new_names) - set(new_cov_names)) -1082 -1083 is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names} -1084 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 +1060 Notes +1061 ----- +1062 For simple mathematical operations it can be practical to use anonymous +1063 functions. For the ratio of two observables one can e.g. use +1064 +1065 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) +1066 """ +1067 +1068 data = np.asarray(data) +1069 raveled_data = data.ravel() +1070 +1071 # Workaround for matrix operations containing non Obs data +1072 if not all(isinstance(x, Obs) for x in raveled_data): +1073 for i in range(len(raveled_data)): +1074 if isinstance(raveled_data[i], (int, float)): +1075 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") +1076 +1077 allcov = {} +1078 for o in raveled_data: +1079 for name in o.cov_names: +1080 if name in allcov: +1081 if not np.allclose(allcov[name], o.covobs[name].cov): +1082 raise Exception('Inconsistent covariance matrices for %s!' % (name)) +1083 else: +1084 allcov[name] = o.covobs[name].cov 1085 -1086 if data.ndim == 1: -1087 values = np.array([o.value for o in data]) -1088 else: -1089 values = np.vectorize(lambda x: x.value)(data) +1086 n_obs = len(raveled_data) +1087 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) +1088 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) +1089 new_sample_names = sorted(set(new_names) - set(new_cov_names)) 1090 -1091 new_values = func(values, **kwargs) -1092 -1093 multi = int(isinstance(new_values, np.ndarray)) -1094 -1095 new_r_values = {} -1096 new_idl_d = {} -1097 for name in new_sample_names: -1098 idl = [] -1099 tmp_values = np.zeros(n_obs) -1100 for i, item in enumerate(raveled_data): -1101 tmp_values[i] = item.r_values.get(name, item.value) -1102 tmp_idl = item.idl.get(name) -1103 if tmp_idl is not None: -1104 idl.append(tmp_idl) -1105 if multi > 0: -1106 tmp_values = np.array(tmp_values).reshape(data.shape) -1107 new_r_values[name] = func(tmp_values, **kwargs) -1108 new_idl_d[name] = _merge_idx(idl) -1109 if not is_merged[name]: -1110 is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]]))) -1111 -1112 if 'man_grad' in kwargs: -1113 deriv = np.asarray(kwargs.get('man_grad')) -1114 if new_values.shape + data.shape != deriv.shape: -1115 raise Exception('Manual derivative does not have correct shape.') -1116 elif kwargs.get('num_grad') is True: -1117 if multi > 0: -1118 raise Exception('Multi mode currently not supported for numerical derivative') -1119 options = { -1120 'base_step': 0.1, -1121 'step_ratio': 2.5} -1122 for key in options.keys(): -1123 kwarg = kwargs.get(key) -1124 if kwarg is not None: -1125 options[key] = kwarg -1126 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) -1127 if tmp_df.size == 1: -1128 deriv = np.array([tmp_df.real]) -1129 else: -1130 deriv = tmp_df.real -1131 else: -1132 deriv = jacobian(func)(values, **kwargs) -1133 -1134 final_result = np.zeros(new_values.shape, dtype=object) -1135 -1136 if array_mode is True: -1137 -1138 class _Zero_grad(): -1139 def __init__(self, N): -1140 self.grad = np.zeros((N, 1)) +1091 is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names} +1092 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 +1093 +1094 if data.ndim == 1: +1095 values = np.array([o.value for o in data]) +1096 else: +1097 values = np.vectorize(lambda x: x.value)(data) +1098 +1099 new_values = func(values, **kwargs) +1100 +1101 multi = int(isinstance(new_values, np.ndarray)) +1102 +1103 new_r_values = {} +1104 new_idl_d = {} +1105 for name in new_sample_names: +1106 idl = [] +1107 tmp_values = np.zeros(n_obs) +1108 for i, item in enumerate(raveled_data): +1109 tmp_values[i] = item.r_values.get(name, item.value) +1110 tmp_idl = item.idl.get(name) +1111 if tmp_idl is not None: +1112 idl.append(tmp_idl) +1113 if multi > 0: +1114 tmp_values = np.array(tmp_values).reshape(data.shape) +1115 new_r_values[name] = func(tmp_values, **kwargs) +1116 new_idl_d[name] = _merge_idx(idl) +1117 if not is_merged[name]: +1118 is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]]))) +1119 +1120 if 'man_grad' in kwargs: +1121 deriv = np.asarray(kwargs.get('man_grad')) +1122 if new_values.shape + data.shape != deriv.shape: +1123 raise Exception('Manual derivative does not have correct shape.') +1124 elif kwargs.get('num_grad') is True: +1125 if multi > 0: +1126 raise Exception('Multi mode currently not supported for numerical derivative') +1127 options = { +1128 'base_step': 0.1, +1129 'step_ratio': 2.5} +1130 for key in options.keys(): +1131 kwarg = kwargs.get(key) +1132 if kwarg is not None: +1133 options[key] = kwarg +1134 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) +1135 if tmp_df.size == 1: +1136 deriv = np.array([tmp_df.real]) +1137 else: +1138 deriv = tmp_df.real +1139 else: +1140 deriv = jacobian(func)(values, **kwargs) 1141 -1142 new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x])) -1143 d_extracted = {} -1144 g_extracted = {} -1145 for name in new_sample_names: -1146 d_extracted[name] = [] -1147 ens_length = len(new_idl_d[name]) -1148 for i_dat, dat in enumerate(data): -1149 d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, ))) -1150 for name in new_cov_names: -1151 g_extracted[name] = [] -1152 zero_grad = _Zero_grad(new_covobs_lengths[name]) -1153 for i_dat, dat in enumerate(data): -1154 g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1))) -1155 -1156 for i_val, new_val in np.ndenumerate(new_values): -1157 new_deltas = {} -1158 new_grad = {} -1159 if array_mode is True: -1160 for name in new_sample_names: -1161 ens_length = d_extracted[name][0].shape[-1] -1162 new_deltas[name] = np.zeros(ens_length) -1163 for i_dat, dat in enumerate(d_extracted[name]): -1164 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1165 for name in new_cov_names: -1166 new_grad[name] = 0 -1167 for i_dat, dat in enumerate(g_extracted[name]): -1168 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1169 else: -1170 for j_obs, obs in np.ndenumerate(data): -1171 for name in obs.names: -1172 if name in obs.cov_names: -1173 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad -1174 else: -1175 new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name]) -1176 -1177 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} -1178 -1179 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): -1180 raise Exception('The same name has been used for deltas and covobs!') -1181 new_samples = [] -1182 new_means = [] -1183 new_idl = [] -1184 new_names_obs = [] -1185 for name in new_names: -1186 if name not in new_covobs: -1187 if is_merged[name]: -1188 filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name]) -1189 else: -1190 filtered_deltas = new_deltas[name] -1191 filtered_idl_d = new_idl_d[name] -1192 -1193 new_samples.append(filtered_deltas) -1194 new_idl.append(filtered_idl_d) -1195 new_means.append(new_r_values[name][i_val]) -1196 new_names_obs.append(name) -1197 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) -1198 for name in new_covobs: -1199 final_result[i_val].names.append(name) -1200 final_result[i_val]._covobs = new_covobs -1201 final_result[i_val]._value = new_val -1202 final_result[i_val].is_merged = is_merged -1203 final_result[i_val].reweighted = reweighted -1204 -1205 if multi == 0: -1206 final_result = final_result.item() -1207 -1208 return final_result -1209 -1210 -1211def _reduce_deltas(deltas, idx_old, idx_new): -1212 """Extract deltas defined on idx_old on all configs of idx_new. -1213 -1214 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they -1215 are ordered in an ascending order. -1216 -1217 Parameters -1218 ---------- -1219 deltas : list -1220 List of fluctuations -1221 idx_old : list -1222 List or range of configs on which the deltas are defined -1223 idx_new : list -1224 List of configs for which we want to extract the deltas. -1225 Has to be a subset of idx_old. -1226 """ -1227 if not len(deltas) == len(idx_old): -1228 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) -1229 if type(idx_old) is range and type(idx_new) is range: -1230 if idx_old == idx_new: -1231 return deltas -1232 shape = len(idx_new) -1233 ret = np.zeros(shape) -1234 oldpos = 0 -1235 for i in range(shape): -1236 pos = -1 -1237 for j in range(oldpos, len(idx_old)): -1238 if idx_old[j] == idx_new[i]: -1239 pos = j -1240 break -1241 if pos < 0: -1242 raise Exception('Error in _reduce_deltas: Config %d not in idx_old' % (idx_new[i])) -1243 ret[i] = deltas[pos] -1244 oldpos = pos -1245 return np.array(ret) -1246 -1247 -1248def reweight(weight, obs, **kwargs): -1249 """Reweight a list of observables. -1250 -1251 Parameters -1252 ---------- -1253 weight : Obs -1254 Reweighting factor. An Observable that has to be defined on a superset of the -1255 configurations in obs[i].idl for all i. -1256 obs : list -1257 list of Obs, e.g. [obs1, obs2, obs3]. -1258 all_configs : bool -1259 if True, the reweighted observables are normalized by the average of -1260 the reweighting factor on all configurations in weight.idl and not -1261 on the configurations in obs[i].idl. -1262 """ -1263 result = [] -1264 for i in range(len(obs)): -1265 if len(obs[i].cov_names): -1266 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') -1267 if not set(obs[i].names).issubset(weight.names): -1268 raise Exception('Error: Ensembles do not fit') -1269 for name in obs[i].names: -1270 if not set(obs[i].idl[name]).issubset(weight.idl[name]): -1271 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) -1272 new_samples = [] -1273 w_deltas = {} -1274 for name in sorted(obs[i].names): -1275 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) -1276 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) -1277 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) -1278 -1279 if kwargs.get('all_configs'): -1280 new_weight = weight -1281 else: -1282 new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) -1283 -1284 result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs)) -1285 result[-1].reweighted = True -1286 result[-1].is_merged = obs[i].is_merged -1287 -1288 return result -1289 -1290 -1291def correlate(obs_a, obs_b): -1292 """Correlate two observables. -1293 -1294 Parameters -1295 ---------- -1296 obs_a : Obs -1297 First observable -1298 obs_b : Obs -1299 Second observable -1300 -1301 Notes -1302 ----- -1303 Keep in mind to only correlate primary observables which have not been reweighted -1304 yet. The reweighting has to be applied after correlating the observables. -1305 Currently only works if ensembles are identical (this is not strictly necessary). -1306 """ -1307 -1308 if sorted(obs_a.names) != sorted(obs_b.names): -1309 raise Exception('Ensembles do not fit') -1310 if len(obs_a.cov_names) or len(obs_b.cov_names): -1311 raise Exception('Error: Not possible to correlate Obs that contain covobs!') -1312 for name in obs_a.names: -1313 if obs_a.shape[name] != obs_b.shape[name]: -1314 raise Exception('Shapes of ensemble', name, 'do not fit') -1315 if obs_a.idl[name] != obs_b.idl[name]: -1316 raise Exception('idl of ensemble', name, 'do not fit') -1317 -1318 if obs_a.reweighted is True: -1319 warnings.warn("The first observable is already reweighted.", RuntimeWarning) -1320 if obs_b.reweighted is True: -1321 warnings.warn("The second observable is already reweighted.", RuntimeWarning) -1322 -1323 new_samples = [] -1324 new_idl = [] -1325 for name in sorted(obs_a.names): -1326 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) -1327 new_idl.append(obs_a.idl[name]) -1328 -1329 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) -1330 o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names} -1331 o.reweighted = obs_a.reweighted or obs_b.reweighted -1332 return o -1333 -1334 -1335def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): -1336 r'''Calculates the covariance matrix of a set of observables. -1337 -1338 The gamma method has to be applied first to all observables. -1339 -1340 Parameters -1341 ---------- -1342 obs : list or numpy.ndarray -1343 List or one dimensional array of Obs -1344 visualize : bool -1345 If True plots the corresponding normalized correlation matrix (default False). -1346 correlation : bool -1347 If True the correlation instead of the covariance is returned (default False). -1348 smooth : None or int -1349 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue -1350 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the -1351 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely -1352 small ones. -1353 -1354 Notes -1355 ----- -1356 The 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 -1357 $$v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. -1358 For 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. -1359 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ -1360 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). -1361 ''' -1362 -1363 length = len(obs) -1364 -1365 max_samples = np.max([o.N for o in obs]) -1366 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: -1367 warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning) -1368 -1369 cov = np.zeros((length, length)) -1370 for i in range(length): -1371 for j in range(i, length): -1372 cov[i, j] = _covariance_element(obs[i], obs[j]) -1373 cov = cov + cov.T - np.diag(np.diag(cov)) -1374 -1375 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) +1142 final_result = np.zeros(new_values.shape, dtype=object) +1143 +1144 if array_mode is True: +1145 +1146 class _Zero_grad(): +1147 def __init__(self, N): +1148 self.grad = np.zeros((N, 1)) +1149 +1150 new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x])) +1151 d_extracted = {} +1152 g_extracted = {} +1153 for name in new_sample_names: +1154 d_extracted[name] = [] +1155 ens_length = len(new_idl_d[name]) +1156 for i_dat, dat in enumerate(data): +1157 d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, ))) +1158 for name in new_cov_names: +1159 g_extracted[name] = [] +1160 zero_grad = _Zero_grad(new_covobs_lengths[name]) +1161 for i_dat, dat in enumerate(data): +1162 g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1))) +1163 +1164 for i_val, new_val in np.ndenumerate(new_values): +1165 new_deltas = {} +1166 new_grad = {} +1167 if array_mode is True: +1168 for name in new_sample_names: +1169 ens_length = d_extracted[name][0].shape[-1] +1170 new_deltas[name] = np.zeros(ens_length) +1171 for i_dat, dat in enumerate(d_extracted[name]): +1172 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1173 for name in new_cov_names: +1174 new_grad[name] = 0 +1175 for i_dat, dat in enumerate(g_extracted[name]): +1176 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1177 else: +1178 for j_obs, obs in np.ndenumerate(data): +1179 for name in obs.names: +1180 if name in obs.cov_names: +1181 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad +1182 else: +1183 new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name]) +1184 +1185 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} +1186 +1187 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): +1188 raise Exception('The same name has been used for deltas and covobs!') +1189 new_samples = [] +1190 new_means = [] +1191 new_idl = [] +1192 new_names_obs = [] +1193 for name in new_names: +1194 if name not in new_covobs: +1195 if is_merged[name]: +1196 filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name]) +1197 else: +1198 filtered_deltas = new_deltas[name] +1199 filtered_idl_d = new_idl_d[name] +1200 +1201 new_samples.append(filtered_deltas) +1202 new_idl.append(filtered_idl_d) +1203 new_means.append(new_r_values[name][i_val]) +1204 new_names_obs.append(name) +1205 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) +1206 for name in new_covobs: +1207 final_result[i_val].names.append(name) +1208 final_result[i_val]._covobs = new_covobs +1209 final_result[i_val]._value = new_val +1210 final_result[i_val].is_merged = is_merged +1211 final_result[i_val].reweighted = reweighted +1212 +1213 if multi == 0: +1214 final_result = final_result.item() +1215 +1216 return final_result +1217 +1218 +1219def _reduce_deltas(deltas, idx_old, idx_new): +1220 """Extract deltas defined on idx_old on all configs of idx_new. +1221 +1222 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they +1223 are ordered in an ascending order. +1224 +1225 Parameters +1226 ---------- +1227 deltas : list +1228 List of fluctuations +1229 idx_old : list +1230 List or range of configs on which the deltas are defined +1231 idx_new : list +1232 List of configs for which we want to extract the deltas. +1233 Has to be a subset of idx_old. +1234 """ +1235 if not len(deltas) == len(idx_old): +1236 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) +1237 if type(idx_old) is range and type(idx_new) is range: +1238 if idx_old == idx_new: +1239 return deltas +1240 shape = len(idx_new) +1241 ret = np.zeros(shape) +1242 oldpos = 0 +1243 for i in range(shape): +1244 pos = -1 +1245 for j in range(oldpos, len(idx_old)): +1246 if idx_old[j] == idx_new[i]: +1247 pos = j +1248 break +1249 if pos < 0: +1250 raise Exception('Error in _reduce_deltas: Config %d not in idx_old' % (idx_new[i])) +1251 ret[i] = deltas[pos] +1252 oldpos = pos +1253 return np.array(ret) +1254 +1255 +1256def reweight(weight, obs, **kwargs): +1257 """Reweight a list of observables. +1258 +1259 Parameters +1260 ---------- +1261 weight : Obs +1262 Reweighting factor. An Observable that has to be defined on a superset of the +1263 configurations in obs[i].idl for all i. +1264 obs : list +1265 list of Obs, e.g. [obs1, obs2, obs3]. +1266 all_configs : bool +1267 if True, the reweighted observables are normalized by the average of +1268 the reweighting factor on all configurations in weight.idl and not +1269 on the configurations in obs[i].idl. +1270 """ +1271 result = [] +1272 for i in range(len(obs)): +1273 if len(obs[i].cov_names): +1274 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') +1275 if not set(obs[i].names).issubset(weight.names): +1276 raise Exception('Error: Ensembles do not fit') +1277 for name in obs[i].names: +1278 if not set(obs[i].idl[name]).issubset(weight.idl[name]): +1279 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) +1280 new_samples = [] +1281 w_deltas = {} +1282 for name in sorted(obs[i].names): +1283 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) +1284 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) +1285 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) +1286 +1287 if kwargs.get('all_configs'): +1288 new_weight = weight +1289 else: +1290 new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) +1291 +1292 result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs)) +1293 result[-1].reweighted = True +1294 result[-1].is_merged = obs[i].is_merged +1295 +1296 return result +1297 +1298 +1299def correlate(obs_a, obs_b): +1300 """Correlate two observables. +1301 +1302 Parameters +1303 ---------- +1304 obs_a : Obs +1305 First observable +1306 obs_b : Obs +1307 Second observable +1308 +1309 Notes +1310 ----- +1311 Keep in mind to only correlate primary observables which have not been reweighted +1312 yet. The reweighting has to be applied after correlating the observables. +1313 Currently only works if ensembles are identical (this is not strictly necessary). +1314 """ +1315 +1316 if sorted(obs_a.names) != sorted(obs_b.names): +1317 raise Exception('Ensembles do not fit') +1318 if len(obs_a.cov_names) or len(obs_b.cov_names): +1319 raise Exception('Error: Not possible to correlate Obs that contain covobs!') +1320 for name in obs_a.names: +1321 if obs_a.shape[name] != obs_b.shape[name]: +1322 raise Exception('Shapes of ensemble', name, 'do not fit') +1323 if obs_a.idl[name] != obs_b.idl[name]: +1324 raise Exception('idl of ensemble', name, 'do not fit') +1325 +1326 if obs_a.reweighted is True: +1327 warnings.warn("The first observable is already reweighted.", RuntimeWarning) +1328 if obs_b.reweighted is True: +1329 warnings.warn("The second observable is already reweighted.", RuntimeWarning) +1330 +1331 new_samples = [] +1332 new_idl = [] +1333 for name in sorted(obs_a.names): +1334 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) +1335 new_idl.append(obs_a.idl[name]) +1336 +1337 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) +1338 o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names} +1339 o.reweighted = obs_a.reweighted or obs_b.reweighted +1340 return o +1341 +1342 +1343def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): +1344 r'''Calculates the covariance matrix of a set of observables. +1345 +1346 The gamma method has to be applied first to all observables. +1347 +1348 Parameters +1349 ---------- +1350 obs : list or numpy.ndarray +1351 List or one dimensional array of Obs +1352 visualize : bool +1353 If True plots the corresponding normalized correlation matrix (default False). +1354 correlation : bool +1355 If True the correlation instead of the covariance is returned (default False). +1356 smooth : None or int +1357 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue +1358 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the +1359 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely +1360 small ones. +1361 +1362 Notes +1363 ----- +1364 The 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 +1365 $$v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. +1366 For 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. +1367 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ +1368 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). +1369 ''' +1370 +1371 length = len(obs) +1372 +1373 max_samples = np.max([o.N for o in obs]) +1374 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: +1375 warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning) 1376 -1377 if isinstance(smooth, int): -1378 corr = _smooth_eigenvalues(corr, smooth) -1379 -1380 errors = [o.dvalue for o in obs] -1381 cov = np.diag(errors) @ corr @ np.diag(errors) +1377 cov = np.zeros((length, length)) +1378 for i in range(length): +1379 for j in range(i, length): +1380 cov[i, j] = _covariance_element(obs[i], obs[j]) +1381 cov = cov + cov.T - np.diag(np.diag(cov)) 1382 -1383 eigenvalues = np.linalg.eigh(cov)[0] -1384 if not np.all(eigenvalues >= 0): -1385 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) -1386 -1387 if visualize: -1388 plt.matshow(corr, vmin=-1, vmax=1) -1389 plt.set_cmap('RdBu') -1390 plt.colorbar() -1391 plt.draw() -1392 -1393 if correlation is True: -1394 return corr -1395 else: -1396 return cov -1397 -1398 -1399def _smooth_eigenvalues(corr, E): -1400 """Eigenvalue smoothing as described in hep-lat/9412087 -1401 -1402 corr : np.ndarray -1403 correlation matrix -1404 E : integer -1405 Number of eigenvalues to be left substantially unchanged -1406 """ -1407 if not (2 < E < corr.shape[0] - 1): -1408 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") -1409 vals, vec = np.linalg.eigh(corr) -1410 lambda_min = np.mean(vals[:-E]) -1411 vals[vals < lambda_min] = lambda_min -1412 vals /= np.mean(vals) -1413 return vec @ np.diag(vals) @ vec.T -1414 -1415 -1416def _covariance_element(obs1, obs2): -1417 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" -1418 -1419 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): -1420 deltas1 = _expand_deltas_for_merge(deltas1, idx1, len(idx1), new_idx) -1421 deltas2 = _expand_deltas_for_merge(deltas2, idx2, len(idx2), new_idx) -1422 return np.sum(deltas1 * deltas2) +1383 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) +1384 +1385 if isinstance(smooth, int): +1386 corr = _smooth_eigenvalues(corr, smooth) +1387 +1388 errors = [o.dvalue for o in obs] +1389 cov = np.diag(errors) @ corr @ np.diag(errors) +1390 +1391 eigenvalues = np.linalg.eigh(cov)[0] +1392 if not np.all(eigenvalues >= 0): +1393 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) +1394 +1395 if visualize: +1396 plt.matshow(corr, vmin=-1, vmax=1) +1397 plt.set_cmap('RdBu') +1398 plt.colorbar() +1399 plt.draw() +1400 +1401 if correlation is True: +1402 return corr +1403 else: +1404 return cov +1405 +1406 +1407def _smooth_eigenvalues(corr, E): +1408 """Eigenvalue smoothing as described in hep-lat/9412087 +1409 +1410 corr : np.ndarray +1411 correlation matrix +1412 E : integer +1413 Number of eigenvalues to be left substantially unchanged +1414 """ +1415 if not (2 < E < corr.shape[0] - 1): +1416 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") +1417 vals, vec = np.linalg.eigh(corr) +1418 lambda_min = np.mean(vals[:-E]) +1419 vals[vals < lambda_min] = lambda_min +1420 vals /= np.mean(vals) +1421 return vec @ np.diag(vals) @ vec.T +1422 1423 -1424 if set(obs1.names).isdisjoint(set(obs2.names)): -1425 return 0.0 +1424def _covariance_element(obs1, obs2): +1425 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" 1426 -1427 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): -1428 raise Exception('The gamma method has to be applied to both Obs first.') -1429 -1430 dvalue = 0.0 +1427 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): +1428 deltas1 = _expand_deltas_for_merge(deltas1, idx1, len(idx1), new_idx) +1429 deltas2 = _expand_deltas_for_merge(deltas2, idx2, len(idx2), new_idx) +1430 return np.sum(deltas1 * deltas2) 1431 -1432 for e_name in obs1.mc_names: -1433 -1434 if e_name not in obs2.mc_names: -1435 continue -1436 -1437 idl_d = {} -1438 for r_name in obs1.e_content[e_name]: -1439 if r_name not in obs2.e_content[e_name]: -1440 continue -1441 idl_d[r_name] = _merge_idx([obs1.idl[r_name], obs2.idl[r_name]]) -1442 -1443 gamma = 0.0 +1432 if set(obs1.names).isdisjoint(set(obs2.names)): +1433 return 0.0 +1434 +1435 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): +1436 raise Exception('The gamma method has to be applied to both Obs first.') +1437 +1438 dvalue = 0.0 +1439 +1440 for e_name in obs1.mc_names: +1441 +1442 if e_name not in obs2.mc_names: +1443 continue 1444 -1445 for r_name in obs1.e_content[e_name]: -1446 if r_name not in obs2.e_content[e_name]: -1447 continue -1448 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) -1449 -1450 if gamma == 0.0: -1451 continue +1445 idl_d = {} +1446 for r_name in obs1.e_content[e_name]: +1447 if r_name not in obs2.e_content[e_name]: +1448 continue +1449 idl_d[r_name] = _merge_idx([obs1.idl[r_name], obs2.idl[r_name]]) +1450 +1451 gamma = 0.0 1452 -1453 gamma_div = 0.0 -1454 e_N = 0 -1455 for r_name in obs1.e_content[e_name]: -1456 if r_name not in obs2.e_content[e_name]: -1457 continue -1458 gamma_div += calc_gamma(np.ones(obs1.shape[r_name]), np.ones(obs2.shape[r_name]), obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) -1459 e_N += len(idl_d[r_name]) -1460 gamma /= max(gamma_div, 1.0) -1461 -1462 # Bias correction hep-lat/0306017 eq. (49) -1463 dvalue += (1 + 1 / e_N) * gamma / e_N -1464 -1465 for e_name in obs1.cov_names: -1466 -1467 if e_name not in obs2.cov_names: -1468 continue +1453 for r_name in obs1.e_content[e_name]: +1454 if r_name not in obs2.e_content[e_name]: +1455 continue +1456 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) +1457 +1458 if gamma == 0.0: +1459 continue +1460 +1461 gamma_div = 0.0 +1462 e_N = 0 +1463 for r_name in obs1.e_content[e_name]: +1464 if r_name not in obs2.e_content[e_name]: +1465 continue +1466 gamma_div += calc_gamma(np.ones(obs1.shape[r_name]), np.ones(obs2.shape[r_name]), obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) +1467 e_N += len(idl_d[r_name]) +1468 gamma /= max(gamma_div, 1.0) 1469 -1470 dvalue += float(np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad))) -1471 -1472 return dvalue -1473 +1470 # Bias correction hep-lat/0306017 eq. (49) +1471 dvalue += (1 + 1 / e_N) * gamma / e_N +1472 +1473 for e_name in obs1.cov_names: 1474 -1475def import_jackknife(jacks, name, idl=None): -1476 """Imports jackknife samples and returns an Obs +1475 if e_name not in obs2.cov_names: +1476 continue 1477 -1478 Parameters -1479 ---------- -1480 jacks : numpy.ndarray -1481 numpy array containing the mean value as zeroth entry and -1482 the N jackknife samples as first to Nth entry. -1483 name : str -1484 name of the ensemble the samples are defined on. -1485 """ -1486 length = len(jacks) - 1 -1487 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) -1488 samples = jacks[1:] @ prj -1489 mean = np.mean(samples) -1490 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) -1491 new_obs._value = jacks[0] -1492 return new_obs -1493 -1494 -1495def merge_obs(list_of_obs): -1496 """Combine all observables in list_of_obs into one new observable -1497 -1498 Parameters -1499 ---------- -1500 list_of_obs : list -1501 list of the Obs object to be combined +1478 dvalue += float(np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad))) +1479 +1480 return dvalue +1481 +1482 +1483def import_jackknife(jacks, name, idl=None): +1484 """Imports jackknife samples and returns an Obs +1485 +1486 Parameters +1487 ---------- +1488 jacks : numpy.ndarray +1489 numpy array containing the mean value as zeroth entry and +1490 the N jackknife samples as first to Nth entry. +1491 name : str +1492 name of the ensemble the samples are defined on. +1493 """ +1494 length = len(jacks) - 1 +1495 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) +1496 samples = jacks[1:] @ prj +1497 mean = np.mean(samples) +1498 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) +1499 new_obs._value = jacks[0] +1500 return new_obs +1501 1502 -1503 Notes -1504 ----- -1505 It is not possible to combine obs which are based on the same replicum -1506 """ -1507 replist = [item for obs in list_of_obs for item in obs.names] -1508 if (len(replist) == len(set(replist))) is False: -1509 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) -1510 if any([len(o.cov_names) for o in list_of_obs]): -1511 raise Exception('Not possible to merge data that contains covobs!') -1512 new_dict = {} -1513 idl_dict = {} -1514 for o in list_of_obs: -1515 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) -1516 for key in set(o.deltas) | set(o.r_values)}) -1517 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) -1518 -1519 names = sorted(new_dict.keys()) -1520 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) -1521 o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names} -1522 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) -1523 return o -1524 -1525 -1526def cov_Obs(means, cov, name, grad=None): -1527 """Create an Obs based on mean(s) and a covariance matrix -1528 -1529 Parameters -1530 ---------- -1531 mean : list of floats or float -1532 N mean value(s) of the new Obs -1533 cov : list or array -1534 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance -1535 name : str -1536 identifier for the covariance matrix -1537 grad : list or array -1538 Gradient of the Covobs wrt. the means belonging to cov. -1539 """ -1540 -1541 def covobs_to_obs(co): -1542 """Make an Obs out of a Covobs -1543 -1544 Parameters -1545 ---------- -1546 co : Covobs -1547 Covobs to be embedded into the Obs -1548 """ -1549 o = Obs([], [], means=[]) -1550 o._value = co.value -1551 o.names.append(co.name) -1552 o._covobs[co.name] = co -1553 o._dvalue = np.sqrt(co.errsq()) -1554 return o -1555 -1556 ol = [] -1557 if isinstance(means, (float, int)): -1558 means = [means] -1559 -1560 for i in range(len(means)): -1561 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) -1562 if ol[0].covobs[name].N != len(means): -1563 raise Exception('You have to provide %d mean values!' % (ol[0].N)) -1564 if len(ol) == 1: -1565 return ol[0] -1566 return ol +1503def merge_obs(list_of_obs): +1504 """Combine all observables in list_of_obs into one new observable +1505 +1506 Parameters +1507 ---------- +1508 list_of_obs : list +1509 list of the Obs object to be combined +1510 +1511 Notes +1512 ----- +1513 It is not possible to combine obs which are based on the same replicum +1514 """ +1515 replist = [item for obs in list_of_obs for item in obs.names] +1516 if (len(replist) == len(set(replist))) is False: +1517 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) +1518 if any([len(o.cov_names) for o in list_of_obs]): +1519 raise Exception('Not possible to merge data that contains covobs!') +1520 new_dict = {} +1521 idl_dict = {} +1522 for o in list_of_obs: +1523 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) +1524 for key in set(o.deltas) | set(o.r_values)}) +1525 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) +1526 +1527 names = sorted(new_dict.keys()) +1528 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) +1529 o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names} +1530 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) +1531 return o +1532 +1533 +1534def cov_Obs(means, cov, name, grad=None): +1535 """Create an Obs based on mean(s) and a covariance matrix +1536 +1537 Parameters +1538 ---------- +1539 mean : list of floats or float +1540 N mean value(s) of the new Obs +1541 cov : list or array +1542 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance +1543 name : str +1544 identifier for the covariance matrix +1545 grad : list or array +1546 Gradient of the Covobs wrt. the means belonging to cov. +1547 """ +1548 +1549 def covobs_to_obs(co): +1550 """Make an Obs out of a Covobs +1551 +1552 Parameters +1553 ---------- +1554 co : Covobs +1555 Covobs to be embedded into the Obs +1556 """ +1557 o = Obs([], [], means=[]) +1558 o._value = co.value +1559 o.names.append(co.name) +1560 o._covobs[co.name] = co +1561 o._dvalue = np.sqrt(co.errsq()) +1562 return o +1563 +1564 ol = [] +1565 if isinstance(means, (float, int)): +1566 means = [means] +1567 +1568 for i in range(len(means)): +1569 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) +1570 if ol[0].covobs[name].N != len(means): +1571 raise Exception('You have to provide %d mean values!' % (ol[0].N)) +1572 if len(ol) == 1: +1573 return ol[0] +1574 return ol @@ -2453,246 +2461,254 @@ 571 plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})') 572 plt.draw() 573 -574 def plot_piechart(self): +574 def plot_piechart(self, save=None): 575 """Plot piechart which shows the fractional contribution of each -576 ensemble to the error and returns a dictionary containing the fractions.""" -577 if not hasattr(self, 'e_dvalue'): -578 raise Exception('Run the gamma method first.') -579 if np.isclose(0.0, self._dvalue, atol=1e-15): -580 raise Exception('Error is 0.0') -581 labels = self.e_names -582 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 -583 fig1, ax1 = plt.subplots() -584 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) -585 ax1.axis('equal') -586 plt.draw() -587 -588 return dict(zip(self.e_names, sizes)) -589 -590 def dump(self, filename, datatype="json.gz", description="", **kwargs): -591 """Dump the Obs to a file 'name' of chosen format. -592 -593 Parameters -594 ---------- -595 filename : str -596 name of the file to be saved. -597 datatype : str -598 Format of the exported file. Supported formats include -599 "json.gz" and "pickle" -600 description : str -601 Description for output file, only relevant for json.gz format. -602 path : str -603 specifies a custom path for the file (default '.') -604 """ -605 if 'path' in kwargs: -606 file_name = kwargs.get('path') + '/' + filename -607 else: -608 file_name = filename -609 -610 if datatype == "json.gz": -611 from .input.json import dump_to_json -612 dump_to_json([self], file_name, description=description) -613 elif datatype == "pickle": -614 with open(file_name + '.p', 'wb') as fb: -615 pickle.dump(self, fb) -616 else: -617 raise Exception("Unknown datatype " + str(datatype)) -618 -619 def export_jackknife(self): -620 """Export jackknife samples from the Obs -621 -622 Returns -623 ------- -624 numpy.ndarray -625 Returns a numpy array of length N + 1 where N is the number of samples -626 for the given ensemble and replicum. The zeroth entry of the array contains -627 the mean value of the Obs, entries 1 to N contain the N jackknife samples -628 derived from the Obs. The current implementation only works for observables -629 defined on exactly one ensemble and replicum. The derived jackknife samples -630 should agree with samples from a full jackknife analysis up to O(1/N). -631 """ -632 -633 if len(self.names) != 1: -634 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") -635 -636 name = self.names[0] -637 full_data = self.deltas[name] + self.r_values[name] -638 n = full_data.size -639 mean = self.value -640 tmp_jacks = np.zeros(n + 1) -641 tmp_jacks[0] = mean -642 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) -643 return tmp_jacks -644 -645 def __float__(self): -646 return float(self.value) -647 -648 def __repr__(self): -649 return 'Obs[' + str(self) + ']' -650 -651 def __str__(self): -652 if self._dvalue == 0.0: -653 return str(self.value) -654 fexp = np.floor(np.log10(self._dvalue)) -655 if fexp < 0.0: -656 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') -657 elif fexp == 0.0: -658 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) -659 else: -660 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) -661 -662 # Overload comparisons -663 def __lt__(self, other): -664 return self.value < other -665 -666 def __le__(self, other): -667 return self.value <= other -668 -669 def __gt__(self, other): -670 return self.value > other -671 -672 def __ge__(self, other): -673 return self.value >= other -674 -675 def __eq__(self, other): -676 return (self - other).is_zero() -677 -678 def __ne__(self, other): -679 return not (self - other).is_zero() -680 -681 # Overload math operations -682 def __add__(self, y): -683 if isinstance(y, Obs): -684 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) -685 else: -686 if isinstance(y, np.ndarray): -687 return np.array([self + o for o in y]) -688 elif y.__class__.__name__ in ['Corr', 'CObs']: -689 return NotImplemented -690 else: -691 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) -692 -693 def __radd__(self, y): -694 return self + y -695 -696 def __mul__(self, y): -697 if isinstance(y, Obs): -698 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) -699 else: -700 if isinstance(y, np.ndarray): -701 return np.array([self * o for o in y]) -702 elif isinstance(y, complex): -703 return CObs(self * y.real, self * y.imag) -704 elif y.__class__.__name__ in ['Corr', 'CObs']: -705 return NotImplemented -706 else: -707 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) -708 -709 def __rmul__(self, y): -710 return self * y -711 -712 def __sub__(self, y): -713 if isinstance(y, Obs): -714 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) -715 else: -716 if isinstance(y, np.ndarray): -717 return np.array([self - o for o in y]) -718 elif y.__class__.__name__ in ['Corr', 'CObs']: -719 return NotImplemented -720 else: -721 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) -722 -723 def __rsub__(self, y): -724 return -1 * (self - y) -725 -726 def __pos__(self): -727 return self -728 -729 def __neg__(self): -730 return -1 * self -731 -732 def __truediv__(self, y): -733 if isinstance(y, Obs): -734 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) -735 else: -736 if isinstance(y, np.ndarray): -737 return np.array([self / o for o in y]) -738 elif y.__class__.__name__ in ['Corr', 'CObs']: -739 return NotImplemented -740 else: -741 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) -742 -743 def __rtruediv__(self, y): -744 if isinstance(y, Obs): -745 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) -746 else: -747 if isinstance(y, np.ndarray): -748 return np.array([o / self for o in y]) -749 elif y.__class__.__name__ in ['Corr', 'CObs']: -750 return NotImplemented -751 else: -752 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) -753 -754 def __pow__(self, y): -755 if isinstance(y, Obs): -756 return derived_observable(lambda x: x[0] ** x[1], [self, y]) -757 else: -758 return derived_observable(lambda x: x[0] ** y, [self]) -759 -760 def __rpow__(self, y): -761 if isinstance(y, Obs): -762 return derived_observable(lambda x: x[0] ** x[1], [y, self]) -763 else: -764 return derived_observable(lambda x: y ** x[0], [self]) -765 -766 def __abs__(self): -767 return derived_observable(lambda x: anp.abs(x[0]), [self]) -768 -769 # Overload numpy functions -770 def sqrt(self): -771 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) -772 -773 def log(self): -774 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) -775 -776 def exp(self): -777 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) -778 -779 def sin(self): -780 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) -781 -782 def cos(self): -783 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) -784 -785 def tan(self): -786 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) -787 -788 def arcsin(self): -789 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) -790 -791 def arccos(self): -792 return derived_observable(lambda x: anp.arccos(x[0]), [self]) -793 -794 def arctan(self): -795 return derived_observable(lambda x: anp.arctan(x[0]), [self]) -796 -797 def sinh(self): -798 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) -799 -800 def cosh(self): -801 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) -802 -803 def tanh(self): -804 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) -805 -806 def arcsinh(self): -807 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) -808 -809 def arccosh(self): -810 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) -811 -812 def arctanh(self): -813 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) +576 ensemble to the error and returns a dictionary containing the fractions. +577 +578 Parameters +579 ---------- +580 save : str +581 saves the figure to a file named 'save' if. +582 """ +583 if not hasattr(self, 'e_dvalue'): +584 raise Exception('Run the gamma method first.') +585 if np.isclose(0.0, self._dvalue, atol=1e-15): +586 raise Exception('Error is 0.0') +587 labels = self.e_names +588 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 +589 fig1, ax1 = plt.subplots() +590 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) +591 ax1.axis('equal') +592 plt.draw() +593 if save: +594 fig1.savefig(save) +595 +596 return dict(zip(self.e_names, sizes)) +597 +598 def dump(self, filename, datatype="json.gz", description="", **kwargs): +599 """Dump the Obs to a file 'name' of chosen format. +600 +601 Parameters +602 ---------- +603 filename : str +604 name of the file to be saved. +605 datatype : str +606 Format of the exported file. Supported formats include +607 "json.gz" and "pickle" +608 description : str +609 Description for output file, only relevant for json.gz format. +610 path : str +611 specifies a custom path for the file (default '.') +612 """ +613 if 'path' in kwargs: +614 file_name = kwargs.get('path') + '/' + filename +615 else: +616 file_name = filename +617 +618 if datatype == "json.gz": +619 from .input.json import dump_to_json +620 dump_to_json([self], file_name, description=description) +621 elif datatype == "pickle": +622 with open(file_name + '.p', 'wb') as fb: +623 pickle.dump(self, fb) +624 else: +625 raise Exception("Unknown datatype " + str(datatype)) +626 +627 def export_jackknife(self): +628 """Export jackknife samples from the Obs +629 +630 Returns +631 ------- +632 numpy.ndarray +633 Returns a numpy array of length N + 1 where N is the number of samples +634 for the given ensemble and replicum. The zeroth entry of the array contains +635 the mean value of the Obs, entries 1 to N contain the N jackknife samples +636 derived from the Obs. The current implementation only works for observables +637 defined on exactly one ensemble and replicum. The derived jackknife samples +638 should agree with samples from a full jackknife analysis up to O(1/N). +639 """ +640 +641 if len(self.names) != 1: +642 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") +643 +644 name = self.names[0] +645 full_data = self.deltas[name] + self.r_values[name] +646 n = full_data.size +647 mean = self.value +648 tmp_jacks = np.zeros(n + 1) +649 tmp_jacks[0] = mean +650 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) +651 return tmp_jacks +652 +653 def __float__(self): +654 return float(self.value) +655 +656 def __repr__(self): +657 return 'Obs[' + str(self) + ']' +658 +659 def __str__(self): +660 if self._dvalue == 0.0: +661 return str(self.value) +662 fexp = np.floor(np.log10(self._dvalue)) +663 if fexp < 0.0: +664 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') +665 elif fexp == 0.0: +666 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) +667 else: +668 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) +669 +670 # Overload comparisons +671 def __lt__(self, other): +672 return self.value < other +673 +674 def __le__(self, other): +675 return self.value <= other +676 +677 def __gt__(self, other): +678 return self.value > other +679 +680 def __ge__(self, other): +681 return self.value >= other +682 +683 def __eq__(self, other): +684 return (self - other).is_zero() +685 +686 def __ne__(self, other): +687 return not (self - other).is_zero() +688 +689 # Overload math operations +690 def __add__(self, y): +691 if isinstance(y, Obs): +692 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) +693 else: +694 if isinstance(y, np.ndarray): +695 return np.array([self + o for o in y]) +696 elif y.__class__.__name__ in ['Corr', 'CObs']: +697 return NotImplemented +698 else: +699 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) +700 +701 def __radd__(self, y): +702 return self + y +703 +704 def __mul__(self, y): +705 if isinstance(y, Obs): +706 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) +707 else: +708 if isinstance(y, np.ndarray): +709 return np.array([self * o for o in y]) +710 elif isinstance(y, complex): +711 return CObs(self * y.real, self * y.imag) +712 elif y.__class__.__name__ in ['Corr', 'CObs']: +713 return NotImplemented +714 else: +715 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) +716 +717 def __rmul__(self, y): +718 return self * y +719 +720 def __sub__(self, y): +721 if isinstance(y, Obs): +722 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) +723 else: +724 if isinstance(y, np.ndarray): +725 return np.array([self - o for o in y]) +726 elif y.__class__.__name__ in ['Corr', 'CObs']: +727 return NotImplemented +728 else: +729 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) +730 +731 def __rsub__(self, y): +732 return -1 * (self - y) +733 +734 def __pos__(self): +735 return self +736 +737 def __neg__(self): +738 return -1 * self +739 +740 def __truediv__(self, y): +741 if isinstance(y, Obs): +742 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) +743 else: +744 if isinstance(y, np.ndarray): +745 return np.array([self / o for o in y]) +746 elif y.__class__.__name__ in ['Corr', 'CObs']: +747 return NotImplemented +748 else: +749 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) +750 +751 def __rtruediv__(self, y): +752 if isinstance(y, Obs): +753 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) +754 else: +755 if isinstance(y, np.ndarray): +756 return np.array([o / self for o in y]) +757 elif y.__class__.__name__ in ['Corr', 'CObs']: +758 return NotImplemented +759 else: +760 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) +761 +762 def __pow__(self, y): +763 if isinstance(y, Obs): +764 return derived_observable(lambda x: x[0] ** x[1], [self, y]) +765 else: +766 return derived_observable(lambda x: x[0] ** y, [self]) +767 +768 def __rpow__(self, y): +769 if isinstance(y, Obs): +770 return derived_observable(lambda x: x[0] ** x[1], [y, self]) +771 else: +772 return derived_observable(lambda x: y ** x[0], [self]) +773 +774 def __abs__(self): +775 return derived_observable(lambda x: anp.abs(x[0]), [self]) +776 +777 # Overload numpy functions +778 def sqrt(self): +779 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) +780 +781 def log(self): +782 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) +783 +784 def exp(self): +785 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) +786 +787 def sin(self): +788 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) +789 +790 def cos(self): +791 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) +792 +793 def tan(self): +794 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) +795 +796 def arcsin(self): +797 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) +798 +799 def arccos(self): +800 return derived_observable(lambda x: anp.arccos(x[0]), [self]) +801 +802 def arctan(self): +803 return derived_observable(lambda x: anp.arctan(x[0]), [self]) +804 +805 def sinh(self): +806 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) +807 +808 def cosh(self): +809 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) +810 +811 def tanh(self): +812 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) +813 +814 def arcsinh(self): +815 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) +816 +817 def arccosh(self): +818 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) +819 +820 def arctanh(self): +821 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) @@ -3660,32 +3676,47 @@ show expanded history for irregular Monte Carlo chains (default: True). def - plot_piechart(self): + plot_piechart(self, save=None):
View Source - 
574    def plot_piechart(self):
+            
574    def plot_piechart(self, save=None):
 575        """Plot piechart which shows the fractional contribution of each
-576        ensemble to the error and returns a dictionary containing the fractions."""
-577        if not hasattr(self, 'e_dvalue'):
-578            raise Exception('Run the gamma method first.')
-579        if np.isclose(0.0, self._dvalue, atol=1e-15):
-580            raise Exception('Error is 0.0')
-581        labels = self.e_names
-582        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
-583        fig1, ax1 = plt.subplots()
-584        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
-585        ax1.axis('equal')
-586        plt.draw()
-587
-588        return dict(zip(self.e_names, sizes))
+576        ensemble to the error and returns a dictionary containing the fractions.
+577
+578        Parameters
+579        ----------
+580        save : str
+581            saves the figure to a file named 'save' if.
+582        """
+583        if not hasattr(self, 'e_dvalue'):
+584            raise Exception('Run the gamma method first.')
+585        if np.isclose(0.0, self._dvalue, atol=1e-15):
+586            raise Exception('Error is 0.0')
+587        labels = self.e_names
+588        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
+589        fig1, ax1 = plt.subplots()
+590        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
+591        ax1.axis('equal')
+592        plt.draw()
+593        if save:
+594            fig1.savefig(save)
+595
+596        return dict(zip(self.e_names, sizes))

Plot piechart which shows the fractional contribution of each ensemble to the error and returns a dictionary containing the fractions.

+ +
Parameters
+ +
@@ -3700,34 +3731,34 @@ ensemble to the error and returns a dictionary containing the fractions.

View Source - 
590    def dump(self, filename, datatype="json.gz", description="", **kwargs):
-591        """Dump the Obs to a file 'name' of chosen format.
-592
-593        Parameters
-594        ----------
-595        filename : str
-596            name of the file to be saved.
-597        datatype : str
-598            Format of the exported file. Supported formats include
-599            "json.gz" and "pickle"
-600        description : str
-601            Description for output file, only relevant for json.gz format.
-602        path : str
-603            specifies a custom path for the file (default '.')
-604        """
-605        if 'path' in kwargs:
-606            file_name = kwargs.get('path') + '/' + filename
-607        else:
-608            file_name = filename
-609
-610        if datatype == "json.gz":
-611            from .input.json import dump_to_json
-612            dump_to_json([self], file_name, description=description)
-613        elif datatype == "pickle":
-614            with open(file_name + '.p', 'wb') as fb:
-615                pickle.dump(self, fb)
-616        else:
-617            raise Exception("Unknown datatype " + str(datatype))
+            
598    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+599        """Dump the Obs to a file 'name' of chosen format.
+600
+601        Parameters
+602        ----------
+603        filename : str
+604            name of the file to be saved.
+605        datatype : str
+606            Format of the exported file. Supported formats include
+607            "json.gz" and "pickle"
+608        description : str
+609            Description for output file, only relevant for json.gz format.
+610        path : str
+611            specifies a custom path for the file (default '.')
+612        """
+613        if 'path' in kwargs:
+614            file_name = kwargs.get('path') + '/' + filename
+615        else:
+616            file_name = filename
+617
+618        if datatype == "json.gz":
+619            from .input.json import dump_to_json
+620            dump_to_json([self], file_name, description=description)
+621        elif datatype == "pickle":
+622            with open(file_name + '.p', 'wb') as fb:
+623                pickle.dump(self, fb)
+624        else:
+625            raise Exception("Unknown datatype " + str(datatype))
@@ -3761,31 +3792,31 @@ specifies a custom path for the file (default '.')
View Source - 
619    def export_jackknife(self):
-620        """Export jackknife samples from the Obs
-621
-622        Returns
-623        -------
-624        numpy.ndarray
-625            Returns a numpy array of length N + 1 where N is the number of samples
-626            for the given ensemble and replicum. The zeroth entry of the array contains
-627            the mean value of the Obs, entries 1 to N contain the N jackknife samples
-628            derived from the Obs. The current implementation only works for observables
-629            defined on exactly one ensemble and replicum. The derived jackknife samples
-630            should agree with samples from a full jackknife analysis up to O(1/N).
-631        """
-632
-633        if len(self.names) != 1:
-634            raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
-635
-636        name = self.names[0]
-637        full_data = self.deltas[name] + self.r_values[name]
-638        n = full_data.size
-639        mean = self.value
-640        tmp_jacks = np.zeros(n + 1)
-641        tmp_jacks[0] = mean
-642        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
-643        return tmp_jacks
+            
627    def export_jackknife(self):
+628        """Export jackknife samples from the Obs
+629
+630        Returns
+631        -------
+632        numpy.ndarray
+633            Returns a numpy array of length N + 1 where N is the number of samples
+634            for the given ensemble and replicum. The zeroth entry of the array contains
+635            the mean value of the Obs, entries 1 to N contain the N jackknife samples
+636            derived from the Obs. The current implementation only works for observables
+637            defined on exactly one ensemble and replicum. The derived jackknife samples
+638            should agree with samples from a full jackknife analysis up to O(1/N).
+639        """
+640
+641        if len(self.names) != 1:
+642            raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
+643
+644        name = self.names[0]
+645        full_data = self.deltas[name] + self.r_values[name]
+646        n = full_data.size
+647        mean = self.value
+648        tmp_jacks = np.zeros(n + 1)
+649        tmp_jacks[0] = mean
+650        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
+651        return tmp_jacks
@@ -3816,8 +3847,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
770    def sqrt(self):
-771        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
+            
778    def sqrt(self):
+779        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
@@ -3835,8 +3866,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
773    def log(self):
-774        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
+            
781    def log(self):
+782        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
@@ -3854,8 +3885,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
776    def exp(self):
-777        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
+            
784    def exp(self):
+785        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
@@ -3873,8 +3904,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
779    def sin(self):
-780        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
+            
787    def sin(self):
+788        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
@@ -3892,8 +3923,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
782    def cos(self):
-783        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
+            
790    def cos(self):
+791        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
@@ -3911,8 +3942,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
785    def tan(self):
-786        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
+            
793    def tan(self):
+794        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
@@ -3930,8 +3961,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
788    def arcsin(self):
-789        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
+            
796    def arcsin(self):
+797        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
@@ -3949,8 +3980,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
791    def arccos(self):
-792        return derived_observable(lambda x: anp.arccos(x[0]), [self])
+            
799    def arccos(self):
+800        return derived_observable(lambda x: anp.arccos(x[0]), [self])
@@ -3968,8 +3999,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
794    def arctan(self):
-795        return derived_observable(lambda x: anp.arctan(x[0]), [self])
+            
802    def arctan(self):
+803        return derived_observable(lambda x: anp.arctan(x[0]), [self])
@@ -3987,8 +4018,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
797    def sinh(self):
-798        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
+            
805    def sinh(self):
+806        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
@@ -4006,8 +4037,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
800    def cosh(self):
-801        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
+            
808    def cosh(self):
+809        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
@@ -4025,8 +4056,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
803    def tanh(self):
-804        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
+            
811    def tanh(self):
+812        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
@@ -4044,8 +4075,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
806    def arcsinh(self):
-807        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
+            
814    def arcsinh(self):
+815        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
@@ -4063,8 +4094,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
809    def arccosh(self):
-810        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
+            
817    def arccosh(self):
+818        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
@@ -4082,8 +4113,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
812    def arctanh(self):
-813        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
+            
820    def arctanh(self):
+821        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
@@ -4223,115 +4254,115 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
816class CObs:
-817    """Class for a complex valued observable."""
-818    __slots__ = ['_real', '_imag', 'tag']
-819
-820    def __init__(self, real, imag=0.0):
-821        self._real = real
-822        self._imag = imag
-823        self.tag = None
-824
-825    @property
-826    def real(self):
-827        return self._real
-828
-829    @property
-830    def imag(self):
-831        return self._imag
+            
824class CObs:
+825    """Class for a complex valued observable."""
+826    __slots__ = ['_real', '_imag', 'tag']
+827
+828    def __init__(self, real, imag=0.0):
+829        self._real = real
+830        self._imag = imag
+831        self.tag = None
 832
-833    def gamma_method(self, **kwargs):
-834        """Executes the gamma_method for the real and the imaginary part."""
-835        if isinstance(self.real, Obs):
-836            self.real.gamma_method(**kwargs)
-837        if isinstance(self.imag, Obs):
-838            self.imag.gamma_method(**kwargs)
-839
-840    def is_zero(self):
-841        """Checks whether both real and imaginary part are zero within machine precision."""
-842        return self.real == 0.0 and self.imag == 0.0
-843
-844    def conjugate(self):
-845        return CObs(self.real, -self.imag)
-846
-847    def __add__(self, other):
-848        if isinstance(other, np.ndarray):
-849            return other + self
-850        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-851            return CObs(self.real + other.real,
-852                        self.imag + other.imag)
-853        else:
-854            return CObs(self.real + other, self.imag)
-855
-856    def __radd__(self, y):
-857        return self + y
-858
-859    def __sub__(self, other):
-860        if isinstance(other, np.ndarray):
-861            return -1 * (other - self)
-862        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-863            return CObs(self.real - other.real, self.imag - other.imag)
-864        else:
-865            return CObs(self.real - other, self.imag)
+833    @property
+834    def real(self):
+835        return self._real
+836
+837    @property
+838    def imag(self):
+839        return self._imag
+840
+841    def gamma_method(self, **kwargs):
+842        """Executes the gamma_method for the real and the imaginary part."""
+843        if isinstance(self.real, Obs):
+844            self.real.gamma_method(**kwargs)
+845        if isinstance(self.imag, Obs):
+846            self.imag.gamma_method(**kwargs)
+847
+848    def is_zero(self):
+849        """Checks whether both real and imaginary part are zero within machine precision."""
+850        return self.real == 0.0 and self.imag == 0.0
+851
+852    def conjugate(self):
+853        return CObs(self.real, -self.imag)
+854
+855    def __add__(self, other):
+856        if isinstance(other, np.ndarray):
+857            return other + self
+858        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+859            return CObs(self.real + other.real,
+860                        self.imag + other.imag)
+861        else:
+862            return CObs(self.real + other, self.imag)
+863
+864    def __radd__(self, y):
+865        return self + y
 866
-867    def __rsub__(self, other):
-868        return -1 * (self - other)
-869
-870    def __mul__(self, other):
-871        if isinstance(other, np.ndarray):
-872            return other * self
-873        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-874            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
-875                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
-876                                               [self.real, other.real, self.imag, other.imag],
-877                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
-878                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
-879                                               [self.real, other.real, self.imag, other.imag],
-880                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
-881            elif getattr(other, 'imag', 0) != 0:
-882                return CObs(self.real * other.real - self.imag * other.imag,
-883                            self.imag * other.real + self.real * other.imag)
-884            else:
-885                return CObs(self.real * other.real, self.imag * other.real)
-886        else:
-887            return CObs(self.real * other, self.imag * other)
-888
-889    def __rmul__(self, other):
-890        return self * other
-891
-892    def __truediv__(self, other):
-893        if isinstance(other, np.ndarray):
-894            return 1 / (other / self)
-895        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-896            r = other.real ** 2 + other.imag ** 2
-897            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
-898        else:
-899            return CObs(self.real / other, self.imag / other)
-900
-901    def __rtruediv__(self, other):
-902        r = self.real ** 2 + self.imag ** 2
-903        if hasattr(other, 'real') and hasattr(other, 'imag'):
-904            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
-905        else:
-906            return CObs(self.real * other / r, -self.imag * other / r)
-907
-908    def __abs__(self):
-909        return np.sqrt(self.real**2 + self.imag**2)
-910
-911    def __pos__(self):
-912        return self
-913
-914    def __neg__(self):
-915        return -1 * self
-916
-917    def __eq__(self, other):
-918        return self.real == other.real and self.imag == other.imag
-919
-920    def __str__(self):
-921        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
-922
-923    def __repr__(self):
-924        return 'CObs[' + str(self) + ']'
+867    def __sub__(self, other):
+868        if isinstance(other, np.ndarray):
+869            return -1 * (other - self)
+870        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+871            return CObs(self.real - other.real, self.imag - other.imag)
+872        else:
+873            return CObs(self.real - other, self.imag)
+874
+875    def __rsub__(self, other):
+876        return -1 * (self - other)
+877
+878    def __mul__(self, other):
+879        if isinstance(other, np.ndarray):
+880            return other * self
+881        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+882            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
+883                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
+884                                               [self.real, other.real, self.imag, other.imag],
+885                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
+886                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
+887                                               [self.real, other.real, self.imag, other.imag],
+888                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
+889            elif getattr(other, 'imag', 0) != 0:
+890                return CObs(self.real * other.real - self.imag * other.imag,
+891                            self.imag * other.real + self.real * other.imag)
+892            else:
+893                return CObs(self.real * other.real, self.imag * other.real)
+894        else:
+895            return CObs(self.real * other, self.imag * other)
+896
+897    def __rmul__(self, other):
+898        return self * other
+899
+900    def __truediv__(self, other):
+901        if isinstance(other, np.ndarray):
+902            return 1 / (other / self)
+903        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+904            r = other.real ** 2 + other.imag ** 2
+905            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
+906        else:
+907            return CObs(self.real / other, self.imag / other)
+908
+909    def __rtruediv__(self, other):
+910        r = self.real ** 2 + self.imag ** 2
+911        if hasattr(other, 'real') and hasattr(other, 'imag'):
+912            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
+913        else:
+914            return CObs(self.real * other / r, -self.imag * other / r)
+915
+916    def __abs__(self):
+917        return np.sqrt(self.real**2 + self.imag**2)
+918
+919    def __pos__(self):
+920        return self
+921
+922    def __neg__(self):
+923        return -1 * self
+924
+925    def __eq__(self, other):
+926        return self.real == other.real and self.imag == other.imag
+927
+928    def __str__(self):
+929        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
+930
+931    def __repr__(self):
+932        return 'CObs[' + str(self) + ']'
@@ -4349,10 +4380,10 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
820    def __init__(self, real, imag=0.0):
-821        self._real = real
-822        self._imag = imag
-823        self.tag = None
+            
828    def __init__(self, real, imag=0.0):
+829        self._real = real
+830        self._imag = imag
+831        self.tag = None
@@ -4400,12 +4431,12 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
833    def gamma_method(self, **kwargs):
-834        """Executes the gamma_method for the real and the imaginary part."""
-835        if isinstance(self.real, Obs):
-836            self.real.gamma_method(**kwargs)
-837        if isinstance(self.imag, Obs):
-838            self.imag.gamma_method(**kwargs)
+            
841    def gamma_method(self, **kwargs):
+842        """Executes the gamma_method for the real and the imaginary part."""
+843        if isinstance(self.real, Obs):
+844            self.real.gamma_method(**kwargs)
+845        if isinstance(self.imag, Obs):
+846            self.imag.gamma_method(**kwargs)
@@ -4425,9 +4456,9 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
840    def is_zero(self):
-841        """Checks whether both real and imaginary part are zero within machine precision."""
-842        return self.real == 0.0 and self.imag == 0.0
+            
848    def is_zero(self):
+849        """Checks whether both real and imaginary part are zero within machine precision."""
+850        return self.real == 0.0 and self.imag == 0.0
@@ -4447,8 +4478,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
844    def conjugate(self):
-845        return CObs(self.real, -self.imag)
+            
852    def conjugate(self):
+853        return CObs(self.real, -self.imag)
@@ -4467,184 +4498,184 @@ should agree with samples from a full jackknife analysis up to O(1/N).
View Source - 
1032def derived_observable(func, data, array_mode=False, **kwargs):
-1033    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
-1034
-1035    Parameters
-1036    ----------
-1037    func : object
-1038        arbitrary function of the form func(data, **kwargs). For the
-1039        automatic differentiation to work, all numpy functions have to have
-1040        the autograd wrapper (use 'import autograd.numpy as anp').
-1041    data : list
-1042        list of Obs, e.g. [obs1, obs2, obs3].
-1043    num_grad : bool
-1044        if True, numerical derivatives are used instead of autograd
-1045        (default False). To control the numerical differentiation the
-1046        kwargs of numdifftools.step_generators.MaxStepGenerator
-1047        can be used.
-1048    man_grad : list
-1049        manually supply a list or an array which contains the jacobian
-1050        of func. Use cautiously, supplying the wrong derivative will
-1051        not be intercepted.
-1052
-1053    Notes
-1054    -----
-1055    For simple mathematical operations it can be practical to use anonymous
-1056    functions. For the ratio of two observables one can e.g. use
-1057
-1058    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
-1059    """
+            
1040def derived_observable(func, data, array_mode=False, **kwargs):
+1041    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
+1042
+1043    Parameters
+1044    ----------
+1045    func : object
+1046        arbitrary function of the form func(data, **kwargs). For the
+1047        automatic differentiation to work, all numpy functions have to have
+1048        the autograd wrapper (use 'import autograd.numpy as anp').
+1049    data : list
+1050        list of Obs, e.g. [obs1, obs2, obs3].
+1051    num_grad : bool
+1052        if True, numerical derivatives are used instead of autograd
+1053        (default False). To control the numerical differentiation the
+1054        kwargs of numdifftools.step_generators.MaxStepGenerator
+1055        can be used.
+1056    man_grad : list
+1057        manually supply a list or an array which contains the jacobian
+1058        of func. Use cautiously, supplying the wrong derivative will
+1059        not be intercepted.
 1060
-1061    data = np.asarray(data)
-1062    raveled_data = data.ravel()
-1063
-1064    # Workaround for matrix operations containing non Obs data
-1065    if not all(isinstance(x, Obs) for x in raveled_data):
-1066        for i in range(len(raveled_data)):
-1067            if isinstance(raveled_data[i], (int, float)):
-1068                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
-1069
-1070    allcov = {}
-1071    for o in raveled_data:
-1072        for name in o.cov_names:
-1073            if name in allcov:
-1074                if not np.allclose(allcov[name], o.covobs[name].cov):
-1075                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
-1076            else:
-1077                allcov[name] = o.covobs[name].cov
-1078
-1079    n_obs = len(raveled_data)
-1080    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
-1081    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
-1082    new_sample_names = sorted(set(new_names) - set(new_cov_names))
-1083
-1084    is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names}
-1085    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1061    Notes
+1062    -----
+1063    For simple mathematical operations it can be practical to use anonymous
+1064    functions. For the ratio of two observables one can e.g. use
+1065
+1066    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
+1067    """
+1068
+1069    data = np.asarray(data)
+1070    raveled_data = data.ravel()
+1071
+1072    # Workaround for matrix operations containing non Obs data
+1073    if not all(isinstance(x, Obs) for x in raveled_data):
+1074        for i in range(len(raveled_data)):
+1075            if isinstance(raveled_data[i], (int, float)):
+1076                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
+1077
+1078    allcov = {}
+1079    for o in raveled_data:
+1080        for name in o.cov_names:
+1081            if name in allcov:
+1082                if not np.allclose(allcov[name], o.covobs[name].cov):
+1083                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
+1084            else:
+1085                allcov[name] = o.covobs[name].cov
 1086
-1087    if data.ndim == 1:
-1088        values = np.array([o.value for o in data])
-1089    else:
-1090        values = np.vectorize(lambda x: x.value)(data)
+1087    n_obs = len(raveled_data)
+1088    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
+1089    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
+1090    new_sample_names = sorted(set(new_names) - set(new_cov_names))
 1091
-1092    new_values = func(values, **kwargs)
-1093
-1094    multi = int(isinstance(new_values, np.ndarray))
-1095
-1096    new_r_values = {}
-1097    new_idl_d = {}
-1098    for name in new_sample_names:
-1099        idl = []
-1100        tmp_values = np.zeros(n_obs)
-1101        for i, item in enumerate(raveled_data):
-1102            tmp_values[i] = item.r_values.get(name, item.value)
-1103            tmp_idl = item.idl.get(name)
-1104            if tmp_idl is not None:
-1105                idl.append(tmp_idl)
-1106        if multi > 0:
-1107            tmp_values = np.array(tmp_values).reshape(data.shape)
-1108        new_r_values[name] = func(tmp_values, **kwargs)
-1109        new_idl_d[name] = _merge_idx(idl)
-1110        if not is_merged[name]:
-1111            is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]])))
-1112
-1113    if 'man_grad' in kwargs:
-1114        deriv = np.asarray(kwargs.get('man_grad'))
-1115        if new_values.shape + data.shape != deriv.shape:
-1116            raise Exception('Manual derivative does not have correct shape.')
-1117    elif kwargs.get('num_grad') is True:
-1118        if multi > 0:
-1119            raise Exception('Multi mode currently not supported for numerical derivative')
-1120        options = {
-1121            'base_step': 0.1,
-1122            'step_ratio': 2.5}
-1123        for key in options.keys():
-1124            kwarg = kwargs.get(key)
-1125            if kwarg is not None:
-1126                options[key] = kwarg
-1127        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
-1128        if tmp_df.size == 1:
-1129            deriv = np.array([tmp_df.real])
-1130        else:
-1131            deriv = tmp_df.real
-1132    else:
-1133        deriv = jacobian(func)(values, **kwargs)
-1134
-1135    final_result = np.zeros(new_values.shape, dtype=object)
-1136
-1137    if array_mode is True:
-1138
-1139        class _Zero_grad():
-1140            def __init__(self, N):
-1141                self.grad = np.zeros((N, 1))
+1092    is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names}
+1093    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1094
+1095    if data.ndim == 1:
+1096        values = np.array([o.value for o in data])
+1097    else:
+1098        values = np.vectorize(lambda x: x.value)(data)
+1099
+1100    new_values = func(values, **kwargs)
+1101
+1102    multi = int(isinstance(new_values, np.ndarray))
+1103
+1104    new_r_values = {}
+1105    new_idl_d = {}
+1106    for name in new_sample_names:
+1107        idl = []
+1108        tmp_values = np.zeros(n_obs)
+1109        for i, item in enumerate(raveled_data):
+1110            tmp_values[i] = item.r_values.get(name, item.value)
+1111            tmp_idl = item.idl.get(name)
+1112            if tmp_idl is not None:
+1113                idl.append(tmp_idl)
+1114        if multi > 0:
+1115            tmp_values = np.array(tmp_values).reshape(data.shape)
+1116        new_r_values[name] = func(tmp_values, **kwargs)
+1117        new_idl_d[name] = _merge_idx(idl)
+1118        if not is_merged[name]:
+1119            is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]])))
+1120
+1121    if 'man_grad' in kwargs:
+1122        deriv = np.asarray(kwargs.get('man_grad'))
+1123        if new_values.shape + data.shape != deriv.shape:
+1124            raise Exception('Manual derivative does not have correct shape.')
+1125    elif kwargs.get('num_grad') is True:
+1126        if multi > 0:
+1127            raise Exception('Multi mode currently not supported for numerical derivative')
+1128        options = {
+1129            'base_step': 0.1,
+1130            'step_ratio': 2.5}
+1131        for key in options.keys():
+1132            kwarg = kwargs.get(key)
+1133            if kwarg is not None:
+1134                options[key] = kwarg
+1135        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
+1136        if tmp_df.size == 1:
+1137            deriv = np.array([tmp_df.real])
+1138        else:
+1139            deriv = tmp_df.real
+1140    else:
+1141        deriv = jacobian(func)(values, **kwargs)
 1142
-1143        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
-1144        d_extracted = {}
-1145        g_extracted = {}
-1146        for name in new_sample_names:
-1147            d_extracted[name] = []
-1148            ens_length = len(new_idl_d[name])
-1149            for i_dat, dat in enumerate(data):
-1150                d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
-1151        for name in new_cov_names:
-1152            g_extracted[name] = []
-1153            zero_grad = _Zero_grad(new_covobs_lengths[name])
-1154            for i_dat, dat in enumerate(data):
-1155                g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1)))
-1156
-1157    for i_val, new_val in np.ndenumerate(new_values):
-1158        new_deltas = {}
-1159        new_grad = {}
-1160        if array_mode is True:
-1161            for name in new_sample_names:
-1162                ens_length = d_extracted[name][0].shape[-1]
-1163                new_deltas[name] = np.zeros(ens_length)
-1164                for i_dat, dat in enumerate(d_extracted[name]):
-1165                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1166            for name in new_cov_names:
-1167                new_grad[name] = 0
-1168                for i_dat, dat in enumerate(g_extracted[name]):
-1169                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1170        else:
-1171            for j_obs, obs in np.ndenumerate(data):
-1172                for name in obs.names:
-1173                    if name in obs.cov_names:
-1174                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
-1175                    else:
-1176                        new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name])
-1177
-1178        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
-1179
-1180        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
-1181            raise Exception('The same name has been used for deltas and covobs!')
-1182        new_samples = []
-1183        new_means = []
-1184        new_idl = []
-1185        new_names_obs = []
-1186        for name in new_names:
-1187            if name not in new_covobs:
-1188                if is_merged[name]:
-1189                    filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name])
-1190                else:
-1191                    filtered_deltas = new_deltas[name]
-1192                    filtered_idl_d = new_idl_d[name]
-1193
-1194                new_samples.append(filtered_deltas)
-1195                new_idl.append(filtered_idl_d)
-1196                new_means.append(new_r_values[name][i_val])
-1197                new_names_obs.append(name)
-1198        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
-1199        for name in new_covobs:
-1200            final_result[i_val].names.append(name)
-1201        final_result[i_val]._covobs = new_covobs
-1202        final_result[i_val]._value = new_val
-1203        final_result[i_val].is_merged = is_merged
-1204        final_result[i_val].reweighted = reweighted
-1205
-1206    if multi == 0:
-1207        final_result = final_result.item()
-1208
-1209    return final_result
+1143    final_result = np.zeros(new_values.shape, dtype=object)
+1144
+1145    if array_mode is True:
+1146
+1147        class _Zero_grad():
+1148            def __init__(self, N):
+1149                self.grad = np.zeros((N, 1))
+1150
+1151        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
+1152        d_extracted = {}
+1153        g_extracted = {}
+1154        for name in new_sample_names:
+1155            d_extracted[name] = []
+1156            ens_length = len(new_idl_d[name])
+1157            for i_dat, dat in enumerate(data):
+1158                d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
+1159        for name in new_cov_names:
+1160            g_extracted[name] = []
+1161            zero_grad = _Zero_grad(new_covobs_lengths[name])
+1162            for i_dat, dat in enumerate(data):
+1163                g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1)))
+1164
+1165    for i_val, new_val in np.ndenumerate(new_values):
+1166        new_deltas = {}
+1167        new_grad = {}
+1168        if array_mode is True:
+1169            for name in new_sample_names:
+1170                ens_length = d_extracted[name][0].shape[-1]
+1171                new_deltas[name] = np.zeros(ens_length)
+1172                for i_dat, dat in enumerate(d_extracted[name]):
+1173                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1174            for name in new_cov_names:
+1175                new_grad[name] = 0
+1176                for i_dat, dat in enumerate(g_extracted[name]):
+1177                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1178        else:
+1179            for j_obs, obs in np.ndenumerate(data):
+1180                for name in obs.names:
+1181                    if name in obs.cov_names:
+1182                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
+1183                    else:
+1184                        new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name])
+1185
+1186        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1187
+1188        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
+1189            raise Exception('The same name has been used for deltas and covobs!')
+1190        new_samples = []
+1191        new_means = []
+1192        new_idl = []
+1193        new_names_obs = []
+1194        for name in new_names:
+1195            if name not in new_covobs:
+1196                if is_merged[name]:
+1197                    filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name])
+1198                else:
+1199                    filtered_deltas = new_deltas[name]
+1200                    filtered_idl_d = new_idl_d[name]
+1201
+1202                new_samples.append(filtered_deltas)
+1203                new_idl.append(filtered_idl_d)
+1204                new_means.append(new_r_values[name][i_val])
+1205                new_names_obs.append(name)
+1206        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
+1207        for name in new_covobs:
+1208            final_result[i_val].names.append(name)
+1209        final_result[i_val]._covobs = new_covobs
+1210        final_result[i_val]._value = new_val
+1211        final_result[i_val].is_merged = is_merged
+1212        final_result[i_val].reweighted = reweighted
+1213
+1214    if multi == 0:
+1215        final_result = final_result.item()
+1216
+1217    return final_result
@@ -4691,47 +4722,47 @@ functions. For the ratio of two observables one can e.g. use

View Source - 
1249def reweight(weight, obs, **kwargs):
-1250    """Reweight a list of observables.
-1251
-1252    Parameters
-1253    ----------
-1254    weight : Obs
-1255        Reweighting factor. An Observable that has to be defined on a superset of the
-1256        configurations in obs[i].idl for all i.
-1257    obs : list
-1258        list of Obs, e.g. [obs1, obs2, obs3].
-1259    all_configs : bool
-1260        if True, the reweighted observables are normalized by the average of
-1261        the reweighting factor on all configurations in weight.idl and not
-1262        on the configurations in obs[i].idl.
-1263    """
-1264    result = []
-1265    for i in range(len(obs)):
-1266        if len(obs[i].cov_names):
-1267            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
-1268        if not set(obs[i].names).issubset(weight.names):
-1269            raise Exception('Error: Ensembles do not fit')
-1270        for name in obs[i].names:
-1271            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
-1272                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
-1273        new_samples = []
-1274        w_deltas = {}
-1275        for name in sorted(obs[i].names):
-1276            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
-1277            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
-1278        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1279
-1280        if kwargs.get('all_configs'):
-1281            new_weight = weight
-1282        else:
-1283            new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1284
-1285        result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs))
-1286        result[-1].reweighted = True
-1287        result[-1].is_merged = obs[i].is_merged
-1288
-1289    return result
+            
1257def reweight(weight, obs, **kwargs):
+1258    """Reweight a list of observables.
+1259
+1260    Parameters
+1261    ----------
+1262    weight : Obs
+1263        Reweighting factor. An Observable that has to be defined on a superset of the
+1264        configurations in obs[i].idl for all i.
+1265    obs : list
+1266        list of Obs, e.g. [obs1, obs2, obs3].
+1267    all_configs : bool
+1268        if True, the reweighted observables are normalized by the average of
+1269        the reweighting factor on all configurations in weight.idl and not
+1270        on the configurations in obs[i].idl.
+1271    """
+1272    result = []
+1273    for i in range(len(obs)):
+1274        if len(obs[i].cov_names):
+1275            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
+1276        if not set(obs[i].names).issubset(weight.names):
+1277            raise Exception('Error: Ensembles do not fit')
+1278        for name in obs[i].names:
+1279            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
+1280                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
+1281        new_samples = []
+1282        w_deltas = {}
+1283        for name in sorted(obs[i].names):
+1284            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
+1285            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
+1286        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1287
+1288        if kwargs.get('all_configs'):
+1289            new_weight = weight
+1290        else:
+1291            new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1292
+1293        result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs))
+1294        result[-1].reweighted = True
+1295        result[-1].is_merged = obs[i].is_merged
+1296
+1297    return result
@@ -4765,48 +4796,48 @@ on the configurations in obs[i].idl.
View Source - 
1292def correlate(obs_a, obs_b):
-1293    """Correlate two observables.
-1294
-1295    Parameters
-1296    ----------
-1297    obs_a : Obs
-1298        First observable
-1299    obs_b : Obs
-1300        Second observable
-1301
-1302    Notes
-1303    -----
-1304    Keep in mind to only correlate primary observables which have not been reweighted
-1305    yet. The reweighting has to be applied after correlating the observables.
-1306    Currently only works if ensembles are identical (this is not strictly necessary).
-1307    """
-1308
-1309    if sorted(obs_a.names) != sorted(obs_b.names):
-1310        raise Exception('Ensembles do not fit')
-1311    if len(obs_a.cov_names) or len(obs_b.cov_names):
-1312        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
-1313    for name in obs_a.names:
-1314        if obs_a.shape[name] != obs_b.shape[name]:
-1315            raise Exception('Shapes of ensemble', name, 'do not fit')
-1316        if obs_a.idl[name] != obs_b.idl[name]:
-1317            raise Exception('idl of ensemble', name, 'do not fit')
-1318
-1319    if obs_a.reweighted is True:
-1320        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
-1321    if obs_b.reweighted is True:
-1322        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
-1323
-1324    new_samples = []
-1325    new_idl = []
-1326    for name in sorted(obs_a.names):
-1327        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
-1328        new_idl.append(obs_a.idl[name])
-1329
-1330    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
-1331    o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names}
-1332    o.reweighted = obs_a.reweighted or obs_b.reweighted
-1333    return o
+            
1300def correlate(obs_a, obs_b):
+1301    """Correlate two observables.
+1302
+1303    Parameters
+1304    ----------
+1305    obs_a : Obs
+1306        First observable
+1307    obs_b : Obs
+1308        Second observable
+1309
+1310    Notes
+1311    -----
+1312    Keep in mind to only correlate primary observables which have not been reweighted
+1313    yet. The reweighting has to be applied after correlating the observables.
+1314    Currently only works if ensembles are identical (this is not strictly necessary).
+1315    """
+1316
+1317    if sorted(obs_a.names) != sorted(obs_b.names):
+1318        raise Exception('Ensembles do not fit')
+1319    if len(obs_a.cov_names) or len(obs_b.cov_names):
+1320        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
+1321    for name in obs_a.names:
+1322        if obs_a.shape[name] != obs_b.shape[name]:
+1323            raise Exception('Shapes of ensemble', name, 'do not fit')
+1324        if obs_a.idl[name] != obs_b.idl[name]:
+1325            raise Exception('idl of ensemble', name, 'do not fit')
+1326
+1327    if obs_a.reweighted is True:
+1328        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
+1329    if obs_b.reweighted is True:
+1330        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
+1331
+1332    new_samples = []
+1333    new_idl = []
+1334    for name in sorted(obs_a.names):
+1335        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
+1336        new_idl.append(obs_a.idl[name])
+1337
+1338    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
+1339    o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names}
+1340    o.reweighted = obs_a.reweighted or obs_b.reweighted
+1341    return o
@@ -4841,68 +4872,68 @@ Currently only works if ensembles are identical (this is not strictly necessary)
View Source - 
1336def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
-1337    r'''Calculates the covariance matrix of a set of observables.
-1338
-1339    The gamma method has to be applied first to all observables.
-1340
-1341    Parameters
-1342    ----------
-1343    obs : list or numpy.ndarray
-1344        List or one dimensional array of Obs
-1345    visualize : bool
-1346        If True plots the corresponding normalized correlation matrix (default False).
-1347    correlation : bool
-1348        If True the correlation instead of the covariance is returned (default False).
-1349    smooth : None or int
-1350        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
-1351        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
-1352        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
-1353        small ones.
-1354
-1355    Notes
-1356    -----
-1357    The 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
-1358    $$v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
-1359    For 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.
-1360    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
-1361    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
-1362    '''
-1363
-1364    length = len(obs)
-1365
-1366    max_samples = np.max([o.N for o in obs])
-1367    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
-1368        warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning)
-1369
-1370    cov = np.zeros((length, length))
-1371    for i in range(length):
-1372        for j in range(i, length):
-1373            cov[i, j] = _covariance_element(obs[i], obs[j])
-1374    cov = cov + cov.T - np.diag(np.diag(cov))
-1375
-1376    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
+            
1344def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+1345    r'''Calculates the covariance matrix of a set of observables.
+1346
+1347    The gamma method has to be applied first to all observables.
+1348
+1349    Parameters
+1350    ----------
+1351    obs : list or numpy.ndarray
+1352        List or one dimensional array of Obs
+1353    visualize : bool
+1354        If True plots the corresponding normalized correlation matrix (default False).
+1355    correlation : bool
+1356        If True the correlation instead of the covariance is returned (default False).
+1357    smooth : None or int
+1358        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
+1359        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
+1360        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
+1361        small ones.
+1362
+1363    Notes
+1364    -----
+1365    The 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
+1366    $$v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
+1367    For 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.
+1368    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
+1369    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
+1370    '''
+1371
+1372    length = len(obs)
+1373
+1374    max_samples = np.max([o.N for o in obs])
+1375    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
+1376        warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning)
 1377
-1378    if isinstance(smooth, int):
-1379        corr = _smooth_eigenvalues(corr, smooth)
-1380
-1381    errors = [o.dvalue for o in obs]
-1382    cov = np.diag(errors) @ corr @ np.diag(errors)
+1378    cov = np.zeros((length, length))
+1379    for i in range(length):
+1380        for j in range(i, length):
+1381            cov[i, j] = _covariance_element(obs[i], obs[j])
+1382    cov = cov + cov.T - np.diag(np.diag(cov))
 1383
-1384    eigenvalues = np.linalg.eigh(cov)[0]
-1385    if not np.all(eigenvalues >= 0):
-1386        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
-1387
-1388    if visualize:
-1389        plt.matshow(corr, vmin=-1, vmax=1)
-1390        plt.set_cmap('RdBu')
-1391        plt.colorbar()
-1392        plt.draw()
-1393
-1394    if correlation is True:
-1395        return corr
-1396    else:
-1397        return cov
+1384    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
+1385
+1386    if isinstance(smooth, int):
+1387        corr = _smooth_eigenvalues(corr, smooth)
+1388
+1389    errors = [o.dvalue for o in obs]
+1390    cov = np.diag(errors) @ corr @ np.diag(errors)
+1391
+1392    eigenvalues = np.linalg.eigh(cov)[0]
+1393    if not np.all(eigenvalues >= 0):
+1394        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
+1395
+1396    if visualize:
+1397        plt.matshow(corr, vmin=-1, vmax=1)
+1398        plt.set_cmap('RdBu')
+1399        plt.colorbar()
+1400        plt.draw()
+1401
+1402    if correlation is True:
+1403        return corr
+1404    else:
+1405        return cov
@@ -4948,24 +4979,24 @@ This construction ensures that the estimated covariance matrix is positive semi-
View Source - 
1476def import_jackknife(jacks, name, idl=None):
-1477    """Imports jackknife samples and returns an Obs
-1478
-1479    Parameters
-1480    ----------
-1481    jacks : numpy.ndarray
-1482        numpy array containing the mean value as zeroth entry and
-1483        the N jackknife samples as first to Nth entry.
-1484    name : str
-1485        name of the ensemble the samples are defined on.
-1486    """
-1487    length = len(jacks) - 1
-1488    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
-1489    samples = jacks[1:] @ prj
-1490    mean = np.mean(samples)
-1491    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
-1492    new_obs._value = jacks[0]
-1493    return new_obs
+            
1484def import_jackknife(jacks, name, idl=None):
+1485    """Imports jackknife samples and returns an Obs
+1486
+1487    Parameters
+1488    ----------
+1489    jacks : numpy.ndarray
+1490        numpy array containing the mean value as zeroth entry and
+1491        the N jackknife samples as first to Nth entry.
+1492    name : str
+1493        name of the ensemble the samples are defined on.
+1494    """
+1495    length = len(jacks) - 1
+1496    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
+1497    samples = jacks[1:] @ prj
+1498    mean = np.mean(samples)
+1499    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
+1500    new_obs._value = jacks[0]
+1501    return new_obs
@@ -4995,35 +5026,35 @@ name of the ensemble the samples are defined on.
View Source - 
1496def merge_obs(list_of_obs):
-1497    """Combine all observables in list_of_obs into one new observable
-1498
-1499    Parameters
-1500    ----------
-1501    list_of_obs : list
-1502        list of the Obs object to be combined
-1503
-1504    Notes
-1505    -----
-1506    It is not possible to combine obs which are based on the same replicum
-1507    """
-1508    replist = [item for obs in list_of_obs for item in obs.names]
-1509    if (len(replist) == len(set(replist))) is False:
-1510        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
-1511    if any([len(o.cov_names) for o in list_of_obs]):
-1512        raise Exception('Not possible to merge data that contains covobs!')
-1513    new_dict = {}
-1514    idl_dict = {}
-1515    for o in list_of_obs:
-1516        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
-1517                        for key in set(o.deltas) | set(o.r_values)})
-1518        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
-1519
-1520    names = sorted(new_dict.keys())
-1521    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
-1522    o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names}
-1523    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
-1524    return o
+            
1504def merge_obs(list_of_obs):
+1505    """Combine all observables in list_of_obs into one new observable
+1506
+1507    Parameters
+1508    ----------
+1509    list_of_obs : list
+1510        list of the Obs object to be combined
+1511
+1512    Notes
+1513    -----
+1514    It is not possible to combine obs which are based on the same replicum
+1515    """
+1516    replist = [item for obs in list_of_obs for item in obs.names]
+1517    if (len(replist) == len(set(replist))) is False:
+1518        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
+1519    if any([len(o.cov_names) for o in list_of_obs]):
+1520        raise Exception('Not possible to merge data that contains covobs!')
+1521    new_dict = {}
+1522    idl_dict = {}
+1523    for o in list_of_obs:
+1524        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
+1525                        for key in set(o.deltas) | set(o.r_values)})
+1526        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
+1527
+1528    names = sorted(new_dict.keys())
+1529    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
+1530    o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names}
+1531    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
+1532    return o
@@ -5054,47 +5085,47 @@ list of the Obs object to be combined
View Source - 
1527def cov_Obs(means, cov, name, grad=None):
-1528    """Create an Obs based on mean(s) and a covariance matrix
-1529
-1530    Parameters
-1531    ----------
-1532    mean : list of floats or float
-1533        N mean value(s) of the new Obs
-1534    cov : list or array
-1535        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
-1536    name : str
-1537        identifier for the covariance matrix
-1538    grad : list or array
-1539        Gradient of the Covobs wrt. the means belonging to cov.
-1540    """
-1541
-1542    def covobs_to_obs(co):
-1543        """Make an Obs out of a Covobs
-1544
-1545        Parameters
-1546        ----------
-1547        co : Covobs
-1548            Covobs to be embedded into the Obs
-1549        """
-1550        o = Obs([], [], means=[])
-1551        o._value = co.value
-1552        o.names.append(co.name)
-1553        o._covobs[co.name] = co
-1554        o._dvalue = np.sqrt(co.errsq())
-1555        return o
-1556
-1557    ol = []
-1558    if isinstance(means, (float, int)):
-1559        means = [means]
-1560
-1561    for i in range(len(means)):
-1562        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
-1563    if ol[0].covobs[name].N != len(means):
-1564        raise Exception('You have to provide %d mean values!' % (ol[0].N))
-1565    if len(ol) == 1:
-1566        return ol[0]
-1567    return ol
+            
1535def cov_Obs(means, cov, name, grad=None):
+1536    """Create an Obs based on mean(s) and a covariance matrix
+1537
+1538    Parameters
+1539    ----------
+1540    mean : list of floats or float
+1541        N mean value(s) of the new Obs
+1542    cov : list or array
+1543        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
+1544    name : str
+1545        identifier for the covariance matrix
+1546    grad : list or array
+1547        Gradient of the Covobs wrt. the means belonging to cov.
+1548    """
+1549
+1550    def covobs_to_obs(co):
+1551        """Make an Obs out of a Covobs
+1552
+1553        Parameters
+1554        ----------
+1555        co : Covobs
+1556            Covobs to be embedded into the Obs
+1557        """
+1558        o = Obs([], [], means=[])
+1559        o._value = co.value
+1560        o.names.append(co.name)
+1561        o._covobs[co.name] = co
+1562        o._dvalue = np.sqrt(co.errsq())
+1563        return o
+1564
+1565    ol = []
+1566    if isinstance(means, (float, int)):
+1567        means = [means]
+1568
+1569    for i in range(len(means)):
+1570        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
+1571    if ol[0].covobs[name].N != len(means):
+1572        raise Exception('You have to provide %d mean values!' % (ol[0].N))
+1573    if len(ol) == 1:
+1574        return ol[0]
+1575    return ol
diff --git a/docs/search.js b/docs/search.js index 79889583..54753b0d 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 liner error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
    • \n
  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
    • \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

There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.

\n\n

Basic example

\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

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
import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\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
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

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
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

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
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

The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.

\n\n

If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.

\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
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

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
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

pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.

\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

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
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

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
# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
\n\n

Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.

\n\n

Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.

\n\n

For the full API see pyerrors.obs.Obs.

\n\n

Correlators

\n\n

When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs

\n\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
\n\n

In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.

\n\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
\n\n

The individual entries of a correlator can be accessed via slicing

\n\n
print(my_corr[3])\n> 0.3227(33)\n
\n\n

Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.

\n\n
my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
\n\n

pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:

\n\n
    \n
  • Corr.gamma_method applies the gamma method to all entries of the correlator.
    • \n
  • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
    • \n
  • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
    • \n
  • Corr.plateau extracts a plateau value from the correlator in a given range.
    • \n
  • Corr.roll periodically shifts the correlator.
    • \n
  • Corr.reverse reverses the time ordering of the correlator.
    • \n
  • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
    • \n
  • Corr.reweight reweights the correlator.
    • \n
\n\n

pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).

\n\n

For the full API see pyerrors.correlators.Corr.

\n\n

Complex valued observables

\n\n

pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.

\n\n
my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
\n\n

Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.

\n\n
my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
\n\n

The Covobs class

\n\n

In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.

\n\n

This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.

\n\n
import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
\n\n

The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.

\n\n

Correlated auxiliary data is defined similarly to above, e.g., via

\n\n
RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
\n\n

where RAP now is a list of two Obs that contains the two correlated parameters.

\n\n

Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via

\n\n
o.covobs[k].grad\n
\n\n

Error propagation in iterative algorithms

\n\n

pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.

\n\n

Least squares fits

\n\n

Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.

\n\n

Fit functions have to be of the following form

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

It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.

\n\n

Fits can then be performed via

\n\n
fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
\n\n

where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.

\n\n

Data stored in Corr objects can be fitted directly using the Corr.fit method.

\n\n
my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
\n\n

this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.

\n\n

For fit functions with multiple independent variables the fit function can be of the form

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

pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.

\n\n

Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.

\n\n

Total least squares fits

\n\n

pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.

\n\n

For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.

\n\n

Matrix operations

\n\n

pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:

\n\n
    \n
  • inv for the matrix inverse.
    • \n
  • cholseky for the Cholesky decomposition.
    • \n
  • det for the matrix determinant.
    • \n
  • eigh for eigenvalues and eigenvectors of hermitean matrices.
    • \n
  • eig for eigenvalues of general matrices.
    • \n
  • pinv for the Moore-Penrose pseudoinverse.
    • \n
  • svd for the singular-value-decomposition.
    • \n
\n\n

For the full API see pyerrors.linalg.

\n\n

Export data

\n\n

The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:

\n\n
    \n
  • What observables are stored? Possibly: How exactly are they defined.
    • \n
  • How does each single ensemble or external quantity contribute to the error of the observable?
    • \n
  • Who did write the file when and on which machine?
    • \n
\n\n

This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example

\n\n
my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
\n\n

The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.

\n\n

json.gz format specification

\n\n

The first entries of the file provide optional auxiliary information:

\n\n
    \n
  • program is a string that indicates which program was used to write the file.
    • \n
  • version is a string that specifies the version of the format.
    • \n
  • who is a string that specifies the user name of the creator of the file.
    • \n
  • date is a string and contains the creation date of the file.
    • \n
  • host is a string and contains the hostname of the machine where the file has been written.
    • \n
  • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
    • \n
\n\n

The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.

\n\n

Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:

\n\n
    \n
  • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
    • \n
  • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
    • \n
  • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
    • \n
  • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
    • \n
  • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
    • \n
  • data is an array that contains the data from MC chains. We will define it below.
    • \n
  • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
    • \n
\n\n

The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:

\n\n
    \n
  • id, a string that contains the name of the ensemble
    • \n
  • replica, an array that contains an entry per replica of the ensemble.
    • \n
\n\n

Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.

\n\n

Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.

\n\n

The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:

\n\n
    \n
  • id, a string that identifies the covariance matrix
    • \n
  • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
    • \n
  • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
    • \n
  • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
    • \n
\n\n

A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.

\n\n

Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.

\n\n

Citing

\n\n

If you use pyerrors for research that leads to a publication please consider citing:

\n\n
    \n
  • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
    • \n
  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
    • \n
  • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
    • \n
\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "

\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "

The class for a correlator (time dependent sequence of pe.Obs).

\n\n

Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.

\n\n

The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.

\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "

Initialize a Corr object.

\n\n
Parameters
\n\n
    \n
  • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
    • \n
  • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
    • \n
  • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
    • \n
\n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "

Apply the gamma method to the content of the Corr.

\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "

We need to project the Correlator with a Vector to get a single value at each timeslice.

\n\n

The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to

\n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "

Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.

\n\n
Parameters
\n\n
    \n
  • i (int):\nFirst index to be picked.
    • \n
  • j (int):\nSecond index to be picked.
    • \n
\n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "

Outputs the correlator in a plotable format.

\n\n

Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "

Symmetrize the correlator around x0=0.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "

Anti-symmetrize the correlator around x0=0.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "

Symmetrizes the correlator matrices on every timeslice.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "

Solve the general eigenvalue problem on the current correlator

\n\n
Parameters
\n\n
    \n
  • t0 (int):\nThe time t0 for G(t)v= lambda G(t_0)v
    • \n
  • ts (int):\nfixed time G(t_s)v= lambda G(t_0)v if return_list=False\nIf return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
    • \n
  • state (int):\nThe state one is interested in, ordered by energy. The lowest state is zero.
    • \n
  • sorted_list (string):\nif this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.\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 [hep-lat] to find the set of v(t) belonging to the state.\n The reference state is identified by its eigenvalue at t=ts
    • \n
\n", "signature": "(self, t0, ts=None, state=0, sorted_list='Eigenvalue')", "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
  • t0 (int):\nThe time t0 for G(t)v= lambda G(t_0)v
    • \n
  • ts (int):\nfixed time G(t_s)v= lambda G(t_0)v if return_list=False\nIf return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
    • \n
  • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
    • \n
  • sorted_list (string):\nif this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.\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 [hep-lat] to find the set of v(t) belonging to the state.\n The reference state is identified by its eigenvalue at t=ts
    • \n
\n", "signature": "(self, t0, ts=None, state=0, sorted_list=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "

Constructs an NxN Hankel matrix

\n\n

C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))

\n\n
Parameters
\n\n
    \n
  • N (int):\nDimension of the Hankel matrix
    • \n
  • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
    • \n
\n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "

Periodically shift the correlator by dt timeslices

\n\n
Parameters
\n\n
    \n
  • dt (int):\nnumber of timeslices
    • \n
\n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "

Reverse the time ordering of the Corr

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "

Thin out a correlator to suppress correlations

\n\n
Parameters
\n\n
    \n
  • spacing (int):\nKeep only every 'spacing'th entry of the correlator
    • \n
  • offset (int):\nOffset the equal spacing
    • \n
\n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "

Correlate the correlator with another correlator or Obs

\n\n
Parameters
\n\n
    \n
  • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
    • \n
\n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "

Reweight the correlator.

\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "

Return the time symmetry average of the correlator and its partner

\n\n
Parameters
\n\n
    \n
  • partner (Corr):\nTime symmetry partner of the Corr
    • \n
  • partity (int):\nParity quantum number of the correlator, can be +1 or -1
    • \n
\n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "

Return the first derivative of the correlator with respect to x0.

\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "

Return the second derivative of the correlator with respect to x0.

\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "

Returns the effective mass of the correlator as correlator object

\n\n
Parameters
\n\n
    \n
  • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
    • \n
  • guess (float):\nguess for the root finder, only relevant for the root variant
    • \n
\n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "

Fits function to the data

\n\n
Parameters
\n\n
    \n
  • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
    • \n
  • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
    • \n
  • silent (bool):\nDecides whether output is printed to the standard output.
    • \n
\n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "

Extract a plateau value from a Corr object

\n\n
Parameters
\n\n
    \n
  • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
    • \n
  • method (str):\nmethod to extract the plateau.\n 'fit' fits a constant to the plateau region\n 'avg', 'average' or 'mean' just average over the given timeslices.
    • \n
  • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
    • \n
\n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "

Sets the attribute prange of the Corr object.

\n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "

Plots the correlator using the tag of the correlator as label if available.

\n\n
Parameters
\n\n
    \n
  • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8]
    • \n
  • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
    • \n
  • logscale (bool):\nSets y-axis to logscale
    • \n
  • plateau (Obs):\nPlateau value to be visualized in the figure
    • \n
  • fit_res (Fit_result):\nFit_result object to be visualized
    • \n
  • ylabel (str):\nLabel for the y-axis
    • \n
  • save (str):\npath to file in which the figure should be saved
    • \n
  • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
    • \n
  • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
    • \n
  • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
    • \n
\n", "signature": "(\n self,\n x_range=None,\n comp=None,\n y_range=None,\n logscale=False,\n plateau=None,\n fit_res=None,\n ylabel=None,\n save=None,\n auto_gamma=False,\n hide_sigma=None,\n references=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "

Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.

\n\n
Parameters
\n\n
    \n
  • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
    • \n
\n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "

Dumps the Corr into a file of chosen type

\n\n
Parameters
\n\n
    \n
  • filename (str):\nName of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "

\n", "signature": "(self, range=[0, None])", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "

Project large correlation matrix to lowest states

\n\n

This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.

\n\n
Parameters
\n\n
    \n
  • Ntrunc (int):\nRank of the target matrix.
    • \n
  • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
    • \n
  • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
    • \n
  • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
    • \n
\n\n
Notes
\n\n

We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.

\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "

\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "

\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "

Initialize Covobs object.

\n\n
Parameters
\n\n
    \n
  • mean (float):\nMean value of the new Obs
    • \n
  • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "

Return the variance (= square of the error) of the Covobs

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "

\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "

\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "

\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "

Rank-3 epsilon tensor

\n\n

Based on https://codegolf.stackexchange.com/a/160375

\n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "

Rank-4 epsilon tensor

\n\n

Extension of https://codegolf.stackexchange.com/a/160375

\n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "

Returns gamma matrix in Grid labeling.

\n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "

\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "

Represents fit results.

\n\n
Attributes
\n\n
    \n
  • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
    • \n
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "

Apply the gamma method to all fit parameters

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "

Performs a non-linear fit to y = func(x).

\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of floats.
    • \n
  • y (list):\nlist of Obs.
    • \n

  • func (object):\nfit function, has to be of the form

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

    For multiple x values func can be of the form

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

    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.

    • \n
  • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters.
    • \n
  • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
    • \n
  • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
    • \n
  • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
    • \n
  • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
    • \n
  • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
    • \n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "

Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.

\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of Obs, or a tuple of lists of Obs
    • \n
  • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
    • \n

  • func (object):\nfunc has to be of the form

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

    For multiple x values func can be of the form

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

    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.

    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
    • \n
  • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
    • \n
\n\n
Notes
\n\n

Based on the orthogonal distance regression module of scipy

\n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "

Performs a linear fit to y = n + m * x and returns two Obs n, m.

\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "

Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.

\n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "

Generates a plot which compares the fit to the data and displays the corresponding residuals

\n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "

Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.

\n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "

Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.

\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "

pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.

\n\n

Jackknife samples

\n\n

For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.

\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "

\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "

Extract generic MCMC data from a bdio file

\n\n

read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "

Write Obs to a bdio file according to ADerrors conventions

\n\n

read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "

Extract mesons data from a bdio file and return it as a dictionary

\n\n

The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)

\n\n

read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "

Extract dSdm data from a bdio file and return it as a dictionary

\n\n

The dictionary can be accessed with a tuple consisting of (type, kappa)

\n\n

read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "

\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.

\n\n

Tags are not written or recovered automatically. The separator | is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.

\n\n

Tags are not written or recovered automatically. The separator | is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n", "signature": "(\n obsl,\n fname,\n name,\n spec='',\n origin='',\n symbol=[],\n enstag=None,\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "

Import a list of Obs from an xml.gz file in the Zeuthen pobs format.

\n\n

Tags are not written or recovered automatically.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "

Import a list of Obs from a string in the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically.

\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "

Import a list of Obs from an xml.gz file in the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n", "signature": "(\n fname,\n noempty=False,\n full_output=False,\n gz=True,\n separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "

Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically. The separator |is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n", "signature": "(\n obsl,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={}\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically. The separator | is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n", "signature": "(\n obsl,\n fname,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={},\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "

\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "

Read hadrons meson hdf5 file and extract the meson labeled 'meson'

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • 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)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "

ndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)

\n\n

An array object represents a multidimensional, homogeneous array\nof fixed-size items. An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)

\n\n

Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.

\n\n

For more information, refer to the numpy module and examine the\nmethods and attributes of an array.

\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator. The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2). This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view). The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n

array: Construct an array.
\nzeros: Create an array, each element of which is zero.
\nempty: Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype: Create a data-type.
\nnumpy.typing.NDArray: An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.

\n\n
Notes
\n\n

There are two modes of creating an array using __new__:

\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n

No __init__ method is needed because the array is fully initialized\nafter the __new__ method.

\n\n
Examples
\n\n

These examples illustrate the low-level ndarray constructor. Refer\nto the See Also section above for easier ways of constructing an\nndarray.

\n\n

First mode, buffer is None:

\n\n
>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n\n

Second mode:

\n\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "

\n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "

Gamma_5 hermitean conjugate

\n\n

Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.

\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "

Read hadrons ExternalLeg hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "

Read hadrons Bilinear hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "

Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • vertices (list):\nVertex functions to be extracted.
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "

\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "

Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
\n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "

Reconstruct a list of Obs or structures containing Obs from a json string.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "

Import a list of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "

Export a dict of Obs or structures containing Obs to a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "

Import a dict of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "

\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "

Read pbp format from given folder structure. Returns a list of length nrw

\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
\n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "

\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "

Read rwms format from given folder structure. Returns a list of length nrw

\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
    • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
    • \n
  • version (str):\nversion of openQCD, default 2.0
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
    • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "

Extract t0 from given .ms.dat files. Returns t0 as Obs.

\n\n

It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.

\n\n

It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "

Read the topologial charge based on openQCD gradient flow measurements.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "

Returns the projection to the topological charge sector defined by target.

\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
\n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "

Constructs reweighting factors to a specified topological sector.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
    • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "

\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "

Read sfcf c format from given folder structure.

\n\n
Parameters
\n\n
    \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n", "signature": "(\n path,\n prefix,\n name,\n quarks='.*',\n corr_type='bi',\n noffset=0,\n wf=0,\n wf2=0,\n version='1.0c',\n cfg_separator='n',\n **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "

Utilities for the input

\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "

Checks if list of configurations is contained in an idl

\n\n
Parameters
\n\n
    \n
  • idl (range or list):\nidl of the current replicum
    • \n
  • che (list):\nlist of configurations to be checked against
    • \n
\n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "

\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "

Matrix multiply all operands.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • This implementation is faster compared to standard multiplication via the @ operator.
    • \n
\n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "

Matrix multiply both operands making use of the jackknife approximation.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • For large matrices this is considerably faster compared to matmul.
    • \n
\n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "

Wrapper for numpy.einsum

\n\n
Parameters
\n\n
    \n
  • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
    • \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
\n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "

Inverse of Obs or CObs valued matrices.

\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "

Cholesky decomposition of Obs valued matrices.

\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "

Determinant of Obs valued matrices.

\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "

Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "

Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "

Computes the Moore-Penrose pseudoinverse of a matrix of Obs.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "

Computes the singular value decomposition of a matrix of Obs.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "

\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "

Dump object into pickle file.

\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
    • \n
  • name (str):\nname of the file
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "

Load object from pickle file.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "

Generate an Obs object with given value, dvalue and name for test purposes

\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
    • \n
  • dvalue (float):\nerror of the Obs to be generated.
    • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
    • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
    • \n
\n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "

Generate observables with given covariance and autocorrelation times.

\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
    • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
    • \n
  • name (str):\nensemble name for the data to be geneated.
    • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
    • \n
  • samples (int):\nnumber of samples to be generated for each observable.
    • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "

\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "

Matrix pencil method to extract k energy levels from data

\n\n

Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)

\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
    • \n
  • k (int):\nNumber of states to extract (default 1).
    • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
    • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "

\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "

Class for a general observable.

\n\n

Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.

\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
    • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
    • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
    • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
    • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "

Initialize Obs object.

\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
    • \n
  • names (list):\nlist of strings labeling the individual samples
    • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
    • \n
\n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "

\n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "

\n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "

\n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "

\n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "

\n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "

\n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "

\n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "

Estimate the error and related properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "

Output detailed properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
    • \n
\n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "

Checks whether the observable is zero within 'sigma' standard errors.

\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
    • \n
  • Works only properly when the gamma method was run.
    • \n
\n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "

Checks whether the observable is zero within a given tolerance.

\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
    • \n
\n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "

Plot integrated autocorrelation time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "

Plot normalized autocorrelation function time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "

Plot replica distribution for each ensemble with more than one replicum.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "

Plot derived Monte Carlo history for each ensemble

\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
    • \n
\n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "

Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "

Dump the Obs to a file 'name' of chosen format.

\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "

Export jackknife samples from the Obs

\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
    • \n
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "

Class for a complex valued observable.

\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "

\n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "

Executes the gamma_method for the real and the imaginary part.

\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "

Checks whether both real and imaginary part are zero within machine precision.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "

Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.

\n\n
Parameters
\n\n
    \n
  • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
    • \n
  • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
    • \n
  • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
    • \n
\n\n
Notes
\n\n

For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use

\n\n

new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])

\n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "

Reweight a list of observables.

\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "

Correlate two observables.

\n\n
Parameters
\n\n
    \n
  • obs_a (Obs):\nFirst observable
    • \n
  • obs_b (Obs):\nSecond observable
    • \n
\n\n
Notes
\n\n

Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).

\n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "

Calculates the 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 instead of the covariance 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 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$$v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).

\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "

Imports jackknife samples and returns an Obs

\n\n
Parameters
\n\n
    \n
  • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
\n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "

Combine all observables in list_of_obs into one new observable

\n\n
Parameters
\n\n
    \n
  • list_of_obs (list):\nlist of the Obs object to be combined
    • \n
\n\n
Notes
\n\n

It is not possible to combine obs which are based on the same replicum

\n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "

Create an Obs based on mean(s) and a covariance matrix

\n\n
Parameters
\n\n
    \n
  • mean (list of floats or float):\nN mean value(s) of the new Obs
    • \n
  • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "

\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "

Finds the root of the function func(x, d) where d is an Obs.

\n\n
Parameters
\n\n
    \n
  • d (Obs):\nObs passed to the function.
    • \n
  • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n return anp.exp(-x ** 2) - d\n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • Obs: Obs valued root of the function.
    • \n
\n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "

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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 liner error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
    • \n
  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
    • \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
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There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.

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Basic example

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import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
\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.

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import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
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Error propagation

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When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.

\n\n

The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.

\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

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
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

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
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

The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.

\n\n

If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.

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Exponential tails

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Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.

\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
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For the full API see pyerrors.obs.Obs.gamma_method.

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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
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

pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.

\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

Error estimation for multiple ensembles

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In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.

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pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
\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

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Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.

\n\n
# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
\n\n

Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.

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Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.

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For the full API see pyerrors.obs.Obs.

\n\n

Correlators

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When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs

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my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
\n\n

In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.

\n\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
\n\n

The individual entries of a correlator can be accessed via slicing

\n\n
print(my_corr[3])\n> 0.3227(33)\n
\n\n

Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.

\n\n
my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
\n\n

pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:

\n\n
    \n
  • Corr.gamma_method applies the gamma method to all entries of the correlator.
    • \n
  • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
    • \n
  • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
    • \n
  • Corr.plateau extracts a plateau value from the correlator in a given range.
    • \n
  • Corr.roll periodically shifts the correlator.
    • \n
  • Corr.reverse reverses the time ordering of the correlator.
    • \n
  • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
    • \n
  • Corr.reweight reweights the correlator.
    • \n
\n\n

pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).

\n\n

For the full API see pyerrors.correlators.Corr.

\n\n

Complex valued observables

\n\n

pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.

\n\n
my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
\n\n

Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.

\n\n
my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
\n\n

The Covobs class

\n\n

In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.

\n\n

This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.

\n\n
import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
\n\n

The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.

\n\n

Correlated auxiliary data is defined similarly to above, e.g., via

\n\n
RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
\n\n

where RAP now is a list of two Obs that contains the two correlated parameters.

\n\n

Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via

\n\n
o.covobs[k].grad\n
\n\n

Error propagation in iterative algorithms

\n\n

pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.

\n\n

Least squares fits

\n\n

Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.

\n\n

Fit functions have to be of the following form

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

It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.

\n\n

Fits can then be performed via

\n\n
fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
\n\n

where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.

\n\n

Data stored in Corr objects can be fitted directly using the Corr.fit method.

\n\n
my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
\n\n

this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.

\n\n

For fit functions with multiple independent variables the fit function can be of the form

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

pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.

\n\n

Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.

\n\n

Total least squares fits

\n\n

pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.

\n\n

For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.

\n\n

Matrix operations

\n\n

pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:

\n\n
    \n
  • inv for the matrix inverse.
    • \n
  • cholseky for the Cholesky decomposition.
    • \n
  • det for the matrix determinant.
    • \n
  • eigh for eigenvalues and eigenvectors of hermitean matrices.
    • \n
  • eig for eigenvalues of general matrices.
    • \n
  • pinv for the Moore-Penrose pseudoinverse.
    • \n
  • svd for the singular-value-decomposition.
    • \n
\n\n

For the full API see pyerrors.linalg.

\n\n

Export data

\n\n

The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:

\n\n
    \n
  • What observables are stored? Possibly: How exactly are they defined.
    • \n
  • How does each single ensemble or external quantity contribute to the error of the observable?
    • \n
  • Who did write the file when and on which machine?
    • \n
\n\n

This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example

\n\n
my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
\n\n

The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.

\n\n

json.gz format specification

\n\n

The first entries of the file provide optional auxiliary information:

\n\n
    \n
  • program is a string that indicates which program was used to write the file.
    • \n
  • version is a string that specifies the version of the format.
    • \n
  • who is a string that specifies the user name of the creator of the file.
    • \n
  • date is a string and contains the creation date of the file.
    • \n
  • host is a string and contains the hostname of the machine where the file has been written.
    • \n
  • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
    • \n
\n\n

The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.

\n\n

Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:

\n\n
    \n
  • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
    • \n
  • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
    • \n
  • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
    • \n
  • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
    • \n
  • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
    • \n
  • data is an array that contains the data from MC chains. We will define it below.
    • \n
  • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
    • \n
\n\n

The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:

\n\n
    \n
  • id, a string that contains the name of the ensemble
    • \n
  • replica, an array that contains an entry per replica of the ensemble.
    • \n
\n\n

Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.

\n\n

Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.

\n\n

The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:

\n\n
    \n
  • id, a string that identifies the covariance matrix
    • \n
  • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
    • \n
  • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
    • \n
  • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
    • \n
\n\n

A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.

\n\n

Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.

\n\n

Citing

\n\n

If you use pyerrors for research that leads to a publication please consider citing:

\n\n
    \n
  • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
    • \n
  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
    • \n
  • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
    • \n
\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "

\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "

The class for a correlator (time dependent sequence of pe.Obs).

\n\n

Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.

\n\n

The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.

\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "

Initialize a Corr object.

\n\n
Parameters
\n\n
    \n
  • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
    • \n
  • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
    • \n
  • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
    • \n
\n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "

Apply the gamma method to the content of the Corr.

\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "

We need to project the Correlator with a Vector to get a single value at each timeslice.

\n\n

The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to

\n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "

Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.

\n\n
Parameters
\n\n
    \n
  • i (int):\nFirst index to be picked.
    • \n
  • j (int):\nSecond index to be picked.
    • \n
\n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "

Outputs the correlator in a plotable format.

\n\n

Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "

Symmetrize the correlator around x0=0.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "

Anti-symmetrize the correlator around x0=0.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "

Symmetrizes the correlator matrices on every timeslice.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "

Solve the general eigenvalue problem on the current correlator

\n\n
Parameters
\n\n
    \n
  • t0 (int):\nThe time t0 for G(t)v= lambda G(t_0)v
    • \n
  • ts (int):\nfixed time G(t_s)v= lambda G(t_0)v if return_list=False\nIf return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
    • \n
  • state (int):\nThe state one is interested in, ordered by energy. The lowest state is zero.
    • \n
  • sorted_list (string):\nif this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.\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 [hep-lat] to find the set of v(t) belonging to the state.\n The reference state is identified by its eigenvalue at t=ts
    • \n
\n", "signature": "(self, t0, ts=None, state=0, sorted_list='Eigenvalue')", "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
  • t0 (int):\nThe time t0 for G(t)v= lambda G(t_0)v
    • \n
  • ts (int):\nfixed time G(t_s)v= lambda G(t_0)v if return_list=False\nIf return_list=True and sorting=Eigenvector it gives a reference point for the sorting method.
    • \n
  • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
    • \n
  • sorted_list (string):\nif this argument is set, a list of vectors (len=self.T) is returned. If it is left as None, only one vector is returned.\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 [hep-lat] to find the set of v(t) belonging to the state.\n The reference state is identified by its eigenvalue at t=ts
    • \n
\n", "signature": "(self, t0, ts=None, state=0, sorted_list=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "

Constructs an NxN Hankel matrix

\n\n

C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))

\n\n
Parameters
\n\n
    \n
  • N (int):\nDimension of the Hankel matrix
    • \n
  • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
    • \n
\n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "

Periodically shift the correlator by dt timeslices

\n\n
Parameters
\n\n
    \n
  • dt (int):\nnumber of timeslices
    • \n
\n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "

Reverse the time ordering of the Corr

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "

Thin out a correlator to suppress correlations

\n\n
Parameters
\n\n
    \n
  • spacing (int):\nKeep only every 'spacing'th entry of the correlator
    • \n
  • offset (int):\nOffset the equal spacing
    • \n
\n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "

Correlate the correlator with another correlator or Obs

\n\n
Parameters
\n\n
    \n
  • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
    • \n
\n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "

Reweight the correlator.

\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "

Return the time symmetry average of the correlator and its partner

\n\n
Parameters
\n\n
    \n
  • partner (Corr):\nTime symmetry partner of the Corr
    • \n
  • partity (int):\nParity quantum number of the correlator, can be +1 or -1
    • \n
\n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "

Return the first derivative of the correlator with respect to x0.

\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "

Return the second derivative of the correlator with respect to x0.

\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "

Returns the effective mass of the correlator as correlator object

\n\n
Parameters
\n\n
    \n
  • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
    • \n
  • guess (float):\nguess for the root finder, only relevant for the root variant
    • \n
\n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "

Fits function to the data

\n\n
Parameters
\n\n
    \n
  • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
    • \n
  • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
    • \n
  • silent (bool):\nDecides whether output is printed to the standard output.
    • \n
\n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "

Extract a plateau value from a Corr object

\n\n
Parameters
\n\n
    \n
  • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
    • \n
  • method (str):\nmethod to extract the plateau.\n 'fit' fits a constant to the plateau region\n 'avg', 'average' or 'mean' just average over the given timeslices.
    • \n
  • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
    • \n
\n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "

Sets the attribute prange of the Corr object.

\n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "

Plots the correlator using the tag of the correlator as label if available.

\n\n
Parameters
\n\n
    \n
  • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8]
    • \n
  • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
    • \n
  • logscale (bool):\nSets y-axis to logscale
    • \n
  • plateau (Obs):\nPlateau value to be visualized in the figure
    • \n
  • fit_res (Fit_result):\nFit_result object to be visualized
    • \n
  • ylabel (str):\nLabel for the y-axis
    • \n
  • save (str):\npath to file in which the figure should be saved
    • \n
  • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
    • \n
  • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
    • \n
  • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
    • \n
\n", "signature": "(\n self,\n x_range=None,\n comp=None,\n y_range=None,\n logscale=False,\n plateau=None,\n fit_res=None,\n ylabel=None,\n save=None,\n auto_gamma=False,\n hide_sigma=None,\n references=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "

Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.

\n\n
Parameters
\n\n
    \n
  • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
    • \n
\n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "

Dumps the Corr into a file of chosen type

\n\n
Parameters
\n\n
    \n
  • filename (str):\nName of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "

\n", "signature": "(self, range=[0, None])", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "

Project large correlation matrix to lowest states

\n\n

This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.

\n\n
Parameters
\n\n
    \n
  • Ntrunc (int):\nRank of the target matrix.
    • \n
  • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
    • \n
  • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
    • \n
  • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
    • \n
\n\n
Notes
\n\n

We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.

\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "

\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "

\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "

Initialize Covobs object.

\n\n
Parameters
\n\n
    \n
  • mean (float):\nMean value of the new Obs
    • \n
  • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "

Return the variance (= square of the error) of the Covobs

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "

\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "

\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "

\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "

Rank-3 epsilon tensor

\n\n

Based on https://codegolf.stackexchange.com/a/160375

\n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "

Rank-4 epsilon tensor

\n\n

Extension of https://codegolf.stackexchange.com/a/160375

\n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "

Returns gamma matrix in Grid labeling.

\n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "

\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "

Represents fit results.

\n\n
Attributes
\n\n
    \n
  • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
    • \n
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "

Apply the gamma method to all fit parameters

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "

Performs a non-linear fit to y = func(x).

\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of floats.
    • \n
  • y (list):\nlist of Obs.
    • \n

  • func (object):\nfit function, has to be of the form

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

    For multiple x values func can be of the form

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

    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.

    • \n
  • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters.
    • \n
  • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
    • \n
  • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
    • \n
  • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
    • \n
  • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
    • \n
  • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
    • \n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "

Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.

\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of Obs, or a tuple of lists of Obs
    • \n
  • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
    • \n

  • func (object):\nfunc has to be of the form

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

    For multiple x values func can be of the form

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

    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.

    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
    • \n
  • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
    • \n
\n\n
Notes
\n\n

Based on the orthogonal distance regression module of scipy

\n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "

Performs a linear fit to y = n + m * x and returns two Obs n, m.

\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "

Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.

\n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "

Generates a plot which compares the fit to the data and displays the corresponding residuals

\n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "

Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.

\n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "

Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.

\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "

pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.

\n\n

Jackknife samples

\n\n

For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.

\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "

\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "

Extract generic MCMC data from a bdio file

\n\n

read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "

Write Obs to a bdio file according to ADerrors conventions

\n\n

read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "

Extract mesons data from a bdio file and return it as a dictionary

\n\n

The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)

\n\n

read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "

Extract dSdm data from a bdio file and return it as a dictionary

\n\n

The dictionary can be accessed with a tuple consisting of (type, kappa)

\n\n

read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to

\n\n

all: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/

\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "

\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.

\n\n

Tags are not written or recovered automatically. The separator | is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.

\n\n

Tags are not written or recovered automatically. The separator | is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n", "signature": "(\n obsl,\n fname,\n name,\n spec='',\n origin='',\n symbol=[],\n enstag=None,\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "

Import a list of Obs from an xml.gz file in the Zeuthen pobs format.

\n\n

Tags are not written or recovered automatically.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "

Import a list of Obs from a string in the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically.

\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "

Import a list of Obs from an xml.gz file in the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n", "signature": "(\n fname,\n noempty=False,\n full_output=False,\n gz=True,\n separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "

Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically. The separator |is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n", "signature": "(\n obsl,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={}\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.

\n\n

Tags are not written or recovered automatically. The separator | is removed from the replica names.

\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n", "signature": "(\n obsl,\n fname,\n name,\n spec='dobs v1.0',\n origin='',\n symbol=[],\n who=None,\n enstags={},\n gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "

\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "

Read hadrons meson hdf5 file and extract the meson labeled 'meson'

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • 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)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "

ndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)

\n\n

An array object represents a multidimensional, homogeneous array\nof fixed-size items. An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)

\n\n

Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.

\n\n

For more information, refer to the numpy module and examine the\nmethods and attributes of an array.

\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator. The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2). This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view). The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n

array: Construct an array.
\nzeros: Create an array, each element of which is zero.
\nempty: Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype: Create a data-type.
\nnumpy.typing.NDArray: An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.

\n\n
Notes
\n\n

There are two modes of creating an array using __new__:

\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n

No __init__ method is needed because the array is fully initialized\nafter the __new__ method.

\n\n
Examples
\n\n

These examples illustrate the low-level ndarray constructor. Refer\nto the See Also section above for easier ways of constructing an\nndarray.

\n\n

First mode, buffer is None:

\n\n
>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n\n

Second mode:

\n\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "

\n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "

Gamma_5 hermitean conjugate

\n\n

Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.

\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "

Read hadrons ExternalLeg hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "

Read hadrons Bilinear hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "

Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • vertices (list):\nVertex functions to be extracted.
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "

\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "

Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
\n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "

Export a list of Obs or structures containing Obs to a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "

Reconstruct a list of Obs or structures containing Obs from a json string.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "

Import a list of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "

Export a dict of Obs or structures containing Obs to a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "

Import a dict of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "

\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "

Read pbp format from given folder structure. Returns a list of length nrw

\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
\n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "

\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "

Read rwms format from given folder structure. Returns a list of length nrw

\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
    • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
    • \n
  • version (str):\nversion of openQCD, default 2.0
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
    • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "

Extract t0 from given .ms.dat files. Returns t0 as Obs.

\n\n

It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.

\n\n

It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "

Read the topologial charge based on openQCD gradient flow measurements.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "

Returns the projection to the topological charge sector defined by target.

\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
\n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "

Constructs reweighting factors to a specified topological sector.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
    • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "

\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "

Read sfcf c format from given folder structure.

\n\n
Parameters
\n\n
    \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n", "signature": "(\n path,\n prefix,\n name,\n quarks='.*',\n corr_type='bi',\n noffset=0,\n wf=0,\n wf2=0,\n version='1.0c',\n cfg_separator='n',\n **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "

Utilities for the input

\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "

Checks if list of configurations is contained in an idl

\n\n
Parameters
\n\n
    \n
  • idl (range or list):\nidl of the current replicum
    • \n
  • che (list):\nlist of configurations to be checked against
    • \n
\n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "

\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "

Matrix multiply all operands.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • This implementation is faster compared to standard multiplication via the @ operator.
    • \n
\n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "

Matrix multiply both operands making use of the jackknife approximation.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • For large matrices this is considerably faster compared to matmul.
    • \n
\n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "

Wrapper for numpy.einsum

\n\n
Parameters
\n\n
    \n
  • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
    • \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
\n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "

Inverse of Obs or CObs valued matrices.

\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "

Cholesky decomposition of Obs valued matrices.

\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "

Determinant of Obs valued matrices.

\n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "

Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "

Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "

Computes the Moore-Penrose pseudoinverse of a matrix of Obs.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "

Computes the singular value decomposition of a matrix of Obs.

\n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "

\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "

Dump object into pickle file.

\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
    • \n
  • name (str):\nname of the file
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "

Load object from pickle file.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "

Generate an Obs object with given value, dvalue and name for test purposes

\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
    • \n
  • dvalue (float):\nerror of the Obs to be generated.
    • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
    • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
    • \n
\n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "

Generate observables with given covariance and autocorrelation times.

\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
    • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
    • \n
  • name (str):\nensemble name for the data to be geneated.
    • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
    • \n
  • samples (int):\nnumber of samples to be generated for each observable.
    • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "

\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "

Matrix pencil method to extract k energy levels from data

\n\n

Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)

\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
    • \n
  • k (int):\nNumber of states to extract (default 1).
    • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
    • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "

\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "

Class for a general observable.

\n\n

Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.

\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
    • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
    • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
    • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
    • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "

Initialize Obs object.

\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
    • \n
  • names (list):\nlist of strings labeling the individual samples
    • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
    • \n
\n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "

\n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "

\n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "

\n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "

\n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "

\n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "

\n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "

\n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "

Estimate the error and related properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "

Output detailed properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
    • \n
\n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "

Checks whether the observable is zero within 'sigma' standard errors.

\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
    • \n
  • Works only properly when the gamma method was run.
    • \n
\n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "

Checks whether the observable is zero within a given tolerance.

\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
    • \n
\n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "

Plot integrated autocorrelation time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "

Plot normalized autocorrelation function time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "

Plot replica distribution for each ensemble with more than one replicum.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "

Plot derived Monte Carlo history for each ensemble

\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
    • \n
\n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "

Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "

Dump the Obs to a file 'name' of chosen format.

\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "

Export jackknife samples from the Obs

\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
    • \n
\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "

Class for a complex valued observable.

\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "

\n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "

Executes the gamma_method for the real and the imaginary part.

\n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "

Checks whether both real and imaginary part are zero within machine precision.

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "

\n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "

Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.

\n\n
Parameters
\n\n
    \n
  • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
    • \n
  • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
    • \n
  • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
    • \n
\n\n
Notes
\n\n

For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use

\n\n

new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])

\n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "

Reweight a list of observables.

\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "

Correlate two observables.

\n\n
Parameters
\n\n
    \n
  • obs_a (Obs):\nFirst observable
    • \n
  • obs_b (Obs):\nSecond observable
    • \n
\n\n
Notes
\n\n

Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).

\n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "

Calculates the 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 instead of the covariance 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 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$$v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).

\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "

Imports jackknife samples and returns an Obs

\n\n
Parameters
\n\n
    \n
  • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
\n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "

Combine all observables in list_of_obs into one new observable

\n\n
Parameters
\n\n
    \n
  • list_of_obs (list):\nlist of the Obs object to be combined
    • \n
\n\n
Notes
\n\n

It is not possible to combine obs which are based on the same replicum

\n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "

Create an Obs based on mean(s) and a covariance matrix

\n\n
Parameters
\n\n
    \n
  • mean (list of floats or float):\nN mean value(s) of the new Obs
    • \n
  • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "

\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "

Finds the root of the function func(x, d) where d is an Obs.

\n\n
Parameters
\n\n
    \n
  • d (Obs):\nObs passed to the function.
    • \n
  • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n return anp.exp(-x ** 2) - d\n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • Obs: Obs valued root of the function.
    • \n
\n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "

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