diff --git a/docs/pyerrors/input/dobs.html b/docs/pyerrors/input/dobs.html index 622f2963..b148d5c3 100644 --- a/docs/pyerrors/input/dobs.html +++ b/docs/pyerrors/input/dobs.html @@ -625,395 +625,396 @@ 529 deltas.append(repdeltas) 530 idl.append(repidl) 531 -532 res.append(Obs(deltas, obs_names, idl=idl)) -533 res[-1]._value = mean[i] -534 _check(len(e_names) == ne) -535 -536 cnames = list(covd.keys()) -537 for i in range(len(res)): -538 new_covobs = {name: Covobs(0, covd[name], name, grad=gradd[name][i]) for name in cnames} -539 for name in cnames: -540 if np.all(new_covobs[name].grad == 0): -541 del new_covobs[name] -542 cnames_loc = list(new_covobs.keys()) -543 for name in cnames_loc: -544 res[i].names.append(name) -545 res[i].shape[name] = 1 -546 res[i].idl[name] = [] -547 res[i]._covobs = new_covobs -548 -549 if symbol: -550 for i in range(len(res)): -551 res[i].tag = symbol[i] -552 if res[i].tag == 'None': -553 res[i].tag = None -554 if full_output: -555 retd = {} -556 tool = file_origin.get('tool', None) -557 if tool: -558 program = tool['name'] + ' ' + tool['version'] -559 else: -560 program = '' -561 retd['program'] = program -562 retd['version'] = version -563 retd['who'] = file_origin['who'] -564 retd['date'] = file_origin['date'] -565 retd['host'] = file_origin['host'] -566 retd['description'] = descriptiond -567 retd['enstags'] = enstags -568 retd['obsdata'] = res -569 return retd -570 else: -571 return res -572 +532 obsmeans = [np.average(deltas[j]) for j in range(len(deltas))] +533 res.append(Obs([np.array(deltas[j]) - obsmeans[j] for j in range(len(obsmeans))], obs_names, idl=idl, means=obsmeans)) +534 res[-1]._value = mean[i] +535 _check(len(e_names) == ne) +536 +537 cnames = list(covd.keys()) +538 for i in range(len(res)): +539 new_covobs = {name: Covobs(0, covd[name], name, grad=gradd[name][i]) for name in cnames} +540 for name in cnames: +541 if np.all(new_covobs[name].grad == 0): +542 del new_covobs[name] +543 cnames_loc = list(new_covobs.keys()) +544 for name in cnames_loc: +545 res[i].names.append(name) +546 res[i].shape[name] = 1 +547 res[i].idl[name] = [] +548 res[i]._covobs = new_covobs +549 +550 if symbol: +551 for i in range(len(res)): +552 res[i].tag = symbol[i] +553 if res[i].tag == 'None': +554 res[i].tag = None +555 if full_output: +556 retd = {} +557 tool = file_origin.get('tool', None) +558 if tool: +559 program = tool['name'] + ' ' + tool['version'] +560 else: +561 program = '' +562 retd['program'] = program +563 retd['version'] = version +564 retd['who'] = file_origin['who'] +565 retd['date'] = file_origin['date'] +566 retd['host'] = file_origin['host'] +567 retd['description'] = descriptiond +568 retd['enstags'] = enstags +569 retd['obsdata'] = res +570 return retd +571 else: +572 return res 573 -574def read_dobs(fname, full_output=False, gz=True, separator_insertion=True): -575 """Import a list of Obs from an xml.gz file in the Zeuthen dobs format. -576 -577 Tags are not written or recovered automatically. -578 -579 Parameters -580 ---------- -581 fname : str -582 Filename of the input file. -583 full_output : bool -584 If True, a dict containing auxiliary information and the data is returned. -585 If False, only the data is returned as list. -586 gz : bool -587 If True, assumes that data is gzipped. If False, assumes XML file. -588 separatior_insertion: str, int or bool -589 str: replace all occurences of "separator_insertion" within the replica names -590 by "|%s" % (separator_insertion) when constructing the names of the replica. -591 int: Insert the separator "|" at the position given by separator_insertion. -592 True (default): separator "|" is inserted after len(ensname), assuming that the -593 ensemble name is a prefix to the replica name. -594 None or False: No separator is inserted. -595 -596 Returns -597 ------- -598 res : list[Obs] -599 Imported data -600 or -601 res : dict -602 Imported data and meta-data -603 """ -604 -605 if not fname.endswith('.xml') and not fname.endswith('.gz'): -606 fname += '.xml' -607 if gz: -608 if not fname.endswith('.gz'): -609 fname += '.gz' -610 with gzip.open(fname, 'r') as fin: -611 content = fin.read() -612 else: -613 if fname.endswith('.gz'): -614 warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning) -615 with open(fname, 'r') as fin: -616 content = fin.read() -617 -618 return import_dobs_string(content, full_output, separator_insertion=separator_insertion) -619 +574 +575def read_dobs(fname, full_output=False, gz=True, separator_insertion=True): +576 """Import a list of Obs from an xml.gz file in the Zeuthen dobs format. +577 +578 Tags are not written or recovered automatically. +579 +580 Parameters +581 ---------- +582 fname : str +583 Filename of the input file. +584 full_output : bool +585 If True, a dict containing auxiliary information and the data is returned. +586 If False, only the data is returned as list. +587 gz : bool +588 If True, assumes that data is gzipped. If False, assumes XML file. +589 separatior_insertion: str, int or bool +590 str: replace all occurences of "separator_insertion" within the replica names +591 by "|%s" % (separator_insertion) when constructing the names of the replica. +592 int: Insert the separator "|" at the position given by separator_insertion. +593 True (default): separator "|" is inserted after len(ensname), assuming that the +594 ensemble name is a prefix to the replica name. +595 None or False: No separator is inserted. +596 +597 Returns +598 ------- +599 res : list[Obs] +600 Imported data +601 or +602 res : dict +603 Imported data and meta-data +604 """ +605 +606 if not fname.endswith('.xml') and not fname.endswith('.gz'): +607 fname += '.xml' +608 if gz: +609 if not fname.endswith('.gz'): +610 fname += '.gz' +611 with gzip.open(fname, 'r') as fin: +612 content = fin.read() +613 else: +614 if fname.endswith('.gz'): +615 warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning) +616 with open(fname, 'r') as fin: +617 content = fin.read() +618 +619 return import_dobs_string(content, full_output, separator_insertion=separator_insertion) 620 -621def _dobsdict_to_xmlstring(d): -622 if isinstance(d, dict): -623 iters = '' -624 for k in d: -625 if k.startswith('#value'): -626 for li in d[k]: -627 iters += li -628 return iters + '\n' -629 elif k.startswith('#'): -630 for li in d[k]: -631 iters += li -632 iters = '<array>\n' + iters + '<%sarray>\n' % ('/') -633 return iters -634 if isinstance(d[k], dict): -635 iters += '<%s>\n' % (k) + _dobsdict_to_xmlstring(d[k]) + '<%s%s>\n' % ('/', k) -636 elif isinstance(d[k], str): -637 if len(d[k]) > 100: -638 iters += '<%s>\n ' % (k) + d[k] + ' \n<%s%s>\n' % ('/', k) -639 else: -640 iters += '<%s> ' % (k) + d[k] + ' <%s%s>\n' % ('/', k) -641 elif isinstance(d[k], list): -642 tmps = '' -643 if k in ['edata', 'cdata']: -644 for i in range(len(d[k])): -645 tmps += '<%s>\n' % (k) + _dobsdict_to_xmlstring(d[k][i]) + '</%s>\n' % (k) -646 else: -647 for i in range(len(d[k])): -648 tmps += _dobsdict_to_xmlstring(d[k][i]) -649 iters += tmps -650 elif isinstance(d[k], (int, float)): -651 iters += '<%s> ' % (k) + str(d[k]) + ' <%s%s>\n' % ('/', k) -652 elif not d[k]: -653 return '\n' -654 else: -655 raise Exception('Type', type(d[k]), 'not supported in export!') -656 else: -657 raise Exception('Type', type(d), 'not supported in export!') -658 return iters -659 +621 +622def _dobsdict_to_xmlstring(d): +623 if isinstance(d, dict): +624 iters = '' +625 for k in d: +626 if k.startswith('#value'): +627 for li in d[k]: +628 iters += li +629 return iters + '\n' +630 elif k.startswith('#'): +631 for li in d[k]: +632 iters += li +633 iters = '<array>\n' + iters + '<%sarray>\n' % ('/') +634 return iters +635 if isinstance(d[k], dict): +636 iters += '<%s>\n' % (k) + _dobsdict_to_xmlstring(d[k]) + '<%s%s>\n' % ('/', k) +637 elif isinstance(d[k], str): +638 if len(d[k]) > 100: +639 iters += '<%s>\n ' % (k) + d[k] + ' \n<%s%s>\n' % ('/', k) +640 else: +641 iters += '<%s> ' % (k) + d[k] + ' <%s%s>\n' % ('/', k) +642 elif isinstance(d[k], list): +643 tmps = '' +644 if k in ['edata', 'cdata']: +645 for i in range(len(d[k])): +646 tmps += '<%s>\n' % (k) + _dobsdict_to_xmlstring(d[k][i]) + '</%s>\n' % (k) +647 else: +648 for i in range(len(d[k])): +649 tmps += _dobsdict_to_xmlstring(d[k][i]) +650 iters += tmps +651 elif isinstance(d[k], (int, float)): +652 iters += '<%s> ' % (k) + str(d[k]) + ' <%s%s>\n' % ('/', k) +653 elif not d[k]: +654 return '\n' +655 else: +656 raise Exception('Type', type(d[k]), 'not supported in export!') +657 else: +658 raise Exception('Type', type(d), 'not supported in export!') +659 return iters 660 -661def _dobsdict_to_xmlstring_spaces(d, space=' '): -662 s = _dobsdict_to_xmlstring(d) -663 o = '' -664 c = 0 -665 cm = False -666 for li in s.split('\n'): -667 if li.startswith('<%s' % ('/')): -668 c -= 1 -669 cm = True -670 for i in range(c): -671 o += space -672 o += li + '\n' -673 if li.startswith('<') and not cm: -674 if '<%s' % ('/') not in li: -675 c += 1 -676 cm = False -677 return o -678 +661 +662def _dobsdict_to_xmlstring_spaces(d, space=' '): +663 s = _dobsdict_to_xmlstring(d) +664 o = '' +665 c = 0 +666 cm = False +667 for li in s.split('\n'): +668 if li.startswith('<%s' % ('/')): +669 c -= 1 +670 cm = True +671 for i in range(c): +672 o += space +673 o += li + '\n' +674 if li.startswith('<') and not cm: +675 if '<%s' % ('/') not in li: +676 c += 1 +677 cm = False +678 return o 679 -680def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None): -681 """Generate the string for the export of a list of Obs or structures containing Obs -682 to a .xml.gz file according to the Zeuthen dobs format. -683 -684 Tags are not written or recovered automatically. The separator |is removed from the replica names. -685 -686 Parameters -687 ---------- -688 obsl : list -689 List of Obs that will be exported. -690 The Obs inside a structure do not have to be defined on the same set of configurations, -691 but the storage requirement is increased, if this is not the case. -692 name : str -693 The name of the observable. -694 spec : str -695 Optional string that describes the contents of the file. -696 origin : str -697 Specify where the data has its origin. -698 symbol : list -699 A list of symbols that describe the observables to be written. May be empty. -700 who : str -701 Provide the name of the person that exports the data. -702 enstags : dict -703 Provide alternative enstag for ensembles in the form enstags = {ename: enstag} -704 Otherwise, the ensemble name is used. -705 -706 Returns -707 ------- -708 xml_str : str -709 XML string generated from the data -710 """ -711 if enstags is None: -712 enstags = {} -713 od = {} -714 r_names = [] -715 for o in obsl: -716 r_names += [name for name in o.names if name.split('|')[0] in o.mc_names] -717 r_names = sorted(set(r_names)) -718 mc_names = sorted(set([n.split('|')[0] for n in r_names])) -719 for tmpname in mc_names: -720 if tmpname not in enstags: -721 enstags[tmpname] = tmpname -722 ne = len(set(mc_names)) -723 cov_names = [] -724 for o in obsl: -725 cov_names += list(o.cov_names) -726 cov_names = sorted(set(cov_names)) -727 nc = len(set(cov_names)) -728 od['OBSERVABLES'] = {} -729 od['OBSERVABLES']['SCHEMA'] = {'NAME': 'lattobs', 'VERSION': '1.0'} -730 if who is None: -731 who = getpass.getuser() -732 od['OBSERVABLES']['origin'] = { -733 'who': who, -734 'date': str(datetime.datetime.now())[:-7], -735 'host': socket.gethostname(), -736 'tool': {'name': 'pyerrors', 'version': pyerrorsversion.__version__}} -737 od['OBSERVABLES']['dobs'] = {} -738 pd = od['OBSERVABLES']['dobs'] -739 pd['spec'] = spec -740 pd['origin'] = origin -741 pd['name'] = name -742 pd['array'] = {} -743 pd['array']['id'] = 'val' -744 pd['array']['layout'] = '1 f%d' % (len(obsl)) -745 osymbol = '' -746 if symbol: -747 if not isinstance(symbol, list): -748 raise Exception('Symbol has to be a list!') -749 if not (len(symbol) == 0 or len(symbol) == len(obsl)): -750 raise Exception('Symbol has to be a list of lenght 0 or %d!' % (len(obsl))) -751 osymbol = symbol[0] -752 for s in symbol[1:]: -753 osymbol += ' %s' % s -754 pd['array']['symbol'] = osymbol -755 -756 pd['array']['#values'] = [' '.join(['%1.16e' % o.value for o in obsl])] -757 pd['ne'] = '%d' % (ne) -758 pd['nc'] = '%d' % (nc) -759 pd['edata'] = [] -760 for name in mc_names: -761 ed = {} -762 ed['enstag'] = enstags[name] -763 onames = sorted([n for n in r_names if (n.startswith(name + '|') or n == name)]) -764 nr = len(onames) -765 ed['nr'] = nr -766 ed[''] = [] -767 -768 for r in range(nr): -769 ad = {} -770 repname = onames[r] -771 ad['id'] = repname.replace('|', '') -772 idx = _merge_idx([o.idl.get(repname, []) for o in obsl]) -773 Nconf = len(idx) -774 layout = '%d i f%d' % (Nconf, len(obsl)) -775 ad['layout'] = layout -776 data = '' -777 counters = [0 for o in obsl] -778 offsets = [o.r_values[repname] - o.value if repname in o.r_values else 0 for o in obsl] -779 for ci in idx: -780 data += '%d ' % ci -781 for oi in range(len(obsl)): -782 o = obsl[oi] -783 if repname in o.idl: -784 if counters[oi] < 0: -785 num = 0 -786 if num == 0: -787 data += '0 ' -788 else: -789 data += '%1.16e ' % (num) -790 continue -791 if o.idl[repname][counters[oi]] == ci: -792 num = o.deltas[repname][counters[oi]] + offsets[oi] -793 if num == 0: -794 data += '0 ' -795 else: -796 data += '%1.16e ' % (num) -797 counters[oi] += 1 -798 if counters[oi] >= len(o.idl[repname]): -799 counters[oi] = -1 -800 else: -801 num = 0 -802 if num == 0: -803 data += '0 ' -804 else: -805 data += '%1.16e ' % (num) -806 else: -807 data += '0 ' -808 data += '\n' -809 ad['#data'] = data -810 ed[''].append(ad) -811 pd['edata'].append(ed) -812 -813 allcov = {} -814 for o in obsl: -815 for cname in o.cov_names: -816 if cname in allcov: -817 if not np.array_equal(allcov[cname], o.covobs[cname].cov): -818 raise Exception('Inconsistent covariance matrices for %s!' % (cname)) -819 else: -820 allcov[cname] = o.covobs[cname].cov -821 pd['cdata'] = [] -822 for cname in cov_names: -823 cd = {} -824 cd['id'] = cname -825 -826 covd = {'id': 'cov'} -827 if allcov[cname].shape == (): -828 ncov = 1 -829 covd['layout'] = '1 1 f' -830 covd['#data'] = '%1.14e' % (allcov[cname]) -831 else: -832 shape = allcov[cname].shape -833 assert (shape[0] == shape[1]) -834 ncov = shape[0] -835 covd['layout'] = '%d %d f' % (ncov, ncov) -836 ds = '' -837 for i in range(ncov): -838 for j in range(ncov): -839 val = allcov[cname][i][j] -840 if val == 0: -841 ds += '0 ' -842 else: -843 ds += '%1.14e ' % (val) -844 ds += '\n' -845 covd['#data'] = ds -846 -847 gradd = {'id': 'grad'} -848 gradd['layout'] = '%d f%d' % (ncov, len(obsl)) -849 ds = '' -850 for i in range(ncov): -851 for o in obsl: -852 if cname in o.covobs: -853 val = o.covobs[cname].grad[i].item() -854 if val != 0: -855 ds += '%1.14e ' % (val) -856 else: -857 ds += '0 ' -858 else: -859 ds += '0 ' -860 gradd['#data'] = ds -861 cd['array'] = [covd, gradd] -862 pd['cdata'].append(cd) -863 -864 rs = '<?xml version="1.0" encoding="utf-8"?>\n' + _dobsdict_to_xmlstring_spaces(od) -865 -866 return rs -867 +680 +681def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None): +682 """Generate the string for the export of a list of Obs or structures containing Obs +683 to a .xml.gz file according to the Zeuthen dobs format. +684 +685 Tags are not written or recovered automatically. The separator |is removed from the replica names. +686 +687 Parameters +688 ---------- +689 obsl : list +690 List of Obs that will be exported. +691 The Obs inside a structure do not have to be defined on the same set of configurations, +692 but the storage requirement is increased, if this is not the case. +693 name : str +694 The name of the observable. +695 spec : str +696 Optional string that describes the contents of the file. +697 origin : str +698 Specify where the data has its origin. +699 symbol : list +700 A list of symbols that describe the observables to be written. May be empty. +701 who : str +702 Provide the name of the person that exports the data. +703 enstags : dict +704 Provide alternative enstag for ensembles in the form enstags = {ename: enstag} +705 Otherwise, the ensemble name is used. +706 +707 Returns +708 ------- +709 xml_str : str +710 XML string generated from the data +711 """ +712 if enstags is None: +713 enstags = {} +714 od = {} +715 r_names = [] +716 for o in obsl: +717 r_names += [name for name in o.names if name.split('|')[0] in o.mc_names] +718 r_names = sorted(set(r_names)) +719 mc_names = sorted(set([n.split('|')[0] for n in r_names])) +720 for tmpname in mc_names: +721 if tmpname not in enstags: +722 enstags[tmpname] = tmpname +723 ne = len(set(mc_names)) +724 cov_names = [] +725 for o in obsl: +726 cov_names += list(o.cov_names) +727 cov_names = sorted(set(cov_names)) +728 nc = len(set(cov_names)) +729 od['OBSERVABLES'] = {} +730 od['OBSERVABLES']['SCHEMA'] = {'NAME': 'lattobs', 'VERSION': '1.0'} +731 if who is None: +732 who = getpass.getuser() +733 od['OBSERVABLES']['origin'] = { +734 'who': who, +735 'date': str(datetime.datetime.now())[:-7], +736 'host': socket.gethostname(), +737 'tool': {'name': 'pyerrors', 'version': pyerrorsversion.__version__}} +738 od['OBSERVABLES']['dobs'] = {} +739 pd = od['OBSERVABLES']['dobs'] +740 pd['spec'] = spec +741 pd['origin'] = origin +742 pd['name'] = name +743 pd['array'] = {} +744 pd['array']['id'] = 'val' +745 pd['array']['layout'] = '1 f%d' % (len(obsl)) +746 osymbol = '' +747 if symbol: +748 if not isinstance(symbol, list): +749 raise Exception('Symbol has to be a list!') +750 if not (len(symbol) == 0 or len(symbol) == len(obsl)): +751 raise Exception('Symbol has to be a list of lenght 0 or %d!' % (len(obsl))) +752 osymbol = symbol[0] +753 for s in symbol[1:]: +754 osymbol += ' %s' % s +755 pd['array']['symbol'] = osymbol +756 +757 pd['array']['#values'] = [' '.join(['%1.16e' % o.value for o in obsl])] +758 pd['ne'] = '%d' % (ne) +759 pd['nc'] = '%d' % (nc) +760 pd['edata'] = [] +761 for name in mc_names: +762 ed = {} +763 ed['enstag'] = enstags[name] +764 onames = sorted([n for n in r_names if (n.startswith(name + '|') or n == name)]) +765 nr = len(onames) +766 ed['nr'] = nr +767 ed[''] = [] +768 +769 for r in range(nr): +770 ad = {} +771 repname = onames[r] +772 ad['id'] = repname.replace('|', '') +773 idx = _merge_idx([o.idl.get(repname, []) for o in obsl]) +774 Nconf = len(idx) +775 layout = '%d i f%d' % (Nconf, len(obsl)) +776 ad['layout'] = layout +777 data = '' +778 counters = [0 for o in obsl] +779 offsets = [o.r_values[repname] - o.value if repname in o.r_values else 0 for o in obsl] +780 for ci in idx: +781 data += '%d ' % ci +782 for oi in range(len(obsl)): +783 o = obsl[oi] +784 if repname in o.idl: +785 if counters[oi] < 0: +786 num = 0 +787 if num == 0: +788 data += '0 ' +789 else: +790 data += '%1.16e ' % (num) +791 continue +792 if o.idl[repname][counters[oi]] == ci: +793 num = o.deltas[repname][counters[oi]] + offsets[oi] +794 if num == 0: +795 data += '0 ' +796 else: +797 data += '%1.16e ' % (num) +798 counters[oi] += 1 +799 if counters[oi] >= len(o.idl[repname]): +800 counters[oi] = -1 +801 else: +802 num = 0 +803 if num == 0: +804 data += '0 ' +805 else: +806 data += '%1.16e ' % (num) +807 else: +808 data += '0 ' +809 data += '\n' +810 ad['#data'] = data +811 ed[''].append(ad) +812 pd['edata'].append(ed) +813 +814 allcov = {} +815 for o in obsl: +816 for cname in o.cov_names: +817 if cname in allcov: +818 if not np.array_equal(allcov[cname], o.covobs[cname].cov): +819 raise Exception('Inconsistent covariance matrices for %s!' % (cname)) +820 else: +821 allcov[cname] = o.covobs[cname].cov +822 pd['cdata'] = [] +823 for cname in cov_names: +824 cd = {} +825 cd['id'] = cname +826 +827 covd = {'id': 'cov'} +828 if allcov[cname].shape == (): +829 ncov = 1 +830 covd['layout'] = '1 1 f' +831 covd['#data'] = '%1.14e' % (allcov[cname]) +832 else: +833 shape = allcov[cname].shape +834 assert (shape[0] == shape[1]) +835 ncov = shape[0] +836 covd['layout'] = '%d %d f' % (ncov, ncov) +837 ds = '' +838 for i in range(ncov): +839 for j in range(ncov): +840 val = allcov[cname][i][j] +841 if val == 0: +842 ds += '0 ' +843 else: +844 ds += '%1.14e ' % (val) +845 ds += '\n' +846 covd['#data'] = ds +847 +848 gradd = {'id': 'grad'} +849 gradd['layout'] = '%d f%d' % (ncov, len(obsl)) +850 ds = '' +851 for i in range(ncov): +852 for o in obsl: +853 if cname in o.covobs: +854 val = o.covobs[cname].grad[i].item() +855 if val != 0: +856 ds += '%1.14e ' % (val) +857 else: +858 ds += '0 ' +859 else: +860 ds += '0 ' +861 gradd['#data'] = ds +862 cd['array'] = [covd, gradd] +863 pd['cdata'].append(cd) +864 +865 rs = '<?xml version="1.0" encoding="utf-8"?>\n' + _dobsdict_to_xmlstring_spaces(od) +866 +867 return rs 868 -869def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True): -870 """Export a list of Obs or structures containing Obs to a .xml.gz file -871 according to the Zeuthen dobs format. -872 -873 Tags are not written or recovered automatically. The separator | is removed from the replica names. -874 -875 Parameters -876 ---------- -877 obsl : list -878 List of Obs that will be exported. -879 The Obs inside a structure do not have to be defined on the same set of configurations, -880 but the storage requirement is increased, if this is not the case. -881 fname : str -882 Filename of the output file. -883 name : str -884 The name of the observable. -885 spec : str -886 Optional string that describes the contents of the file. -887 origin : str -888 Specify where the data has its origin. -889 symbol : list -890 A list of symbols that describe the observables to be written. May be empty. -891 who : str -892 Provide the name of the person that exports the data. -893 enstags : dict -894 Provide alternative enstag for ensembles in the form enstags = {ename: enstag} -895 Otherwise, the ensemble name is used. -896 gz : bool -897 If True, the output is a gzipped XML. If False, the output is a XML file. -898 -899 Returns -900 ------- -901 None -902 """ -903 if enstags is None: -904 enstags = {} -905 -906 dobsstring = create_dobs_string(obsl, name, spec, origin, symbol, who, enstags=enstags) -907 -908 if not fname.endswith('.xml') and not fname.endswith('.gz'): -909 fname += '.xml' -910 -911 if gz: -912 if not fname.endswith('.gz'): -913 fname += '.gz' -914 -915 fp = gzip.open(fname, 'wb') -916 fp.write(dobsstring.encode('utf-8')) -917 else: -918 fp = open(fname, 'w', encoding='utf-8') -919 fp.write(dobsstring) -920 fp.close() +869 +870def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True): +871 """Export a list of Obs or structures containing Obs to a .xml.gz file +872 according to the Zeuthen dobs format. +873 +874 Tags are not written or recovered automatically. The separator | is removed from the replica names. +875 +876 Parameters +877 ---------- +878 obsl : list +879 List of Obs that will be exported. +880 The Obs inside a structure do not have to be defined on the same set of configurations, +881 but the storage requirement is increased, if this is not the case. +882 fname : str +883 Filename of the output file. +884 name : str +885 The name of the observable. +886 spec : str +887 Optional string that describes the contents of the file. +888 origin : str +889 Specify where the data has its origin. +890 symbol : list +891 A list of symbols that describe the observables to be written. May be empty. +892 who : str +893 Provide the name of the person that exports the data. +894 enstags : dict +895 Provide alternative enstag for ensembles in the form enstags = {ename: enstag} +896 Otherwise, the ensemble name is used. +897 gz : bool +898 If True, the output is a gzipped XML. If False, the output is a XML file. +899 +900 Returns +901 ------- +902 None +903 """ +904 if enstags is None: +905 enstags = {} +906 +907 dobsstring = create_dobs_string(obsl, name, spec, origin, symbol, who, enstags=enstags) +908 +909 if not fname.endswith('.xml') and not fname.endswith('.gz'): +910 fname += '.xml' +911 +912 if gz: +913 if not fname.endswith('.gz'): +914 fname += '.gz' +915 +916 fp = gzip.open(fname, 'wb') +917 fp.write(dobsstring.encode('utf-8')) +918 else: +919 fp = open(fname, 'w', encoding='utf-8') +920 fp.write(dobsstring) +921 fp.close() @@ -1535,46 +1536,47 @@ Imported data and meta-data 530 deltas.append(repdeltas) 531 idl.append(repidl) 532 -533 res.append(Obs(deltas, obs_names, idl=idl)) -534 res[-1]._value = mean[i] -535 _check(len(e_names) == ne) -536 -537 cnames = list(covd.keys()) -538 for i in range(len(res)): -539 new_covobs = {name: Covobs(0, covd[name], name, grad=gradd[name][i]) for name in cnames} -540 for name in cnames: -541 if np.all(new_covobs[name].grad == 0): -542 del new_covobs[name] -543 cnames_loc = list(new_covobs.keys()) -544 for name in cnames_loc: -545 res[i].names.append(name) -546 res[i].shape[name] = 1 -547 res[i].idl[name] = [] -548 res[i]._covobs = new_covobs -549 -550 if symbol: -551 for i in range(len(res)): -552 res[i].tag = symbol[i] -553 if res[i].tag == 'None': -554 res[i].tag = None -555 if full_output: -556 retd = {} -557 tool = file_origin.get('tool', None) -558 if tool: -559 program = tool['name'] + ' ' + tool['version'] -560 else: -561 program = '' -562 retd['program'] = program -563 retd['version'] = version -564 retd['who'] = file_origin['who'] -565 retd['date'] = file_origin['date'] -566 retd['host'] = file_origin['host'] -567 retd['description'] = descriptiond -568 retd['enstags'] = enstags -569 retd['obsdata'] = res -570 return retd -571 else: -572 return res +533 obsmeans = [np.average(deltas[j]) for j in range(len(deltas))] +534 res.append(Obs([np.array(deltas[j]) - obsmeans[j] for j in range(len(obsmeans))], obs_names, idl=idl, means=obsmeans)) +535 res[-1]._value = mean[i] +536 _check(len(e_names) == ne) +537 +538 cnames = list(covd.keys()) +539 for i in range(len(res)): +540 new_covobs = {name: Covobs(0, covd[name], name, grad=gradd[name][i]) for name in cnames} +541 for name in cnames: +542 if np.all(new_covobs[name].grad == 0): +543 del new_covobs[name] +544 cnames_loc = list(new_covobs.keys()) +545 for name in cnames_loc: +546 res[i].names.append(name) +547 res[i].shape[name] = 1 +548 res[i].idl[name] = [] +549 res[i]._covobs = new_covobs +550 +551 if symbol: +552 for i in range(len(res)): +553 res[i].tag = symbol[i] +554 if res[i].tag == 'None': +555 res[i].tag = None +556 if full_output: +557 retd = {} +558 tool = file_origin.get('tool', None) +559 if tool: +560 program = tool['name'] + ' ' + tool['version'] +561 else: +562 program = '' +563 retd['program'] = program +564 retd['version'] = version +565 retd['who'] = file_origin['who'] +566 retd['date'] = file_origin['date'] +567 retd['host'] = file_origin['host'] +568 retd['description'] = descriptiond +569 retd['enstags'] = enstags +570 retd['obsdata'] = res +571 return retd +572 else: +573 return res @@ -1623,51 +1625,51 @@ Imported data and meta-data - 
575def read_dobs(fname, full_output=False, gz=True, separator_insertion=True):
-576    """Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
-577
-578    Tags are not written or recovered automatically.
-579
-580    Parameters
-581    ----------
-582    fname : str
-583        Filename of the input file.
-584    full_output : bool
-585        If True, a dict containing auxiliary information and the data is returned.
-586        If False, only the data is returned as list.
-587    gz : bool
-588        If True, assumes that data is gzipped. If False, assumes XML file.
-589    separatior_insertion: str, int or bool
-590        str: replace all occurences of "separator_insertion" within the replica names
-591        by "|%s" % (separator_insertion) when constructing the names of the replica.
-592        int: Insert the separator "|" at the position given by separator_insertion.
-593        True (default): separator "|" is inserted after len(ensname), assuming that the
-594        ensemble name is a prefix to the replica name.
-595        None or False: No separator is inserted.
-596
-597    Returns
-598    -------
-599    res : list[Obs]
-600        Imported data
-601    or
-602    res : dict
-603        Imported data and meta-data
-604    """
-605
-606    if not fname.endswith('.xml') and not fname.endswith('.gz'):
-607        fname += '.xml'
-608    if gz:
-609        if not fname.endswith('.gz'):
-610            fname += '.gz'
-611        with gzip.open(fname, 'r') as fin:
-612            content = fin.read()
-613    else:
-614        if fname.endswith('.gz'):
-615            warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning)
-616        with open(fname, 'r') as fin:
-617            content = fin.read()
-618
-619    return import_dobs_string(content, full_output, separator_insertion=separator_insertion)
+            
576def read_dobs(fname, full_output=False, gz=True, separator_insertion=True):
+577    """Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
+578
+579    Tags are not written or recovered automatically.
+580
+581    Parameters
+582    ----------
+583    fname : str
+584        Filename of the input file.
+585    full_output : bool
+586        If True, a dict containing auxiliary information and the data is returned.
+587        If False, only the data is returned as list.
+588    gz : bool
+589        If True, assumes that data is gzipped. If False, assumes XML file.
+590    separatior_insertion: str, int or bool
+591        str: replace all occurences of "separator_insertion" within the replica names
+592        by "|%s" % (separator_insertion) when constructing the names of the replica.
+593        int: Insert the separator "|" at the position given by separator_insertion.
+594        True (default): separator "|" is inserted after len(ensname), assuming that the
+595        ensemble name is a prefix to the replica name.
+596        None or False: No separator is inserted.
+597
+598    Returns
+599    -------
+600    res : list[Obs]
+601        Imported data
+602    or
+603    res : dict
+604        Imported data and meta-data
+605    """
+606
+607    if not fname.endswith('.xml') and not fname.endswith('.gz'):
+608        fname += '.xml'
+609    if gz:
+610        if not fname.endswith('.gz'):
+611            fname += '.gz'
+612        with gzip.open(fname, 'r') as fin:
+613            content = fin.read()
+614    else:
+615        if fname.endswith('.gz'):
+616            warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning)
+617        with open(fname, 'r') as fin:
+618            content = fin.read()
+619
+620    return import_dobs_string(content, full_output, separator_insertion=separator_insertion)
 

 
 
@@ -1718,193 +1720,193 @@ Imported data and meta-data
- 
681def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None):
-682    """Generate the string for the export of a list of Obs or structures containing Obs
-683    to a .xml.gz file according to the Zeuthen dobs format.
-684
-685    Tags are not written or recovered automatically. The separator |is removed from the replica names.
-686
-687    Parameters
-688    ----------
-689    obsl : list
-690        List of Obs that will be exported.
-691        The Obs inside a structure do not have to be defined on the same set of configurations,
-692        but the storage requirement is increased, if this is not the case.
-693    name : str
-694        The name of the observable.
-695    spec : str
-696        Optional string that describes the contents of the file.
-697    origin : str
-698        Specify where the data has its origin.
-699    symbol : list
-700        A list of symbols that describe the observables to be written. May be empty.
-701    who : str
-702        Provide the name of the person that exports the data.
-703    enstags : dict
-704        Provide alternative enstag for ensembles in the form enstags = {ename: enstag}
-705        Otherwise, the ensemble name is used.
-706
-707    Returns
-708    -------
-709    xml_str : str
-710        XML string generated from the data
-711    """
-712    if enstags is None:
-713        enstags = {}
-714    od = {}
-715    r_names = []
-716    for o in obsl:
-717        r_names += [name for name in o.names if name.split('|')[0] in o.mc_names]
-718    r_names = sorted(set(r_names))
-719    mc_names = sorted(set([n.split('|')[0] for n in r_names]))
-720    for tmpname in mc_names:
-721        if tmpname not in enstags:
-722            enstags[tmpname] = tmpname
-723    ne = len(set(mc_names))
-724    cov_names = []
-725    for o in obsl:
-726        cov_names += list(o.cov_names)
-727    cov_names = sorted(set(cov_names))
-728    nc = len(set(cov_names))
-729    od['OBSERVABLES'] = {}
-730    od['OBSERVABLES']['SCHEMA'] = {'NAME': 'lattobs', 'VERSION': '1.0'}
-731    if who is None:
-732        who = getpass.getuser()
-733    od['OBSERVABLES']['origin'] = {
-734        'who': who,
-735        'date': str(datetime.datetime.now())[:-7],
-736        'host': socket.gethostname(),
-737        'tool': {'name': 'pyerrors', 'version': pyerrorsversion.__version__}}
-738    od['OBSERVABLES']['dobs'] = {}
-739    pd = od['OBSERVABLES']['dobs']
-740    pd['spec'] = spec
-741    pd['origin'] = origin
-742    pd['name'] = name
-743    pd['array'] = {}
-744    pd['array']['id'] = 'val'
-745    pd['array']['layout'] = '1 f%d' % (len(obsl))
-746    osymbol = ''
-747    if symbol:
-748        if not isinstance(symbol, list):
-749            raise Exception('Symbol has to be a list!')
-750        if not (len(symbol) == 0 or len(symbol) == len(obsl)):
-751            raise Exception('Symbol has to be a list of lenght 0 or %d!' % (len(obsl)))
-752        osymbol = symbol[0]
-753        for s in symbol[1:]:
-754            osymbol += ' %s' % s
-755        pd['array']['symbol'] = osymbol
-756
-757    pd['array']['#values'] = ['  '.join(['%1.16e' % o.value for o in obsl])]
-758    pd['ne'] = '%d' % (ne)
-759    pd['nc'] = '%d' % (nc)
-760    pd['edata'] = []
-761    for name in mc_names:
-762        ed = {}
-763        ed['enstag'] = enstags[name]
-764        onames = sorted([n for n in r_names if (n.startswith(name + '|') or n == name)])
-765        nr = len(onames)
-766        ed['nr'] = nr
-767        ed[''] = []
-768
-769        for r in range(nr):
-770            ad = {}
-771            repname = onames[r]
-772            ad['id'] = repname.replace('|', '')
-773            idx = _merge_idx([o.idl.get(repname, []) for o in obsl])
-774            Nconf = len(idx)
-775            layout = '%d i f%d' % (Nconf, len(obsl))
-776            ad['layout'] = layout
-777            data = ''
-778            counters = [0 for o in obsl]
-779            offsets = [o.r_values[repname] - o.value if repname in o.r_values else 0 for o in obsl]
-780            for ci in idx:
-781                data += '%d ' % ci
-782                for oi in range(len(obsl)):
-783                    o = obsl[oi]
-784                    if repname in o.idl:
-785                        if counters[oi] < 0:
-786                            num = 0
-787                            if num == 0:
-788                                data += '0 '
-789                            else:
-790                                data += '%1.16e ' % (num)
-791                            continue
-792                        if o.idl[repname][counters[oi]] == ci:
-793                            num = o.deltas[repname][counters[oi]] + offsets[oi]
-794                            if num == 0:
-795                                data += '0 '
-796                            else:
-797                                data += '%1.16e ' % (num)
-798                            counters[oi] += 1
-799                            if counters[oi] >= len(o.idl[repname]):
-800                                counters[oi] = -1
-801                        else:
-802                            num = 0
-803                            if num == 0:
-804                                data += '0 '
-805                            else:
-806                                data += '%1.16e ' % (num)
-807                    else:
-808                        data += '0 '
-809                data += '\n'
-810            ad['#data'] = data
-811            ed[''].append(ad)
-812        pd['edata'].append(ed)
-813
-814        allcov = {}
-815        for o in obsl:
-816            for cname in o.cov_names:
-817                if cname in allcov:
-818                    if not np.array_equal(allcov[cname], o.covobs[cname].cov):
-819                        raise Exception('Inconsistent covariance matrices for %s!' % (cname))
-820                else:
-821                    allcov[cname] = o.covobs[cname].cov
-822        pd['cdata'] = []
-823        for cname in cov_names:
-824            cd = {}
-825            cd['id'] = cname
-826
-827            covd = {'id': 'cov'}
-828            if allcov[cname].shape == ():
-829                ncov = 1
-830                covd['layout'] = '1 1 f'
-831                covd['#data'] = '%1.14e' % (allcov[cname])
-832            else:
-833                shape = allcov[cname].shape
-834                assert (shape[0] == shape[1])
-835                ncov = shape[0]
-836                covd['layout'] = '%d %d f' % (ncov, ncov)
-837                ds = ''
-838                for i in range(ncov):
-839                    for j in range(ncov):
-840                        val = allcov[cname][i][j]
-841                        if val == 0:
-842                            ds += '0 '
-843                        else:
-844                            ds += '%1.14e ' % (val)
-845                    ds += '\n'
-846                covd['#data'] = ds
-847
-848            gradd = {'id': 'grad'}
-849            gradd['layout'] = '%d f%d' % (ncov, len(obsl))
-850            ds = ''
-851            for i in range(ncov):
-852                for o in obsl:
-853                    if cname in o.covobs:
-854                        val = o.covobs[cname].grad[i].item()
-855                        if val != 0:
-856                            ds += '%1.14e ' % (val)
-857                        else:
-858                            ds += '0 '
-859                    else:
-860                        ds += '0 '
-861            gradd['#data'] = ds
-862            cd['array'] = [covd, gradd]
-863            pd['cdata'].append(cd)
-864
-865    rs = '<?xml version="1.0" encoding="utf-8"?>\n' + _dobsdict_to_xmlstring_spaces(od)
-866
-867    return rs
+            
682def create_dobs_string(obsl, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None):
+683    """Generate the string for the export of a list of Obs or structures containing Obs
+684    to a .xml.gz file according to the Zeuthen dobs format.
+685
+686    Tags are not written or recovered automatically. The separator |is removed from the replica names.
+687
+688    Parameters
+689    ----------
+690    obsl : list
+691        List of Obs that will be exported.
+692        The Obs inside a structure do not have to be defined on the same set of configurations,
+693        but the storage requirement is increased, if this is not the case.
+694    name : str
+695        The name of the observable.
+696    spec : str
+697        Optional string that describes the contents of the file.
+698    origin : str
+699        Specify where the data has its origin.
+700    symbol : list
+701        A list of symbols that describe the observables to be written. May be empty.
+702    who : str
+703        Provide the name of the person that exports the data.
+704    enstags : dict
+705        Provide alternative enstag for ensembles in the form enstags = {ename: enstag}
+706        Otherwise, the ensemble name is used.
+707
+708    Returns
+709    -------
+710    xml_str : str
+711        XML string generated from the data
+712    """
+713    if enstags is None:
+714        enstags = {}
+715    od = {}
+716    r_names = []
+717    for o in obsl:
+718        r_names += [name for name in o.names if name.split('|')[0] in o.mc_names]
+719    r_names = sorted(set(r_names))
+720    mc_names = sorted(set([n.split('|')[0] for n in r_names]))
+721    for tmpname in mc_names:
+722        if tmpname not in enstags:
+723            enstags[tmpname] = tmpname
+724    ne = len(set(mc_names))
+725    cov_names = []
+726    for o in obsl:
+727        cov_names += list(o.cov_names)
+728    cov_names = sorted(set(cov_names))
+729    nc = len(set(cov_names))
+730    od['OBSERVABLES'] = {}
+731    od['OBSERVABLES']['SCHEMA'] = {'NAME': 'lattobs', 'VERSION': '1.0'}
+732    if who is None:
+733        who = getpass.getuser()
+734    od['OBSERVABLES']['origin'] = {
+735        'who': who,
+736        'date': str(datetime.datetime.now())[:-7],
+737        'host': socket.gethostname(),
+738        'tool': {'name': 'pyerrors', 'version': pyerrorsversion.__version__}}
+739    od['OBSERVABLES']['dobs'] = {}
+740    pd = od['OBSERVABLES']['dobs']
+741    pd['spec'] = spec
+742    pd['origin'] = origin
+743    pd['name'] = name
+744    pd['array'] = {}
+745    pd['array']['id'] = 'val'
+746    pd['array']['layout'] = '1 f%d' % (len(obsl))
+747    osymbol = ''
+748    if symbol:
+749        if not isinstance(symbol, list):
+750            raise Exception('Symbol has to be a list!')
+751        if not (len(symbol) == 0 or len(symbol) == len(obsl)):
+752            raise Exception('Symbol has to be a list of lenght 0 or %d!' % (len(obsl)))
+753        osymbol = symbol[0]
+754        for s in symbol[1:]:
+755            osymbol += ' %s' % s
+756        pd['array']['symbol'] = osymbol
+757
+758    pd['array']['#values'] = ['  '.join(['%1.16e' % o.value for o in obsl])]
+759    pd['ne'] = '%d' % (ne)
+760    pd['nc'] = '%d' % (nc)
+761    pd['edata'] = []
+762    for name in mc_names:
+763        ed = {}
+764        ed['enstag'] = enstags[name]
+765        onames = sorted([n for n in r_names if (n.startswith(name + '|') or n == name)])
+766        nr = len(onames)
+767        ed['nr'] = nr
+768        ed[''] = []
+769
+770        for r in range(nr):
+771            ad = {}
+772            repname = onames[r]
+773            ad['id'] = repname.replace('|', '')
+774            idx = _merge_idx([o.idl.get(repname, []) for o in obsl])
+775            Nconf = len(idx)
+776            layout = '%d i f%d' % (Nconf, len(obsl))
+777            ad['layout'] = layout
+778            data = ''
+779            counters = [0 for o in obsl]
+780            offsets = [o.r_values[repname] - o.value if repname in o.r_values else 0 for o in obsl]
+781            for ci in idx:
+782                data += '%d ' % ci
+783                for oi in range(len(obsl)):
+784                    o = obsl[oi]
+785                    if repname in o.idl:
+786                        if counters[oi] < 0:
+787                            num = 0
+788                            if num == 0:
+789                                data += '0 '
+790                            else:
+791                                data += '%1.16e ' % (num)
+792                            continue
+793                        if o.idl[repname][counters[oi]] == ci:
+794                            num = o.deltas[repname][counters[oi]] + offsets[oi]
+795                            if num == 0:
+796                                data += '0 '
+797                            else:
+798                                data += '%1.16e ' % (num)
+799                            counters[oi] += 1
+800                            if counters[oi] >= len(o.idl[repname]):
+801                                counters[oi] = -1
+802                        else:
+803                            num = 0
+804                            if num == 0:
+805                                data += '0 '
+806                            else:
+807                                data += '%1.16e ' % (num)
+808                    else:
+809                        data += '0 '
+810                data += '\n'
+811            ad['#data'] = data
+812            ed[''].append(ad)
+813        pd['edata'].append(ed)
+814
+815        allcov = {}
+816        for o in obsl:
+817            for cname in o.cov_names:
+818                if cname in allcov:
+819                    if not np.array_equal(allcov[cname], o.covobs[cname].cov):
+820                        raise Exception('Inconsistent covariance matrices for %s!' % (cname))
+821                else:
+822                    allcov[cname] = o.covobs[cname].cov
+823        pd['cdata'] = []
+824        for cname in cov_names:
+825            cd = {}
+826            cd['id'] = cname
+827
+828            covd = {'id': 'cov'}
+829            if allcov[cname].shape == ():
+830                ncov = 1
+831                covd['layout'] = '1 1 f'
+832                covd['#data'] = '%1.14e' % (allcov[cname])
+833            else:
+834                shape = allcov[cname].shape
+835                assert (shape[0] == shape[1])
+836                ncov = shape[0]
+837                covd['layout'] = '%d %d f' % (ncov, ncov)
+838                ds = ''
+839                for i in range(ncov):
+840                    for j in range(ncov):
+841                        val = allcov[cname][i][j]
+842                        if val == 0:
+843                            ds += '0 '
+844                        else:
+845                            ds += '%1.14e ' % (val)
+846                    ds += '\n'
+847                covd['#data'] = ds
+848
+849            gradd = {'id': 'grad'}
+850            gradd['layout'] = '%d f%d' % (ncov, len(obsl))
+851            ds = ''
+852            for i in range(ncov):
+853                for o in obsl:
+854                    if cname in o.covobs:
+855                        val = o.covobs[cname].grad[i].item()
+856                        if val != 0:
+857                            ds += '%1.14e ' % (val)
+858                        else:
+859                            ds += '0 '
+860                    else:
+861                        ds += '0 '
+862            gradd['#data'] = ds
+863            cd['array'] = [covd, gradd]
+864            pd['cdata'].append(cd)
+865
+866    rs = '<?xml version="1.0" encoding="utf-8"?>\n' + _dobsdict_to_xmlstring_spaces(od)
+867
+868    return rs
 

 
 
@@ -1956,58 +1958,58 @@ XML string generated from the data
- 
870def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True):
-871    """Export a list of Obs or structures containing Obs to a .xml.gz file
-872    according to the Zeuthen dobs format.
-873
-874    Tags are not written or recovered automatically. The separator | is removed from the replica names.
-875
-876    Parameters
-877    ----------
-878    obsl : list
-879        List of Obs that will be exported.
-880        The Obs inside a structure do not have to be defined on the same set of configurations,
-881        but the storage requirement is increased, if this is not the case.
-882    fname : str
-883        Filename of the output file.
-884    name : str
-885        The name of the observable.
-886    spec : str
-887        Optional string that describes the contents of the file.
-888    origin : str
-889        Specify where the data has its origin.
-890    symbol : list
-891        A list of symbols that describe the observables to be written. May be empty.
-892    who : str
-893        Provide the name of the person that exports the data.
-894    enstags : dict
-895        Provide alternative enstag for ensembles in the form enstags = {ename: enstag}
-896        Otherwise, the ensemble name is used.
-897    gz : bool
-898        If True, the output is a gzipped XML. If False, the output is a XML file.
-899
-900    Returns
-901    -------
-902    None
-903    """
-904    if enstags is None:
-905        enstags = {}
-906
-907    dobsstring = create_dobs_string(obsl, name, spec, origin, symbol, who, enstags=enstags)
-908
-909    if not fname.endswith('.xml') and not fname.endswith('.gz'):
-910        fname += '.xml'
-911
-912    if gz:
-913        if not fname.endswith('.gz'):
-914            fname += '.gz'
-915
-916        fp = gzip.open(fname, 'wb')
-917        fp.write(dobsstring.encode('utf-8'))
-918    else:
-919        fp = open(fname, 'w', encoding='utf-8')
-920        fp.write(dobsstring)
-921    fp.close()
+            
871def write_dobs(obsl, fname, name, spec='dobs v1.0', origin='', symbol=[], who=None, enstags=None, gz=True):
+872    """Export a list of Obs or structures containing Obs to a .xml.gz file
+873    according to the Zeuthen dobs format.
+874
+875    Tags are not written or recovered automatically. The separator | is removed from the replica names.
+876
+877    Parameters
+878    ----------
+879    obsl : list
+880        List of Obs that will be exported.
+881        The Obs inside a structure do not have to be defined on the same set of configurations,
+882        but the storage requirement is increased, if this is not the case.
+883    fname : str
+884        Filename of the output file.
+885    name : str
+886        The name of the observable.
+887    spec : str
+888        Optional string that describes the contents of the file.
+889    origin : str
+890        Specify where the data has its origin.
+891    symbol : list
+892        A list of symbols that describe the observables to be written. May be empty.
+893    who : str
+894        Provide the name of the person that exports the data.
+895    enstags : dict
+896        Provide alternative enstag for ensembles in the form enstags = {ename: enstag}
+897        Otherwise, the ensemble name is used.
+898    gz : bool
+899        If True, the output is a gzipped XML. If False, the output is a XML file.
+900
+901    Returns
+902    -------
+903    None
+904    """
+905    if enstags is None:
+906        enstags = {}
+907
+908    dobsstring = create_dobs_string(obsl, name, spec, origin, symbol, who, enstags=enstags)
+909
+910    if not fname.endswith('.xml') and not fname.endswith('.gz'):
+911        fname += '.xml'
+912
+913    if gz:
+914        if not fname.endswith('.gz'):
+915            fname += '.gz'
+916
+917        fp = gzip.open(fname, 'wb')
+918        fp.write(dobsstring.encode('utf-8'))
+919    else:
+920        fp = open(fname, 'w', encoding='utf-8')
+921        fp.write(dobsstring)
+922    fp.close()
 

 
 
diff --git a/docs/pyerrors/input/json.html b/docs/pyerrors/input/json.html
index c6ad22a8..b7217b7f 100644
--- a/docs/pyerrors/input/json.html
+++ b/docs/pyerrors/input/json.html
@@ -226,640 +226,644 @@
 133        names = []
 134        idl = []
 135        for key, value in obs.idl.items():
-136            samples.append([np.nan] * len(value))
+136            samples.append(np.array([np.nan] * len(value)))
 137            names.append(key)
 138            idl.append(value)
-139        my_obs = Obs(samples, names, idl)
-140        my_obs._covobs = obs._covobs
-141        for name in obs._covobs:
-142            my_obs.names.append(name)
-143        my_obs.reweighted = obs.reweighted
-144        return my_obs
-145
-146    def write_Corr_to_dict(my_corr):
-147        first_not_none = next(i for i, j in enumerate(my_corr.content) if np.all(j))
-148        dummy_array = np.empty((my_corr.N, my_corr.N), dtype=object)
-149        dummy_array[:] = _nan_Obs_like(my_corr.content[first_not_none].ravel()[0])
-150        content = [o if o is not None else dummy_array for o in my_corr.content]
-151        dat = write_Array_to_dict(np.array(content, dtype=object))
-152        dat['type'] = 'Corr'
-153        corr_meta_data = str(my_corr.tag)
-154        if 'tag' in dat.keys():
-155            dat['tag'].append(corr_meta_data)
-156        else:
-157            dat['tag'] = [corr_meta_data]
-158        taglist = dat['tag']
-159        dat['tag'] = {}  # tag is now a dictionary, that contains the previous taglist in the key "tag"
-160        dat['tag']['tag'] = taglist
-161        if my_corr.prange is not None:
-162            dat['tag']['prange'] = my_corr.prange
-163        return dat
-164
-165    if not isinstance(ol, list):
-166        ol = [ol]
-167
-168    d = {}
-169    d['program'] = 'pyerrors %s' % (pyerrorsversion.__version__)
-170    d['version'] = '1.1'
-171    d['who'] = getpass.getuser()
-172    d['date'] = datetime.datetime.now().astimezone().strftime('%Y-%m-%d %H:%M:%S %z')
-173    d['host'] = socket.gethostname() + ', ' + platform.platform()
-174
-175    if description:
-176        d['description'] = description
-177
-178    d['obsdata'] = []
-179    for io in ol:
-180        if isinstance(io, Obs):
-181            d['obsdata'].append(write_Obs_to_dict(io))
-182        elif isinstance(io, list):
-183            d['obsdata'].append(write_List_to_dict(io))
-184        elif isinstance(io, np.ndarray):
-185            d['obsdata'].append(write_Array_to_dict(io))
-186        elif isinstance(io, Corr):
-187            d['obsdata'].append(write_Corr_to_dict(io))
-188        else:
-189            raise Exception("Unkown datatype.")
-190
-191    def _jsonifier(obj):
-192        if isinstance(obj, dict):
-193            result = {}
-194            for key in obj:
-195                if key is True:
-196                    result['true'] = obj[key]
-197                elif key is False:
-198                    result['false'] = obj[key]
-199                elif key is None:
-200                    result['null'] = obj[key]
-201                elif isinstance(key, (int, float, np.floating, np.integer)):
-202                    result[str(key)] = obj[key]
-203                else:
-204                    raise TypeError('keys must be str, int, float, bool or None')
-205            return result
-206        elif isinstance(obj, np.integer):
-207            return int(obj)
-208        elif isinstance(obj, np.floating):
-209            return float(obj)
-210        else:
-211            raise ValueError('%r is not JSON serializable' % (obj,))
-212
-213    if indent:
-214        return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_SINGLE_LINE_ARRAY)
-215    else:
-216        return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_COMPACT)
-217
+139        my_obs = Obs(samples, names, idl, means=[np.nan for n in names])
+140        my_obs._value = np.nan
+141        my_obs._covobs = obs._covobs
+142        for name in obs._covobs:
+143            my_obs.names.append(name)
+144        my_obs.reweighted = obs.reweighted
+145        return my_obs
+146
+147    def write_Corr_to_dict(my_corr):
+148        first_not_none = next(i for i, j in enumerate(my_corr.content) if np.all(j))
+149        dummy_array = np.empty((my_corr.N, my_corr.N), dtype=object)
+150        dummy_array[:] = _nan_Obs_like(my_corr.content[first_not_none].ravel()[0])
+151        content = [o if o is not None else dummy_array for o in my_corr.content]
+152        dat = write_Array_to_dict(np.array(content, dtype=object))
+153        dat['type'] = 'Corr'
+154        corr_meta_data = str(my_corr.tag)
+155        if 'tag' in dat.keys():
+156            dat['tag'].append(corr_meta_data)
+157        else:
+158            dat['tag'] = [corr_meta_data]
+159        taglist = dat['tag']
+160        dat['tag'] = {}  # tag is now a dictionary, that contains the previous taglist in the key "tag"
+161        dat['tag']['tag'] = taglist
+162        if my_corr.prange is not None:
+163            dat['tag']['prange'] = my_corr.prange
+164        return dat
+165
+166    if not isinstance(ol, list):
+167        ol = [ol]
+168
+169    d = {}
+170    d['program'] = 'pyerrors %s' % (pyerrorsversion.__version__)
+171    d['version'] = '1.1'
+172    d['who'] = getpass.getuser()
+173    d['date'] = datetime.datetime.now().astimezone().strftime('%Y-%m-%d %H:%M:%S %z')
+174    d['host'] = socket.gethostname() + ', ' + platform.platform()
+175
+176    if description:
+177        d['description'] = description
+178
+179    d['obsdata'] = []
+180    for io in ol:
+181        if isinstance(io, Obs):
+182            d['obsdata'].append(write_Obs_to_dict(io))
+183        elif isinstance(io, list):
+184            d['obsdata'].append(write_List_to_dict(io))
+185        elif isinstance(io, np.ndarray):
+186            d['obsdata'].append(write_Array_to_dict(io))
+187        elif isinstance(io, Corr):
+188            d['obsdata'].append(write_Corr_to_dict(io))
+189        else:
+190            raise Exception("Unkown datatype.")
+191
+192    def _jsonifier(obj):
+193        if isinstance(obj, dict):
+194            result = {}
+195            for key in obj:
+196                if key is True:
+197                    result['true'] = obj[key]
+198                elif key is False:
+199                    result['false'] = obj[key]
+200                elif key is None:
+201                    result['null'] = obj[key]
+202                elif isinstance(key, (int, float, np.floating, np.integer)):
+203                    result[str(key)] = obj[key]
+204                else:
+205                    raise TypeError('keys must be str, int, float, bool or None')
+206            return result
+207        elif isinstance(obj, np.integer):
+208            return int(obj)
+209        elif isinstance(obj, np.floating):
+210            return float(obj)
+211        else:
+212            raise ValueError('%r is not JSON serializable' % (obj,))
+213
+214    if indent:
+215        return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_SINGLE_LINE_ARRAY)
+216    else:
+217        return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_COMPACT)
 218
-219def dump_to_json(ol, fname, description='', indent=1, gz=True):
-220    """Export a list of Obs or structures containing Obs to a .json(.gz) file.
-221    Dict keys that are not JSON-serializable such as floats are converted to strings.
-222
-223    Parameters
-224    ----------
-225    ol : list
-226        List of objects that will be exported. At the moment, these objects can be
-227        either of: Obs, list, numpy.ndarray, Corr.
-228        All Obs inside a structure have to be defined on the same set of configurations.
-229    fname : str
-230        Filename of the output file.
-231    description : str
-232        Optional string that describes the contents of the json file.
-233    indent : int
-234        Specify the indentation level of the json file. None or 0 is permissible and
-235        saves disk space.
-236    gz : bool
-237        If True, the output is a gzipped json. If False, the output is a json file.
-238
-239    Returns
-240    -------
-241    Null
-242    """
-243
-244    jsonstring = create_json_string(ol, description, indent)
-245
-246    if not fname.endswith('.json') and not fname.endswith('.gz'):
-247        fname += '.json'
-248
-249    if gz:
-250        if not fname.endswith('.gz'):
-251            fname += '.gz'
-252
-253        fp = gzip.open(fname, 'wb')
-254        fp.write(jsonstring.encode('utf-8'))
-255    else:
-256        fp = open(fname, 'w', encoding='utf-8')
-257        fp.write(jsonstring)
-258    fp.close()
-259
+219
+220def dump_to_json(ol, fname, description='', indent=1, gz=True):
+221    """Export a list of Obs or structures containing Obs to a .json(.gz) file.
+222    Dict keys that are not JSON-serializable such as floats are converted to strings.
+223
+224    Parameters
+225    ----------
+226    ol : list
+227        List of objects that will be exported. At the moment, these objects can be
+228        either of: Obs, list, numpy.ndarray, Corr.
+229        All Obs inside a structure have to be defined on the same set of configurations.
+230    fname : str
+231        Filename of the output file.
+232    description : str
+233        Optional string that describes the contents of the json file.
+234    indent : int
+235        Specify the indentation level of the json file. None or 0 is permissible and
+236        saves disk space.
+237    gz : bool
+238        If True, the output is a gzipped json. If False, the output is a json file.
+239
+240    Returns
+241    -------
+242    Null
+243    """
+244
+245    jsonstring = create_json_string(ol, description, indent)
+246
+247    if not fname.endswith('.json') and not fname.endswith('.gz'):
+248        fname += '.json'
+249
+250    if gz:
+251        if not fname.endswith('.gz'):
+252            fname += '.gz'
+253
+254        fp = gzip.open(fname, 'wb')
+255        fp.write(jsonstring.encode('utf-8'))
+256    else:
+257        fp = open(fname, 'w', encoding='utf-8')
+258        fp.write(jsonstring)
+259    fp.close()
 260
-261def _parse_json_dict(json_dict, verbose=True, full_output=False):
-262    """Reconstruct a list of Obs or structures containing Obs from a dict that
-263    was built out of a json string.
-264
-265    The following structures are supported: Obs, list, numpy.ndarray, Corr
-266    If the list contains only one element, it is unpacked from the list.
-267
-268    Parameters
-269    ----------
-270    json_string : str
-271        json string containing the data.
-272    verbose : bool
-273        Print additional information that was written to the file.
-274    full_output : bool
-275        If True, a dict containing auxiliary information and the data is returned.
-276        If False, only the data is returned.
-277
-278    Returns
-279    -------
-280    result : list[Obs]
-281        reconstructed list of observables from the json string
-282    or
-283    result : Obs
-284        only one observable if the list only has one entry
-285    or
-286    result : dict
-287        if full_output=True
-288    """
-289
-290    def _gen_obsd_from_datad(d):
-291        retd = {}
-292        if d:
-293            retd['names'] = []
-294            retd['idl'] = []
-295            retd['deltas'] = []
-296            for ens in d:
-297                for rep in ens['replica']:
-298                    rep_name = rep['name']
-299                    if len(rep_name) > len(ens["id"]):
-300                        if rep_name[len(ens["id"])] != "|":
-301                            tmp_list = list(rep_name)
-302                            tmp_list = tmp_list[:len(ens["id"])] + ["|"] + tmp_list[len(ens["id"]):]
-303                            rep_name = ''.join(tmp_list)
-304                    retd['names'].append(rep_name)
-305                    retd['idl'].append([di[0] for di in rep['deltas']])
-306                    retd['deltas'].append(np.array([di[1:] for di in rep['deltas']]))
-307        return retd
-308
-309    def _gen_covobsd_from_cdatad(d):
-310        retd = {}
-311        for ens in d:
-312            retl = []
-313            name = ens['id']
-314            layouts = ens.get('layout', '1').strip()
-315            layout = [int(ls.strip()) for ls in layouts.split(',') if len(ls) > 0]
-316            cov = np.reshape(ens['cov'], layout)
-317            grad = ens['grad']
-318            nobs = len(grad[0])
-319            for i in range(nobs):
-320                retl.append({'name': name, 'cov': cov, 'grad': [g[i] for g in grad]})
-321            retd[name] = retl
-322        return retd
-323
-324    def get_Obs_from_dict(o):
-325        layouts = o.get('layout', '1').strip()
-326        if layouts != '1':
-327            raise Exception("layout is %s has to be 1 for type Obs." % (layouts), RuntimeWarning)
-328
-329        values = o['value']
-330        od = _gen_obsd_from_datad(o.get('data', {}))
-331        cd = _gen_covobsd_from_cdatad(o.get('cdata', {}))
-332
-333        if od:
-334            ret = Obs([[ddi[0] + values[0] for ddi in di] for di in od['deltas']], od['names'], idl=od['idl'])
-335            ret._value = values[0]
-336        else:
-337            ret = Obs([], [], means=[])
-338            ret._value = values[0]
-339        for name in cd:
-340            co = cd[name][0]
-341            ret._covobs[name] = Covobs(None, co['cov'], co['name'], grad=co['grad'])
-342            ret.names.append(co['name'])
-343
-344        ret.reweighted = o.get('reweighted', False)
-345        ret.tag = o.get('tag', [None])[0]
-346        return ret
-347
-348    def get_List_from_dict(o):
-349        layouts = o.get('layout', '1').strip()
-350        layout = int(layouts)
-351        values = o['value']
-352        od = _gen_obsd_from_datad(o.get('data', {}))
-353        cd = _gen_covobsd_from_cdatad(o.get('cdata', {}))
-354
-355        ret = []
-356        taglist = o.get('tag', layout * [None])
-357        for i in range(layout):
-358            if od:
-359                ret.append(Obs([list(di[:, i] + values[i]) for di in od['deltas']], od['names'], idl=od['idl']))
-360                ret[-1]._value = values[i]
-361            else:
-362                ret.append(Obs([], [], means=[]))
+261
+262def _parse_json_dict(json_dict, verbose=True, full_output=False):
+263    """Reconstruct a list of Obs or structures containing Obs from a dict that
+264    was built out of a json string.
+265
+266    The following structures are supported: Obs, list, numpy.ndarray, Corr
+267    If the list contains only one element, it is unpacked from the list.
+268
+269    Parameters
+270    ----------
+271    json_string : str
+272        json string containing the data.
+273    verbose : bool
+274        Print additional information that was written to the file.
+275    full_output : bool
+276        If True, a dict containing auxiliary information and the data is returned.
+277        If False, only the data is returned.
+278
+279    Returns
+280    -------
+281    result : list[Obs]
+282        reconstructed list of observables from the json string
+283    or
+284    result : Obs
+285        only one observable if the list only has one entry
+286    or
+287    result : dict
+288        if full_output=True
+289    """
+290
+291    def _gen_obsd_from_datad(d):
+292        retd = {}
+293        if d:
+294            retd['names'] = []
+295            retd['idl'] = []
+296            retd['deltas'] = []
+297            for ens in d:
+298                for rep in ens['replica']:
+299                    rep_name = rep['name']
+300                    if len(rep_name) > len(ens["id"]):
+301                        if rep_name[len(ens["id"])] != "|":
+302                            tmp_list = list(rep_name)
+303                            tmp_list = tmp_list[:len(ens["id"])] + ["|"] + tmp_list[len(ens["id"]):]
+304                            rep_name = ''.join(tmp_list)
+305                    retd['names'].append(rep_name)
+306                    retd['idl'].append([di[0] for di in rep['deltas']])
+307                    retd['deltas'].append(np.array([di[1:] for di in rep['deltas']]))
+308        return retd
+309
+310    def _gen_covobsd_from_cdatad(d):
+311        retd = {}
+312        for ens in d:
+313            retl = []
+314            name = ens['id']
+315            layouts = ens.get('layout', '1').strip()
+316            layout = [int(ls.strip()) for ls in layouts.split(',') if len(ls) > 0]
+317            cov = np.reshape(ens['cov'], layout)
+318            grad = ens['grad']
+319            nobs = len(grad[0])
+320            for i in range(nobs):
+321                retl.append({'name': name, 'cov': cov, 'grad': [g[i] for g in grad]})
+322            retd[name] = retl
+323        return retd
+324
+325    def get_Obs_from_dict(o):
+326        layouts = o.get('layout', '1').strip()
+327        if layouts != '1':
+328            raise Exception("layout is %s has to be 1 for type Obs." % (layouts), RuntimeWarning)
+329
+330        values = o['value']
+331        od = _gen_obsd_from_datad(o.get('data', {}))
+332        cd = _gen_covobsd_from_cdatad(o.get('cdata', {}))
+333
+334        if od:
+335            r_offsets = [np.average([ddi[0] for ddi in di]) for di in od['deltas']]
+336            ret = Obs([np.array([ddi[0] for ddi in od['deltas'][i]]) - r_offsets[i] for i in range(len(od['deltas']))], od['names'], idl=od['idl'], means=[ro + values[0] for ro in r_offsets])
+337            ret._value = values[0]
+338        else:
+339            ret = Obs([], [], means=[])
+340            ret._value = values[0]
+341        for name in cd:
+342            co = cd[name][0]
+343            ret._covobs[name] = Covobs(None, co['cov'], co['name'], grad=co['grad'])
+344            ret.names.append(co['name'])
+345
+346        ret.reweighted = o.get('reweighted', False)
+347        ret.tag = o.get('tag', [None])[0]
+348        return ret
+349
+350    def get_List_from_dict(o):
+351        layouts = o.get('layout', '1').strip()
+352        layout = int(layouts)
+353        values = o['value']
+354        od = _gen_obsd_from_datad(o.get('data', {}))
+355        cd = _gen_covobsd_from_cdatad(o.get('cdata', {}))
+356
+357        ret = []
+358        taglist = o.get('tag', layout * [None])
+359        for i in range(layout):
+360            if od:
+361                r_offsets = np.array([np.average(di[:, i]) for di in od['deltas']])
+362                ret.append(Obs([od['deltas'][j][:, i] - r_offsets[j] for j in range(len(od['deltas']))], od['names'], idl=od['idl'], means=[ro + values[i] for ro in r_offsets]))
 363                ret[-1]._value = values[i]
-364                print('Created Obs with means= ', values[i])
-365            for name in cd:
-366                co = cd[name][i]
-367                ret[-1]._covobs[name] = Covobs(None, co['cov'], co['name'], grad=co['grad'])
-368                ret[-1].names.append(co['name'])
-369
-370            ret[-1].reweighted = o.get('reweighted', False)
-371            ret[-1].tag = taglist[i]
-372        return ret
-373
-374    def get_Array_from_dict(o):
-375        layouts = o.get('layout', '1').strip()
-376        layout = [int(ls.strip()) for ls in layouts.split(',') if len(ls) > 0]
-377        N = np.prod(layout)
-378        values = o['value']
-379        od = _gen_obsd_from_datad(o.get('data', {}))
-380        cd = _gen_covobsd_from_cdatad(o.get('cdata', {}))
-381
-382        ret = []
-383        taglist = o.get('tag', N * [None])
-384        for i in range(N):
-385            if od:
-386                ret.append(Obs([di[:, i] + values[i] for di in od['deltas']], od['names'], idl=od['idl']))
-387                ret[-1]._value = values[i]
-388            else:
-389                ret.append(Obs([], [], means=[]))
-390                ret[-1]._value = values[i]
-391            for name in cd:
-392                co = cd[name][i]
-393                ret[-1]._covobs[name] = Covobs(None, co['cov'], co['name'], grad=co['grad'])
-394                ret[-1].names.append(co['name'])
-395            ret[-1].reweighted = o.get('reweighted', False)
-396            ret[-1].tag = taglist[i]
-397        return np.reshape(ret, layout)
-398
-399    def get_Corr_from_dict(o):
-400        if isinstance(o.get('tag'), list):  # supports the old way
-401            taglist = o.get('tag')  # This had to be modified to get the taglist from the dictionary
-402            temp_prange = None
-403        elif isinstance(o.get('tag'), dict):
-404            tagdic = o.get('tag')
-405            taglist = tagdic['tag']
-406            if 'prange' in tagdic:
-407                temp_prange = tagdic['prange']
-408            else:
-409                temp_prange = None
-410        else:
-411            raise Exception("The tag is not a list or dict")
-412
-413        corr_tag = taglist[-1]
-414        tmp_o = o
-415        tmp_o['tag'] = taglist[:-1]
-416        if len(tmp_o['tag']) == 0:
-417            del tmp_o['tag']
-418        dat = get_Array_from_dict(tmp_o)
-419        my_corr = Corr([None if np.isnan(o.ravel()[0].value) else o for o in list(dat)])
-420        if corr_tag != 'None':
-421            my_corr.tag = corr_tag
-422
-423        my_corr.prange = temp_prange
-424        return my_corr
-425
-426    prog = json_dict.get('program', '')
-427    version = json_dict.get('version', '')
-428    who = json_dict.get('who', '')
-429    date = json_dict.get('date', '')
-430    host = json_dict.get('host', '')
-431    if prog and verbose:
-432        print('Data has been written using %s.' % (prog))
-433    if version and verbose:
-434        print('Format version %s' % (version))
-435    if np.any([who, date, host] and verbose):
-436        print('Written by %s on %s on host %s' % (who, date, host))
-437    description = json_dict.get('description', '')
-438    if description and verbose:
-439        print()
-440        print('Description: ', description)
-441    obsdata = json_dict['obsdata']
-442    ol = []
-443    for io in obsdata:
-444        if io['type'] == 'Obs':
-445            ol.append(get_Obs_from_dict(io))
-446        elif io['type'] == 'List':
-447            ol.append(get_List_from_dict(io))
-448        elif io['type'] == 'Array':
-449            ol.append(get_Array_from_dict(io))
-450        elif io['type'] == 'Corr':
-451            ol.append(get_Corr_from_dict(io))
-452        else:
-453            raise Exception("Unknown datatype.")
-454
-455    if full_output:
-456        retd = {}
-457        retd['program'] = prog
-458        retd['version'] = version
-459        retd['who'] = who
-460        retd['date'] = date
-461        retd['host'] = host
-462        retd['description'] = description
-463        retd['obsdata'] = ol
-464
-465        return retd
-466    else:
-467        if len(obsdata) == 1:
-468            ol = ol[0]
-469
-470        return ol
-471
-472
-473def import_json_string(json_string, verbose=True, full_output=False):
-474    """Reconstruct a list of Obs or structures containing Obs from a json string.
+364            else:
+365                ret.append(Obs([], [], means=[]))
+366                ret[-1]._value = values[i]
+367                print('Created Obs with means= ', values[i])
+368            for name in cd:
+369                co = cd[name][i]
+370                ret[-1]._covobs[name] = Covobs(None, co['cov'], co['name'], grad=co['grad'])
+371                ret[-1].names.append(co['name'])
+372
+373            ret[-1].reweighted = o.get('reweighted', False)
+374            ret[-1].tag = taglist[i]
+375        return ret
+376
+377    def get_Array_from_dict(o):
+378        layouts = o.get('layout', '1').strip()
+379        layout = [int(ls.strip()) for ls in layouts.split(',') if len(ls) > 0]
+380        N = np.prod(layout)
+381        values = o['value']
+382        od = _gen_obsd_from_datad(o.get('data', {}))
+383        cd = _gen_covobsd_from_cdatad(o.get('cdata', {}))
+384
+385        ret = []
+386        taglist = o.get('tag', N * [None])
+387        for i in range(N):
+388            if od:
+389                r_offsets = np.array([np.average(di[:, i]) for di in od['deltas']])
+390                ret.append(Obs([od['deltas'][j][:, i] - r_offsets[j] for j in range(len(od['deltas']))], od['names'], idl=od['idl'], means=[ro + values[i] for ro in r_offsets]))
+391                ret[-1]._value = values[i]
+392            else:
+393                ret.append(Obs([], [], means=[]))
+394                ret[-1]._value = values[i]
+395            for name in cd:
+396                co = cd[name][i]
+397                ret[-1]._covobs[name] = Covobs(None, co['cov'], co['name'], grad=co['grad'])
+398                ret[-1].names.append(co['name'])
+399            ret[-1].reweighted = o.get('reweighted', False)
+400            ret[-1].tag = taglist[i]
+401        return np.reshape(ret, layout)
+402
+403    def get_Corr_from_dict(o):
+404        if isinstance(o.get('tag'), list):  # supports the old way
+405            taglist = o.get('tag')  # This had to be modified to get the taglist from the dictionary
+406            temp_prange = None
+407        elif isinstance(o.get('tag'), dict):
+408            tagdic = o.get('tag')
+409            taglist = tagdic['tag']
+410            if 'prange' in tagdic:
+411                temp_prange = tagdic['prange']
+412            else:
+413                temp_prange = None
+414        else:
+415            raise Exception("The tag is not a list or dict")
+416
+417        corr_tag = taglist[-1]
+418        tmp_o = o
+419        tmp_o['tag'] = taglist[:-1]
+420        if len(tmp_o['tag']) == 0:
+421            del tmp_o['tag']
+422        dat = get_Array_from_dict(tmp_o)
+423        my_corr = Corr([None if np.isnan(o.ravel()[0].value) else o for o in list(dat)])
+424        if corr_tag != 'None':
+425            my_corr.tag = corr_tag
+426
+427        my_corr.prange = temp_prange
+428        return my_corr
+429
+430    prog = json_dict.get('program', '')
+431    version = json_dict.get('version', '')
+432    who = json_dict.get('who', '')
+433    date = json_dict.get('date', '')
+434    host = json_dict.get('host', '')
+435    if prog and verbose:
+436        print('Data has been written using %s.' % (prog))
+437    if version and verbose:
+438        print('Format version %s' % (version))
+439    if np.any([who, date, host] and verbose):
+440        print('Written by %s on %s on host %s' % (who, date, host))
+441    description = json_dict.get('description', '')
+442    if description and verbose:
+443        print()
+444        print('Description: ', description)
+445    obsdata = json_dict['obsdata']
+446    ol = []
+447    for io in obsdata:
+448        if io['type'] == 'Obs':
+449            ol.append(get_Obs_from_dict(io))
+450        elif io['type'] == 'List':
+451            ol.append(get_List_from_dict(io))
+452        elif io['type'] == 'Array':
+453            ol.append(get_Array_from_dict(io))
+454        elif io['type'] == 'Corr':
+455            ol.append(get_Corr_from_dict(io))
+456        else:
+457            raise Exception("Unknown datatype.")
+458
+459    if full_output:
+460        retd = {}
+461        retd['program'] = prog
+462        retd['version'] = version
+463        retd['who'] = who
+464        retd['date'] = date
+465        retd['host'] = host
+466        retd['description'] = description
+467        retd['obsdata'] = ol
+468
+469        return retd
+470    else:
+471        if len(obsdata) == 1:
+472            ol = ol[0]
+473
+474        return ol
 475
-476    The following structures are supported: Obs, list, numpy.ndarray, Corr
-477    If the list contains only one element, it is unpacked from the list.
-478
-479    Parameters
-480    ----------
-481    json_string : str
-482        json string containing the data.
-483    verbose : bool
-484        Print additional information that was written to the file.
-485    full_output : bool
-486        If True, a dict containing auxiliary information and the data is returned.
-487        If False, only the data is returned.
-488
-489    Returns
-490    -------
-491    result : list[Obs]
-492        reconstructed list of observables from the json string
-493    or
-494    result : Obs
-495        only one observable if the list only has one entry
-496    or
-497    result : dict
-498        if full_output=True
-499    """
-500    return _parse_json_dict(json.loads(json_string), verbose, full_output)
-501
-502
-503def load_json(fname, verbose=True, gz=True, full_output=False):
-504    """Import a list of Obs or structures containing Obs from a .json(.gz) file.
+476
+477def import_json_string(json_string, verbose=True, full_output=False):
+478    """Reconstruct a list of Obs or structures containing Obs from a json string.
+479
+480    The following structures are supported: Obs, list, numpy.ndarray, Corr
+481    If the list contains only one element, it is unpacked from the list.
+482
+483    Parameters
+484    ----------
+485    json_string : str
+486        json string containing the data.
+487    verbose : bool
+488        Print additional information that was written to the file.
+489    full_output : bool
+490        If True, a dict containing auxiliary information and the data is returned.
+491        If False, only the data is returned.
+492
+493    Returns
+494    -------
+495    result : list[Obs]
+496        reconstructed list of observables from the json string
+497    or
+498    result : Obs
+499        only one observable if the list only has one entry
+500    or
+501    result : dict
+502        if full_output=True
+503    """
+504    return _parse_json_dict(json.loads(json_string), verbose, full_output)
 505
-506    The following structures are supported: Obs, list, numpy.ndarray, Corr
-507    If the list contains only one element, it is unpacked from the list.
-508
-509    Parameters
-510    ----------
-511    fname : str
-512        Filename of the input file.
-513    verbose : bool
-514        Print additional information that was written to the file.
-515    gz : bool
-516        If True, assumes that data is gzipped. If False, assumes JSON file.
-517    full_output : bool
-518        If True, a dict containing auxiliary information and the data is returned.
-519        If False, only the data is returned.
-520
-521    Returns
-522    -------
-523    result : list[Obs]
-524        reconstructed list of observables from the json string
-525    or
-526    result : Obs
-527        only one observable if the list only has one entry
-528    or
-529    result : dict
-530        if full_output=True
-531    """
-532    if not fname.endswith('.json') and not fname.endswith('.gz'):
-533        fname += '.json'
-534    if gz:
-535        if not fname.endswith('.gz'):
-536            fname += '.gz'
-537        with gzip.open(fname, 'r') as fin:
-538            d = json.load(fin)
-539    else:
-540        if fname.endswith('.gz'):
-541            warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning)
-542        with open(fname, 'r', encoding='utf-8') as fin:
-543            d = json.loads(fin.read())
-544
-545    return _parse_json_dict(d, verbose, full_output)
-546
-547
-548def _ol_from_dict(ind, reps='DICTOBS'):
-549    """Convert a dictionary of Obs objects to a list and a dictionary that contains
-550    placeholders instead of the Obs objects.
+506
+507def load_json(fname, verbose=True, gz=True, full_output=False):
+508    """Import a list of Obs or structures containing Obs from a .json(.gz) file.
+509
+510    The following structures are supported: Obs, list, numpy.ndarray, Corr
+511    If the list contains only one element, it is unpacked from the list.
+512
+513    Parameters
+514    ----------
+515    fname : str
+516        Filename of the input file.
+517    verbose : bool
+518        Print additional information that was written to the file.
+519    gz : bool
+520        If True, assumes that data is gzipped. If False, assumes JSON file.
+521    full_output : bool
+522        If True, a dict containing auxiliary information and the data is returned.
+523        If False, only the data is returned.
+524
+525    Returns
+526    -------
+527    result : list[Obs]
+528        reconstructed list of observables from the json string
+529    or
+530    result : Obs
+531        only one observable if the list only has one entry
+532    or
+533    result : dict
+534        if full_output=True
+535    """
+536    if not fname.endswith('.json') and not fname.endswith('.gz'):
+537        fname += '.json'
+538    if gz:
+539        if not fname.endswith('.gz'):
+540            fname += '.gz'
+541        with gzip.open(fname, 'r') as fin:
+542            d = json.load(fin)
+543    else:
+544        if fname.endswith('.gz'):
+545            warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning)
+546        with open(fname, 'r', encoding='utf-8') as fin:
+547            d = json.loads(fin.read())
+548
+549    return _parse_json_dict(d, verbose, full_output)
+550
 551
-552    Parameters
-553    ----------
-554    ind : dict
-555        Dict of JSON valid structures and objects that will be exported.
-556        At the moment, these object can be either of: Obs, list, numpy.ndarray, Corr.
-557        All Obs inside a structure have to be defined on the same set of configurations.
-558    reps : str
-559        Specify the structure of the placeholder in exported dict to be reps[0-9]+.
-560    """
-561
-562    obstypes = (Obs, Corr, np.ndarray)
-563
-564    if not reps.isalnum():
-565        raise Exception('Placeholder string has to be alphanumeric!')
-566    ol = []
-567    counter = 0
-568
-569    def dict_replace_obs(d):
-570        nonlocal ol
-571        nonlocal counter
-572        x = {}
-573        for k, v in d.items():
-574            if isinstance(v, dict):
-575                v = dict_replace_obs(v)
-576            elif isinstance(v, list) and all([isinstance(o, Obs) for o in v]):
-577                v = obslist_replace_obs(v)
-578            elif isinstance(v, list):
-579                v = list_replace_obs(v)
-580            elif isinstance(v, obstypes):
-581                ol.append(v)
-582                v = reps + '%d' % (counter)
-583                counter += 1
-584            elif isinstance(v, str):
-585                if bool(re.match(r'%s[0-9]+' % (reps), v)):
-586                    raise Exception('Dict contains string %s that matches the placeholder! %s Cannot be safely exported.' % (v, reps))
-587            x[k] = v
-588        return x
-589
-590    def list_replace_obs(li):
-591        nonlocal ol
-592        nonlocal counter
-593        x = []
-594        for e in li:
-595            if isinstance(e, list):
-596                e = list_replace_obs(e)
-597            elif isinstance(e, list) and all([isinstance(o, Obs) for o in e]):
-598                e = obslist_replace_obs(e)
-599            elif isinstance(e, dict):
-600                e = dict_replace_obs(e)
-601            elif isinstance(e, obstypes):
-602                ol.append(e)
-603                e = reps + '%d' % (counter)
-604                counter += 1
-605            elif isinstance(e, str):
-606                if bool(re.match(r'%s[0-9]+' % (reps), e)):
-607                    raise Exception('Dict contains string %s that matches the placeholder! %s Cannot be safely exported.' % (e, reps))
-608            x.append(e)
-609        return x
-610
-611    def obslist_replace_obs(li):
-612        nonlocal ol
-613        nonlocal counter
-614        il = []
-615        for e in li:
-616            il.append(e)
-617
-618        ol.append(il)
-619        x = reps + '%d' % (counter)
-620        counter += 1
-621        return x
-622
-623    nd = dict_replace_obs(ind)
-624
-625    return ol, nd
+552def _ol_from_dict(ind, reps='DICTOBS'):
+553    """Convert a dictionary of Obs objects to a list and a dictionary that contains
+554    placeholders instead of the Obs objects.
+555
+556    Parameters
+557    ----------
+558    ind : dict
+559        Dict of JSON valid structures and objects that will be exported.
+560        At the moment, these object can be either of: Obs, list, numpy.ndarray, Corr.
+561        All Obs inside a structure have to be defined on the same set of configurations.
+562    reps : str
+563        Specify the structure of the placeholder in exported dict to be reps[0-9]+.
+564    """
+565
+566    obstypes = (Obs, Corr, np.ndarray)
+567
+568    if not reps.isalnum():
+569        raise Exception('Placeholder string has to be alphanumeric!')
+570    ol = []
+571    counter = 0
+572
+573    def dict_replace_obs(d):
+574        nonlocal ol
+575        nonlocal counter
+576        x = {}
+577        for k, v in d.items():
+578            if isinstance(v, dict):
+579                v = dict_replace_obs(v)
+580            elif isinstance(v, list) and all([isinstance(o, Obs) for o in v]):
+581                v = obslist_replace_obs(v)
+582            elif isinstance(v, list):
+583                v = list_replace_obs(v)
+584            elif isinstance(v, obstypes):
+585                ol.append(v)
+586                v = reps + '%d' % (counter)
+587                counter += 1
+588            elif isinstance(v, str):
+589                if bool(re.match(r'%s[0-9]+' % (reps), v)):
+590                    raise Exception('Dict contains string %s that matches the placeholder! %s Cannot be safely exported.' % (v, reps))
+591            x[k] = v
+592        return x
+593
+594    def list_replace_obs(li):
+595        nonlocal ol
+596        nonlocal counter
+597        x = []
+598        for e in li:
+599            if isinstance(e, list):
+600                e = list_replace_obs(e)
+601            elif isinstance(e, list) and all([isinstance(o, Obs) for o in e]):
+602                e = obslist_replace_obs(e)
+603            elif isinstance(e, dict):
+604                e = dict_replace_obs(e)
+605            elif isinstance(e, obstypes):
+606                ol.append(e)
+607                e = reps + '%d' % (counter)
+608                counter += 1
+609            elif isinstance(e, str):
+610                if bool(re.match(r'%s[0-9]+' % (reps), e)):
+611                    raise Exception('Dict contains string %s that matches the placeholder! %s Cannot be safely exported.' % (e, reps))
+612            x.append(e)
+613        return x
+614
+615    def obslist_replace_obs(li):
+616        nonlocal ol
+617        nonlocal counter
+618        il = []
+619        for e in li:
+620            il.append(e)
+621
+622        ol.append(il)
+623        x = reps + '%d' % (counter)
+624        counter += 1
+625        return x
 626
-627
-628def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
-629    """Export a dict of Obs or structures containing Obs to a .json(.gz) file
+627    nd = dict_replace_obs(ind)
+628
+629    return ol, nd
 630
-631    Parameters
-632    ----------
-633    od : dict
-634        Dict of JSON valid structures and objects that will be exported.
-635        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.
-636        All Obs inside a structure have to be defined on the same set of configurations.
-637    fname : str
-638        Filename of the output file.
-639    description : str
-640        Optional string that describes the contents of the json file.
-641    indent : int
-642        Specify the indentation level of the json file. None or 0 is permissible and
-643        saves disk space.
-644    reps : str
-645        Specify the structure of the placeholder in exported dict to be reps[0-9]+.
-646    gz : bool
-647        If True, the output is a gzipped json. If False, the output is a json file.
-648
-649    Returns
-650    -------
-651    None
-652    """
-653
-654    if not isinstance(od, dict):
-655        raise Exception('od has to be a dictionary. Did you want to use dump_to_json?')
-656
-657    infostring = ('This JSON file contains a python dictionary that has been parsed to a list of structures. '
-658                  'OBSDICT contains the dictionary, where Obs or other structures have been replaced by '
-659                  '' + reps + '[0-9]+. The field description contains the additional description of this JSON file. '
-660                  'This file may be parsed to a dict with the pyerrors routine load_json_dict.')
-661
-662    desc_dict = {'INFO': infostring, 'OBSDICT': {}, 'description': description}
-663    ol, desc_dict['OBSDICT'] = _ol_from_dict(od, reps=reps)
-664
-665    dump_to_json(ol, fname, description=desc_dict, indent=indent, gz=gz)
-666
-667
-668def _od_from_list_and_dict(ol, ind, reps='DICTOBS'):
-669    """Parse a list of Obs or structures containing Obs and an accompanying
-670    dict, where the structures have been replaced by placeholders to a
-671    dict that contains the structures.
-672
-673    The following structures are supported: Obs, list, numpy.ndarray, Corr
-674
-675    Parameters
-676    ----------
-677    ol : list
-678        List of objects -
-679        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.
-680        All Obs inside a structure have to be defined on the same set of configurations.
-681    ind : dict
-682        Dict that defines the structure of the resulting dict and contains placeholders
-683    reps : str
-684        Specify the structure of the placeholder in imported dict to be reps[0-9]+.
-685    """
-686    if not reps.isalnum():
-687        raise Exception('Placeholder string has to be alphanumeric!')
-688
-689    counter = 0
-690
-691    def dict_replace_string(d):
-692        nonlocal counter
-693        nonlocal ol
-694        x = {}
-695        for k, v in d.items():
-696            if isinstance(v, dict):
-697                v = dict_replace_string(v)
-698            elif isinstance(v, list):
-699                v = list_replace_string(v)
-700            elif isinstance(v, str) and bool(re.match(r'%s[0-9]+' % (reps), v)):
-701                index = int(v[len(reps):])
-702                v = ol[index]
-703                counter += 1
-704            x[k] = v
-705        return x
-706
-707    def list_replace_string(li):
-708        nonlocal counter
-709        nonlocal ol
-710        x = []
-711        for e in li:
-712            if isinstance(e, list):
-713                e = list_replace_string(e)
-714            elif isinstance(e, dict):
-715                e = dict_replace_string(e)
-716            elif isinstance(e, str) and bool(re.match(r'%s[0-9]+' % (reps), e)):
-717                index = int(e[len(reps):])
-718                e = ol[index]
-719                counter += 1
-720            x.append(e)
-721        return x
-722
-723    nd = dict_replace_string(ind)
-724
-725    if counter == 0:
-726        raise Exception('No placeholder has been replaced! Check if reps is set correctly.')
-727
-728    return nd
-729
-730
-731def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
-732    """Import a dict of Obs or structures containing Obs from a .json(.gz) file.
+631
+632def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
+633    """Export a dict of Obs or structures containing Obs to a .json(.gz) file
+634
+635    Parameters
+636    ----------
+637    od : dict
+638        Dict of JSON valid structures and objects that will be exported.
+639        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.
+640        All Obs inside a structure have to be defined on the same set of configurations.
+641    fname : str
+642        Filename of the output file.
+643    description : str
+644        Optional string that describes the contents of the json file.
+645    indent : int
+646        Specify the indentation level of the json file. None or 0 is permissible and
+647        saves disk space.
+648    reps : str
+649        Specify the structure of the placeholder in exported dict to be reps[0-9]+.
+650    gz : bool
+651        If True, the output is a gzipped json. If False, the output is a json file.
+652
+653    Returns
+654    -------
+655    None
+656    """
+657
+658    if not isinstance(od, dict):
+659        raise Exception('od has to be a dictionary. Did you want to use dump_to_json?')
+660
+661    infostring = ('This JSON file contains a python dictionary that has been parsed to a list of structures. '
+662                  'OBSDICT contains the dictionary, where Obs or other structures have been replaced by '
+663                  '' + reps + '[0-9]+. The field description contains the additional description of this JSON file. '
+664                  'This file may be parsed to a dict with the pyerrors routine load_json_dict.')
+665
+666    desc_dict = {'INFO': infostring, 'OBSDICT': {}, 'description': description}
+667    ol, desc_dict['OBSDICT'] = _ol_from_dict(od, reps=reps)
+668
+669    dump_to_json(ol, fname, description=desc_dict, indent=indent, gz=gz)
+670
+671
+672def _od_from_list_and_dict(ol, ind, reps='DICTOBS'):
+673    """Parse a list of Obs or structures containing Obs and an accompanying
+674    dict, where the structures have been replaced by placeholders to a
+675    dict that contains the structures.
+676
+677    The following structures are supported: Obs, list, numpy.ndarray, Corr
+678
+679    Parameters
+680    ----------
+681    ol : list
+682        List of objects -
+683        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.
+684        All Obs inside a structure have to be defined on the same set of configurations.
+685    ind : dict
+686        Dict that defines the structure of the resulting dict and contains placeholders
+687    reps : str
+688        Specify the structure of the placeholder in imported dict to be reps[0-9]+.
+689    """
+690    if not reps.isalnum():
+691        raise Exception('Placeholder string has to be alphanumeric!')
+692
+693    counter = 0
+694
+695    def dict_replace_string(d):
+696        nonlocal counter
+697        nonlocal ol
+698        x = {}
+699        for k, v in d.items():
+700            if isinstance(v, dict):
+701                v = dict_replace_string(v)
+702            elif isinstance(v, list):
+703                v = list_replace_string(v)
+704            elif isinstance(v, str) and bool(re.match(r'%s[0-9]+' % (reps), v)):
+705                index = int(v[len(reps):])
+706                v = ol[index]
+707                counter += 1
+708            x[k] = v
+709        return x
+710
+711    def list_replace_string(li):
+712        nonlocal counter
+713        nonlocal ol
+714        x = []
+715        for e in li:
+716            if isinstance(e, list):
+717                e = list_replace_string(e)
+718            elif isinstance(e, dict):
+719                e = dict_replace_string(e)
+720            elif isinstance(e, str) and bool(re.match(r'%s[0-9]+' % (reps), e)):
+721                index = int(e[len(reps):])
+722                e = ol[index]
+723                counter += 1
+724            x.append(e)
+725        return x
+726
+727    nd = dict_replace_string(ind)
+728
+729    if counter == 0:
+730        raise Exception('No placeholder has been replaced! Check if reps is set correctly.')
+731
+732    return nd
 733
-734    The following structures are supported: Obs, list, numpy.ndarray, Corr
-735
-736    Parameters
-737    ----------
-738    fname : str
-739        Filename of the input file.
-740    verbose : bool
-741        Print additional information that was written to the file.
-742    gz : bool
-743        If True, assumes that data is gzipped. If False, assumes JSON file.
-744    full_output : bool
-745        If True, a dict containing auxiliary information and the data is returned.
-746        If False, only the data is returned.
-747    reps : str
-748        Specify the structure of the placeholder in imported dict to be reps[0-9]+.
-749
-750    Returns
-751    -------
-752    data : Obs / list / Corr
-753        Read data
-754    or
-755    data : dict
-756        Read data and meta-data
-757    """
-758    indata = load_json(fname, verbose=verbose, gz=gz, full_output=True)
-759    description = indata['description']['description']
-760    indict = indata['description']['OBSDICT']
-761    ol = indata['obsdata']
-762    od = _od_from_list_and_dict(ol, indict, reps=reps)
-763
-764    if full_output:
-765        indata['description'] = description
-766        indata['obsdata'] = od
-767        return indata
-768    else:
-769        return od
+734
+735def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
+736    """Import a dict of Obs or structures containing Obs from a .json(.gz) file.
+737
+738    The following structures are supported: Obs, list, numpy.ndarray, Corr
+739
+740    Parameters
+741    ----------
+742    fname : str
+743        Filename of the input file.
+744    verbose : bool
+745        Print additional information that was written to the file.
+746    gz : bool
+747        If True, assumes that data is gzipped. If False, assumes JSON file.
+748    full_output : bool
+749        If True, a dict containing auxiliary information and the data is returned.
+750        If False, only the data is returned.
+751    reps : str
+752        Specify the structure of the placeholder in imported dict to be reps[0-9]+.
+753
+754    Returns
+755    -------
+756    data : Obs / list / Corr
+757        Read data
+758    or
+759    data : dict
+760        Read data and meta-data
+761    """
+762    indata = load_json(fname, verbose=verbose, gz=gz, full_output=True)
+763    description = indata['description']['description']
+764    indict = indata['description']['OBSDICT']
+765    ol = indata['obsdata']
+766    od = _od_from_list_and_dict(ol, indict, reps=reps)
+767
+768    if full_output:
+769        indata['description'] = description
+770        indata['obsdata'] = od
+771        return indata
+772    else:
+773        return od
@@ -994,87 +998,88 @@ 134 names = [] 135 idl = [] 136 for key, value in obs.idl.items(): -137 samples.append([np.nan] * len(value)) +137 samples.append(np.array([np.nan] * len(value))) 138 names.append(key) 139 idl.append(value) -140 my_obs = Obs(samples, names, idl) -141 my_obs._covobs = obs._covobs -142 for name in obs._covobs: -143 my_obs.names.append(name) -144 my_obs.reweighted = obs.reweighted -145 return my_obs -146 -147 def write_Corr_to_dict(my_corr): -148 first_not_none = next(i for i, j in enumerate(my_corr.content) if np.all(j)) -149 dummy_array = np.empty((my_corr.N, my_corr.N), dtype=object) -150 dummy_array[:] = _nan_Obs_like(my_corr.content[first_not_none].ravel()[0]) -151 content = [o if o is not None else dummy_array for o in my_corr.content] -152 dat = write_Array_to_dict(np.array(content, dtype=object)) -153 dat['type'] = 'Corr' -154 corr_meta_data = str(my_corr.tag) -155 if 'tag' in dat.keys(): -156 dat['tag'].append(corr_meta_data) -157 else: -158 dat['tag'] = [corr_meta_data] -159 taglist = dat['tag'] -160 dat['tag'] = {} # tag is now a dictionary, that contains the previous taglist in the key "tag" -161 dat['tag']['tag'] = taglist -162 if my_corr.prange is not None: -163 dat['tag']['prange'] = my_corr.prange -164 return dat -165 -166 if not isinstance(ol, list): -167 ol = [ol] -168 -169 d = {} -170 d['program'] = 'pyerrors %s' % (pyerrorsversion.__version__) -171 d['version'] = '1.1' -172 d['who'] = getpass.getuser() -173 d['date'] = datetime.datetime.now().astimezone().strftime('%Y-%m-%d %H:%M:%S %z') -174 d['host'] = socket.gethostname() + ', ' + platform.platform() -175 -176 if description: -177 d['description'] = description -178 -179 d['obsdata'] = [] -180 for io in ol: -181 if isinstance(io, Obs): -182 d['obsdata'].append(write_Obs_to_dict(io)) -183 elif isinstance(io, list): -184 d['obsdata'].append(write_List_to_dict(io)) -185 elif isinstance(io, np.ndarray): -186 d['obsdata'].append(write_Array_to_dict(io)) -187 elif isinstance(io, Corr): -188 d['obsdata'].append(write_Corr_to_dict(io)) -189 else: -190 raise Exception("Unkown datatype.") -191 -192 def _jsonifier(obj): -193 if isinstance(obj, dict): -194 result = {} -195 for key in obj: -196 if key is True: -197 result['true'] = obj[key] -198 elif key is False: -199 result['false'] = obj[key] -200 elif key is None: -201 result['null'] = obj[key] -202 elif isinstance(key, (int, float, np.floating, np.integer)): -203 result[str(key)] = obj[key] -204 else: -205 raise TypeError('keys must be str, int, float, bool or None') -206 return result -207 elif isinstance(obj, np.integer): -208 return int(obj) -209 elif isinstance(obj, np.floating): -210 return float(obj) -211 else: -212 raise ValueError('%r is not JSON serializable' % (obj,)) -213 -214 if indent: -215 return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_SINGLE_LINE_ARRAY) -216 else: -217 return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_COMPACT) +140 my_obs = Obs(samples, names, idl, means=[np.nan for n in names]) +141 my_obs._value = np.nan +142 my_obs._covobs = obs._covobs +143 for name in obs._covobs: +144 my_obs.names.append(name) +145 my_obs.reweighted = obs.reweighted +146 return my_obs +147 +148 def write_Corr_to_dict(my_corr): +149 first_not_none = next(i for i, j in enumerate(my_corr.content) if np.all(j)) +150 dummy_array = np.empty((my_corr.N, my_corr.N), dtype=object) +151 dummy_array[:] = _nan_Obs_like(my_corr.content[first_not_none].ravel()[0]) +152 content = [o if o is not None else dummy_array for o in my_corr.content] +153 dat = write_Array_to_dict(np.array(content, dtype=object)) +154 dat['type'] = 'Corr' +155 corr_meta_data = str(my_corr.tag) +156 if 'tag' in dat.keys(): +157 dat['tag'].append(corr_meta_data) +158 else: +159 dat['tag'] = [corr_meta_data] +160 taglist = dat['tag'] +161 dat['tag'] = {} # tag is now a dictionary, that contains the previous taglist in the key "tag" +162 dat['tag']['tag'] = taglist +163 if my_corr.prange is not None: +164 dat['tag']['prange'] = my_corr.prange +165 return dat +166 +167 if not isinstance(ol, list): +168 ol = [ol] +169 +170 d = {} +171 d['program'] = 'pyerrors %s' % (pyerrorsversion.__version__) +172 d['version'] = '1.1' +173 d['who'] = getpass.getuser() +174 d['date'] = datetime.datetime.now().astimezone().strftime('%Y-%m-%d %H:%M:%S %z') +175 d['host'] = socket.gethostname() + ', ' + platform.platform() +176 +177 if description: +178 d['description'] = description +179 +180 d['obsdata'] = [] +181 for io in ol: +182 if isinstance(io, Obs): +183 d['obsdata'].append(write_Obs_to_dict(io)) +184 elif isinstance(io, list): +185 d['obsdata'].append(write_List_to_dict(io)) +186 elif isinstance(io, np.ndarray): +187 d['obsdata'].append(write_Array_to_dict(io)) +188 elif isinstance(io, Corr): +189 d['obsdata'].append(write_Corr_to_dict(io)) +190 else: +191 raise Exception("Unkown datatype.") +192 +193 def _jsonifier(obj): +194 if isinstance(obj, dict): +195 result = {} +196 for key in obj: +197 if key is True: +198 result['true'] = obj[key] +199 elif key is False: +200 result['false'] = obj[key] +201 elif key is None: +202 result['null'] = obj[key] +203 elif isinstance(key, (int, float, np.floating, np.integer)): +204 result[str(key)] = obj[key] +205 else: +206 raise TypeError('keys must be str, int, float, bool or None') +207 return result +208 elif isinstance(obj, np.integer): +209 return int(obj) +210 elif isinstance(obj, np.floating): +211 return float(obj) +212 else: +213 raise ValueError('%r is not JSON serializable' % (obj,)) +214 +215 if indent: +216 return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_SINGLE_LINE_ARRAY) +217 else: +218 return json.dumps(d, indent=indent, ensure_ascii=False, default=_jsonifier, write_mode=json.WM_COMPACT) @@ -1116,46 +1121,46 @@ String for export to pyerrors.input.json(.gz) file - 
220def dump_to_json(ol, fname, description='', indent=1, gz=True):
-221    """Export a list of Obs or structures containing Obs to a .json(.gz) file.
-222    Dict keys that are not JSON-serializable such as floats are converted to strings.
-223
-224    Parameters
-225    ----------
-226    ol : list
-227        List of objects that will be exported. At the moment, these objects can be
-228        either of: Obs, list, numpy.ndarray, Corr.
-229        All Obs inside a structure have to be defined on the same set of configurations.
-230    fname : str
-231        Filename of the output file.
-232    description : str
-233        Optional string that describes the contents of the json file.
-234    indent : int
-235        Specify the indentation level of the json file. None or 0 is permissible and
-236        saves disk space.
-237    gz : bool
-238        If True, the output is a gzipped json. If False, the output is a json file.
-239
-240    Returns
-241    -------
-242    Null
-243    """
-244
-245    jsonstring = create_json_string(ol, description, indent)
-246
-247    if not fname.endswith('.json') and not fname.endswith('.gz'):
-248        fname += '.json'
-249
-250    if gz:
-251        if not fname.endswith('.gz'):
-252            fname += '.gz'
-253
-254        fp = gzip.open(fname, 'wb')
-255        fp.write(jsonstring.encode('utf-8'))
-256    else:
-257        fp = open(fname, 'w', encoding='utf-8')
-258        fp.write(jsonstring)
-259    fp.close()
+            
221def dump_to_json(ol, fname, description='', indent=1, gz=True):
+222    """Export a list of Obs or structures containing Obs to a .json(.gz) file.
+223    Dict keys that are not JSON-serializable such as floats are converted to strings.
+224
+225    Parameters
+226    ----------
+227    ol : list
+228        List of objects that will be exported. At the moment, these objects can be
+229        either of: Obs, list, numpy.ndarray, Corr.
+230        All Obs inside a structure have to be defined on the same set of configurations.
+231    fname : str
+232        Filename of the output file.
+233    description : str
+234        Optional string that describes the contents of the json file.
+235    indent : int
+236        Specify the indentation level of the json file. None or 0 is permissible and
+237        saves disk space.
+238    gz : bool
+239        If True, the output is a gzipped json. If False, the output is a json file.
+240
+241    Returns
+242    -------
+243    Null
+244    """
+245
+246    jsonstring = create_json_string(ol, description, indent)
+247
+248    if not fname.endswith('.json') and not fname.endswith('.gz'):
+249        fname += '.json'
+250
+251    if gz:
+252        if not fname.endswith('.gz'):
+253            fname += '.gz'
+254
+255        fp = gzip.open(fname, 'wb')
+256        fp.write(jsonstring.encode('utf-8'))
+257    else:
+258        fp = open(fname, 'w', encoding='utf-8')
+259        fp.write(jsonstring)
+260    fp.close()
 

 
 
@@ -1200,34 +1205,34 @@ If True, the output is a gzipped json. If False, the output is a json file.
- 
474def import_json_string(json_string, verbose=True, full_output=False):
-475    """Reconstruct a list of Obs or structures containing Obs from a json string.
-476
-477    The following structures are supported: Obs, list, numpy.ndarray, Corr
-478    If the list contains only one element, it is unpacked from the list.
-479
-480    Parameters
-481    ----------
-482    json_string : str
-483        json string containing the data.
-484    verbose : bool
-485        Print additional information that was written to the file.
-486    full_output : bool
-487        If True, a dict containing auxiliary information and the data is returned.
-488        If False, only the data is returned.
-489
-490    Returns
-491    -------
-492    result : list[Obs]
-493        reconstructed list of observables from the json string
-494    or
-495    result : Obs
-496        only one observable if the list only has one entry
-497    or
-498    result : dict
-499        if full_output=True
-500    """
-501    return _parse_json_dict(json.loads(json_string), verbose, full_output)
+            
478def import_json_string(json_string, verbose=True, full_output=False):
+479    """Reconstruct a list of Obs or structures containing Obs from a json string.
+480
+481    The following structures are supported: Obs, list, numpy.ndarray, Corr
+482    If the list contains only one element, it is unpacked from the list.
+483
+484    Parameters
+485    ----------
+486    json_string : str
+487        json string containing the data.
+488    verbose : bool
+489        Print additional information that was written to the file.
+490    full_output : bool
+491        If True, a dict containing auxiliary information and the data is returned.
+492        If False, only the data is returned.
+493
+494    Returns
+495    -------
+496    result : list[Obs]
+497        reconstructed list of observables from the json string
+498    or
+499    result : Obs
+500        only one observable if the list only has one entry
+501    or
+502    result : dict
+503        if full_output=True
+504    """
+505    return _parse_json_dict(json.loads(json_string), verbose, full_output)
 

 
 
@@ -1275,49 +1280,49 @@ if full_output=True
- 
504def load_json(fname, verbose=True, gz=True, full_output=False):
-505    """Import a list of Obs or structures containing Obs from a .json(.gz) file.
-506
-507    The following structures are supported: Obs, list, numpy.ndarray, Corr
-508    If the list contains only one element, it is unpacked from the list.
-509
-510    Parameters
-511    ----------
-512    fname : str
-513        Filename of the input file.
-514    verbose : bool
-515        Print additional information that was written to the file.
-516    gz : bool
-517        If True, assumes that data is gzipped. If False, assumes JSON file.
-518    full_output : bool
-519        If True, a dict containing auxiliary information and the data is returned.
-520        If False, only the data is returned.
-521
-522    Returns
-523    -------
-524    result : list[Obs]
-525        reconstructed list of observables from the json string
-526    or
-527    result : Obs
-528        only one observable if the list only has one entry
-529    or
-530    result : dict
-531        if full_output=True
-532    """
-533    if not fname.endswith('.json') and not fname.endswith('.gz'):
-534        fname += '.json'
-535    if gz:
-536        if not fname.endswith('.gz'):
-537            fname += '.gz'
-538        with gzip.open(fname, 'r') as fin:
-539            d = json.load(fin)
-540    else:
-541        if fname.endswith('.gz'):
-542            warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning)
-543        with open(fname, 'r', encoding='utf-8') as fin:
-544            d = json.loads(fin.read())
-545
-546    return _parse_json_dict(d, verbose, full_output)
+            
508def load_json(fname, verbose=True, gz=True, full_output=False):
+509    """Import a list of Obs or structures containing Obs from a .json(.gz) file.
+510
+511    The following structures are supported: Obs, list, numpy.ndarray, Corr
+512    If the list contains only one element, it is unpacked from the list.
+513
+514    Parameters
+515    ----------
+516    fname : str
+517        Filename of the input file.
+518    verbose : bool
+519        Print additional information that was written to the file.
+520    gz : bool
+521        If True, assumes that data is gzipped. If False, assumes JSON file.
+522    full_output : bool
+523        If True, a dict containing auxiliary information and the data is returned.
+524        If False, only the data is returned.
+525
+526    Returns
+527    -------
+528    result : list[Obs]
+529        reconstructed list of observables from the json string
+530    or
+531    result : Obs
+532        only one observable if the list only has one entry
+533    or
+534    result : dict
+535        if full_output=True
+536    """
+537    if not fname.endswith('.json') and not fname.endswith('.gz'):
+538        fname += '.json'
+539    if gz:
+540        if not fname.endswith('.gz'):
+541            fname += '.gz'
+542        with gzip.open(fname, 'r') as fin:
+543            d = json.load(fin)
+544    else:
+545        if fname.endswith('.gz'):
+546            warnings.warn("Trying to read from %s without unzipping!" % fname, UserWarning)
+547        with open(fname, 'r', encoding='utf-8') as fin:
+548            d = json.loads(fin.read())
+549
+550    return _parse_json_dict(d, verbose, full_output)
 

 
 
@@ -1367,44 +1372,44 @@ if full_output=True
- 
629def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
-630    """Export a dict of Obs or structures containing Obs to a .json(.gz) file
-631
-632    Parameters
-633    ----------
-634    od : dict
-635        Dict of JSON valid structures and objects that will be exported.
-636        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.
-637        All Obs inside a structure have to be defined on the same set of configurations.
-638    fname : str
-639        Filename of the output file.
-640    description : str
-641        Optional string that describes the contents of the json file.
-642    indent : int
-643        Specify the indentation level of the json file. None or 0 is permissible and
-644        saves disk space.
-645    reps : str
-646        Specify the structure of the placeholder in exported dict to be reps[0-9]+.
-647    gz : bool
-648        If True, the output is a gzipped json. If False, the output is a json file.
-649
-650    Returns
-651    -------
-652    None
-653    """
-654
-655    if not isinstance(od, dict):
-656        raise Exception('od has to be a dictionary. Did you want to use dump_to_json?')
-657
-658    infostring = ('This JSON file contains a python dictionary that has been parsed to a list of structures. '
-659                  'OBSDICT contains the dictionary, where Obs or other structures have been replaced by '
-660                  '' + reps + '[0-9]+. The field description contains the additional description of this JSON file. '
-661                  'This file may be parsed to a dict with the pyerrors routine load_json_dict.')
-662
-663    desc_dict = {'INFO': infostring, 'OBSDICT': {}, 'description': description}
-664    ol, desc_dict['OBSDICT'] = _ol_from_dict(od, reps=reps)
-665
-666    dump_to_json(ol, fname, description=desc_dict, indent=indent, gz=gz)
+            
633def dump_dict_to_json(od, fname, description='', indent=1, reps='DICTOBS', gz=True):
+634    """Export a dict of Obs or structures containing Obs to a .json(.gz) file
+635
+636    Parameters
+637    ----------
+638    od : dict
+639        Dict of JSON valid structures and objects that will be exported.
+640        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.
+641        All Obs inside a structure have to be defined on the same set of configurations.
+642    fname : str
+643        Filename of the output file.
+644    description : str
+645        Optional string that describes the contents of the json file.
+646    indent : int
+647        Specify the indentation level of the json file. None or 0 is permissible and
+648        saves disk space.
+649    reps : str
+650        Specify the structure of the placeholder in exported dict to be reps[0-9]+.
+651    gz : bool
+652        If True, the output is a gzipped json. If False, the output is a json file.
+653
+654    Returns
+655    -------
+656    None
+657    """
+658
+659    if not isinstance(od, dict):
+660        raise Exception('od has to be a dictionary. Did you want to use dump_to_json?')
+661
+662    infostring = ('This JSON file contains a python dictionary that has been parsed to a list of structures. '
+663                  'OBSDICT contains the dictionary, where Obs or other structures have been replaced by '
+664                  '' + reps + '[0-9]+. The field description contains the additional description of this JSON file. '
+665                  'This file may be parsed to a dict with the pyerrors routine load_json_dict.')
+666
+667    desc_dict = {'INFO': infostring, 'OBSDICT': {}, 'description': description}
+668    ol, desc_dict['OBSDICT'] = _ol_from_dict(od, reps=reps)
+669
+670    dump_to_json(ol, fname, description=desc_dict, indent=indent, gz=gz)
 

 
 
@@ -1450,45 +1455,45 @@ If True, the output is a gzipped json. If False, the output is a json file.
- 
732def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
-733    """Import a dict of Obs or structures containing Obs from a .json(.gz) file.
-734
-735    The following structures are supported: Obs, list, numpy.ndarray, Corr
-736
-737    Parameters
-738    ----------
-739    fname : str
-740        Filename of the input file.
-741    verbose : bool
-742        Print additional information that was written to the file.
-743    gz : bool
-744        If True, assumes that data is gzipped. If False, assumes JSON file.
-745    full_output : bool
-746        If True, a dict containing auxiliary information and the data is returned.
-747        If False, only the data is returned.
-748    reps : str
-749        Specify the structure of the placeholder in imported dict to be reps[0-9]+.
-750
-751    Returns
-752    -------
-753    data : Obs / list / Corr
-754        Read data
-755    or
-756    data : dict
-757        Read data and meta-data
-758    """
-759    indata = load_json(fname, verbose=verbose, gz=gz, full_output=True)
-760    description = indata['description']['description']
-761    indict = indata['description']['OBSDICT']
-762    ol = indata['obsdata']
-763    od = _od_from_list_and_dict(ol, indict, reps=reps)
-764
-765    if full_output:
-766        indata['description'] = description
-767        indata['obsdata'] = od
-768        return indata
-769    else:
-770        return od
+            
736def load_json_dict(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):
+737    """Import a dict of Obs or structures containing Obs from a .json(.gz) file.
+738
+739    The following structures are supported: Obs, list, numpy.ndarray, Corr
+740
+741    Parameters
+742    ----------
+743    fname : str
+744        Filename of the input file.
+745    verbose : bool
+746        Print additional information that was written to the file.
+747    gz : bool
+748        If True, assumes that data is gzipped. If False, assumes JSON file.
+749    full_output : bool
+750        If True, a dict containing auxiliary information and the data is returned.
+751        If False, only the data is returned.
+752    reps : str
+753        Specify the structure of the placeholder in imported dict to be reps[0-9]+.
+754
+755    Returns
+756    -------
+757    data : Obs / list / Corr
+758        Read data
+759    or
+760    data : dict
+761        Read data and meta-data
+762    """
+763    indata = load_json(fname, verbose=verbose, gz=gz, full_output=True)
+764    description = indata['description']['description']
+765    indict = indata['description']['OBSDICT']
+766    ol = indata['obsdata']
+767    od = _od_from_list_and_dict(ol, indict, reps=reps)
+768
+769    if full_output:
+770        indata['description'] = description
+771        indata['obsdata'] = od
+772        return indata
+773    else:
+774        return od
 

 
 
diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html
index 5bfeabaf..39569843 100644
--- a/docs/pyerrors/obs.html
+++ b/docs/pyerrors/obs.html
@@ -418,1779 +418,1790 @@
   82                    raise ValueError('Names are not unique.')
   83                if not all(isinstance(x, str) for x in names):
   84                    raise TypeError('All names have to be strings.')
-  85            else:
-  86                if not isinstance(names[0], str):
-  87                    raise TypeError('All names have to be strings.')
-  88            if min(len(x) for x in samples) <= 4:
-  89                raise ValueError('Samples have to have at least 5 entries.')
-  90
-  91        self.names = sorted(names)
-  92        self.shape = {}
-  93        self.r_values = {}
-  94        self.deltas = {}
-  95        self._covobs = {}
-  96
-  97        self._value = 0
-  98        self.N = 0
-  99        self.idl = {}
- 100        if idl is not None:
- 101            for name, idx in sorted(zip(names, idl)):
- 102                if isinstance(idx, range):
- 103                    self.idl[name] = idx
- 104                elif isinstance(idx, (list, np.ndarray)):
- 105                    dc = np.unique(np.diff(idx))
- 106                    if np.any(dc < 0):
- 107                        raise ValueError("Unsorted idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) < 0)[0]])))
- 108                    elif np.any(dc == 0):
- 109                        raise ValueError("Duplicate entries in idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) == 0)[0]])))
- 110                    if len(dc) == 1:
- 111                        self.idl[name] = range(idx[0], idx[-1] + dc[0], dc[0])
- 112                    else:
- 113                        self.idl[name] = list(idx)
- 114                else:
- 115                    raise TypeError('incompatible type for idl[%s].' % (name))
- 116        else:
- 117            for name, sample in sorted(zip(names, samples)):
- 118                self.idl[name] = range(1, len(sample) + 1)
- 119
- 120        if kwargs.get("means") is not None:
- 121            for name, sample, mean in sorted(zip(names, samples, kwargs.get("means"))):
- 122                self.shape[name] = len(self.idl[name])
- 123                self.N += self.shape[name]
- 124                self.r_values[name] = mean
- 125                self.deltas[name] = sample
- 126        else:
- 127            for name, sample in sorted(zip(names, samples)):
- 128                self.shape[name] = len(self.idl[name])
- 129                self.N += self.shape[name]
- 130                if len(sample) != self.shape[name]:
- 131                    raise ValueError('Incompatible samples and idx for %s: %d vs. %d' % (name, len(sample), self.shape[name]))
- 132                self.r_values[name] = np.mean(sample)
- 133                self.deltas[name] = sample - self.r_values[name]
- 134                self._value += self.shape[name] * self.r_values[name]
- 135            self._value /= self.N
- 136
- 137        self._dvalue = 0.0
- 138        self.ddvalue = 0.0
- 139        self.reweighted = False
- 140
- 141        self.tag = None
+  85                if len(set([o.split('|')[0] for o in names])) > 1:
+  86                    raise ValueError('Cannot initialize Obs based on multiple ensembles. Please average separate Obs from each ensemble.')
+  87            else:
+  88                if not isinstance(names[0], str):
+  89                    raise TypeError('All names have to be strings.')
+  90            if min(len(x) for x in samples) <= 4:
+  91                raise ValueError('Samples have to have at least 5 entries.')
+  92
+  93        self.names = sorted(names)
+  94        self.shape = {}
+  95        self.r_values = {}
+  96        self.deltas = {}
+  97        self._covobs = {}
+  98
+  99        self._value = 0
+ 100        self.N = 0
+ 101        self.idl = {}
+ 102        if idl is not None:
+ 103            for name, idx in sorted(zip(names, idl)):
+ 104                if isinstance(idx, range):
+ 105                    self.idl[name] = idx
+ 106                elif isinstance(idx, (list, np.ndarray)):
+ 107                    dc = np.unique(np.diff(idx))
+ 108                    if np.any(dc < 0):
+ 109                        raise ValueError("Unsorted idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) < 0)[0]])))
+ 110                    elif np.any(dc == 0):
+ 111                        raise ValueError("Duplicate entries in idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) == 0)[0]])))
+ 112                    if len(dc) == 1:
+ 113                        self.idl[name] = range(idx[0], idx[-1] + dc[0], dc[0])
+ 114                    else:
+ 115                        self.idl[name] = list(idx)
+ 116                else:
+ 117                    raise TypeError('incompatible type for idl[%s].' % (name))
+ 118        else:
+ 119            for name, sample in sorted(zip(names, samples)):
+ 120                self.idl[name] = range(1, len(sample) + 1)
+ 121
+ 122        if kwargs.get("means") is not None:
+ 123            for name, sample, mean in sorted(zip(names, samples, kwargs.get("means"))):
+ 124                self.shape[name] = len(self.idl[name])
+ 125                self.N += self.shape[name]
+ 126                self.r_values[name] = mean
+ 127                self.deltas[name] = sample
+ 128        else:
+ 129            for name, sample in sorted(zip(names, samples)):
+ 130                self.shape[name] = len(self.idl[name])
+ 131                self.N += self.shape[name]
+ 132                if len(sample) != self.shape[name]:
+ 133                    raise ValueError('Incompatible samples and idx for %s: %d vs. %d' % (name, len(sample), self.shape[name]))
+ 134                self.r_values[name] = np.mean(sample)
+ 135                self.deltas[name] = sample - self.r_values[name]
+ 136                self._value += self.shape[name] * self.r_values[name]
+ 137            self._value /= self.N
+ 138
+ 139        self._dvalue = 0.0
+ 140        self.ddvalue = 0.0
+ 141        self.reweighted = False
  142
- 143    @property
- 144    def value(self):
- 145        return self._value
- 146
- 147    @property
- 148    def dvalue(self):
- 149        return self._dvalue
- 150
- 151    @property
- 152    def e_names(self):
- 153        return sorted(set([o.split('|')[0] for o in self.names]))
- 154
- 155    @property
- 156    def cov_names(self):
- 157        return sorted(set([o for o in self.covobs.keys()]))
- 158
- 159    @property
- 160    def mc_names(self):
- 161        return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names]))
- 162
- 163    @property
- 164    def e_content(self):
- 165        res = {}
- 166        for e, e_name in enumerate(self.e_names):
- 167            res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names))
- 168            if e_name in self.names:
- 169                res[e_name].append(e_name)
- 170        return res
- 171
- 172    @property
- 173    def covobs(self):
- 174        return self._covobs
- 175
- 176    def gamma_method(self, **kwargs):
- 177        """Estimate the error and related properties of the Obs.
- 178
- 179        Parameters
- 180        ----------
- 181        S : float
- 182            specifies a custom value for the parameter S (default 2.0).
- 183            If set to 0 it is assumed that the data exhibits no
- 184            autocorrelation. In this case the error estimates coincides
- 185            with the sample standard error.
- 186        tau_exp : float
- 187            positive value triggers the critical slowing down analysis
- 188            (default 0.0).
- 189        N_sigma : float
- 190            number of standard deviations from zero until the tail is
- 191            attached to the autocorrelation function (default 1).
- 192        fft : bool
- 193            determines whether the fft algorithm is used for the computation
- 194            of the autocorrelation function (default True)
- 195        """
- 196
- 197        e_content = self.e_content
- 198        self.e_dvalue = {}
- 199        self.e_ddvalue = {}
- 200        self.e_tauint = {}
- 201        self.e_dtauint = {}
- 202        self.e_windowsize = {}
- 203        self.e_n_tauint = {}
- 204        self.e_n_dtauint = {}
- 205        e_gamma = {}
- 206        self.e_rho = {}
- 207        self.e_drho = {}
- 208        self._dvalue = 0
- 209        self.ddvalue = 0
- 210
- 211        self.S = {}
- 212        self.tau_exp = {}
- 213        self.N_sigma = {}
- 214
- 215        if kwargs.get('fft') is False:
- 216            fft = False
- 217        else:
- 218            fft = True
- 219
- 220        def _parse_kwarg(kwarg_name):
- 221            if kwarg_name in kwargs:
- 222                tmp = kwargs.get(kwarg_name)
- 223                if isinstance(tmp, (int, float)):
- 224                    if tmp < 0:
- 225                        raise ValueError(kwarg_name + ' has to be larger or equal to 0.')
- 226                    for e, e_name in enumerate(self.e_names):
- 227                        getattr(self, kwarg_name)[e_name] = tmp
- 228                else:
- 229                    raise TypeError(kwarg_name + ' is not in proper format.')
- 230            else:
- 231                for e, e_name in enumerate(self.e_names):
- 232                    if e_name in getattr(Obs, kwarg_name + '_dict'):
- 233                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name]
- 234                    else:
- 235                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global')
- 236
- 237        _parse_kwarg('S')
- 238        _parse_kwarg('tau_exp')
- 239        _parse_kwarg('N_sigma')
- 240
- 241        for e, e_name in enumerate(self.mc_names):
- 242            gapsize = _determine_gap(self, e_content, e_name)
- 243
- 244            r_length = []
- 245            for r_name in e_content[e_name]:
- 246                if isinstance(self.idl[r_name], range):
- 247                    r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize)
- 248                else:
- 249                    r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize)
- 250
- 251            e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]])
- 252            w_max = max(r_length) // 2
- 253            e_gamma[e_name] = np.zeros(w_max)
- 254            self.e_rho[e_name] = np.zeros(w_max)
- 255            self.e_drho[e_name] = np.zeros(w_max)
- 256
- 257            for r_name in e_content[e_name]:
- 258                e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
- 259
- 260            gamma_div = np.zeros(w_max)
- 261            for r_name in e_content[e_name]:
- 262                gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
- 263            gamma_div[gamma_div < 1] = 1.0
- 264            e_gamma[e_name] /= gamma_div[:w_max]
- 265
- 266            if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny:  # Prevent division by zero
- 267                self.e_tauint[e_name] = 0.5
- 268                self.e_dtauint[e_name] = 0.0
- 269                self.e_dvalue[e_name] = 0.0
- 270                self.e_ddvalue[e_name] = 0.0
- 271                self.e_windowsize[e_name] = 0
- 272                continue
- 273
- 274            self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
- 275            self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:])))
- 276            # Make sure no entry of tauint is smaller than 0.5
- 277            self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps
- 278            # hep-lat/0306017 eq. (42)
- 279            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
- 280            self.e_n_dtauint[e_name][0] = 0.0
- 281
- 282            def _compute_drho(i):
- 283                tmp = (self.e_rho[e_name][i + 1:w_max]
- 284                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
- 285                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
- 286                       - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i])
- 287                self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N)
- 288
- 289            if self.tau_exp[e_name] > 0:
- 290                _compute_drho(1)
- 291                texp = self.tau_exp[e_name]
- 292                # Critical slowing down analysis
- 293                if w_max // 2 <= 1:
- 294                    raise ValueError("Need at least 8 samples for tau_exp error analysis")
- 295                for n in range(1, w_max // 2):
- 296                    _compute_drho(n + 1)
- 297                    if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2:
- 298                        # Bias correction hep-lat/0306017 eq. (49) included
- 299                        self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1])  # The absolute makes sure, that the tail contribution is always positive
- 300                        self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2)
- 301                        # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2
- 302                        self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
- 303                        self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
- 304                        self.e_windowsize[e_name] = n
- 305                        break
- 306            else:
- 307                if self.S[e_name] == 0.0:
- 308                    self.e_tauint[e_name] = 0.5
- 309                    self.e_dtauint[e_name] = 0.0
- 310                    self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1))
- 311                    self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N)
- 312                    self.e_windowsize[e_name] = 0
- 313                else:
- 314                    # Standard automatic windowing procedure
- 315                    tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1))
- 316                    g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N)
- 317                    for n in range(1, w_max):
- 318                        if g_w[n - 1] < 0 or n >= w_max - 1:
- 319                            _compute_drho(n)
- 320                            self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N)  # Bias correction hep-lat/0306017 eq. (49)
- 321                            self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n]
- 322                            self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
- 323                            self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
- 324                            self.e_windowsize[e_name] = n
- 325                            break
- 326
- 327            self._dvalue += self.e_dvalue[e_name] ** 2
- 328            self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2
- 329
- 330        for e_name in self.cov_names:
- 331            self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq())
- 332            self.e_ddvalue[e_name] = 0
- 333            self._dvalue += self.e_dvalue[e_name]**2
- 334
- 335        self._dvalue = np.sqrt(self._dvalue)
- 336        if self._dvalue == 0.0:
- 337            self.ddvalue = 0.0
- 338        else:
- 339            self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue
- 340        return
- 341
- 342    gm = gamma_method
+ 143        self.tag = None
+ 144
+ 145    @property
+ 146    def value(self):
+ 147        return self._value
+ 148
+ 149    @property
+ 150    def dvalue(self):
+ 151        return self._dvalue
+ 152
+ 153    @property
+ 154    def e_names(self):
+ 155        return sorted(set([o.split('|')[0] for o in self.names]))
+ 156
+ 157    @property
+ 158    def cov_names(self):
+ 159        return sorted(set([o for o in self.covobs.keys()]))
+ 160
+ 161    @property
+ 162    def mc_names(self):
+ 163        return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names]))
+ 164
+ 165    @property
+ 166    def e_content(self):
+ 167        res = {}
+ 168        for e, e_name in enumerate(self.e_names):
+ 169            res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names))
+ 170            if e_name in self.names:
+ 171                res[e_name].append(e_name)
+ 172        return res
+ 173
+ 174    @property
+ 175    def covobs(self):
+ 176        return self._covobs
+ 177
+ 178    def gamma_method(self, **kwargs):
+ 179        """Estimate the error and related properties of the Obs.
+ 180
+ 181        Parameters
+ 182        ----------
+ 183        S : float
+ 184            specifies a custom value for the parameter S (default 2.0).
+ 185            If set to 0 it is assumed that the data exhibits no
+ 186            autocorrelation. In this case the error estimates coincides
+ 187            with the sample standard error.
+ 188        tau_exp : float
+ 189            positive value triggers the critical slowing down analysis
+ 190            (default 0.0).
+ 191        N_sigma : float
+ 192            number of standard deviations from zero until the tail is
+ 193            attached to the autocorrelation function (default 1).
+ 194        fft : bool
+ 195            determines whether the fft algorithm is used for the computation
+ 196            of the autocorrelation function (default True)
+ 197        """
+ 198
+ 199        e_content = self.e_content
+ 200        self.e_dvalue = {}
+ 201        self.e_ddvalue = {}
+ 202        self.e_tauint = {}
+ 203        self.e_dtauint = {}
+ 204        self.e_windowsize = {}
+ 205        self.e_n_tauint = {}
+ 206        self.e_n_dtauint = {}
+ 207        e_gamma = {}
+ 208        self.e_rho = {}
+ 209        self.e_drho = {}
+ 210        self._dvalue = 0
+ 211        self.ddvalue = 0
+ 212
+ 213        self.S = {}
+ 214        self.tau_exp = {}
+ 215        self.N_sigma = {}
+ 216
+ 217        if kwargs.get('fft') is False:
+ 218            fft = False
+ 219        else:
+ 220            fft = True
+ 221
+ 222        def _parse_kwarg(kwarg_name):
+ 223            if kwarg_name in kwargs:
+ 224                tmp = kwargs.get(kwarg_name)
+ 225                if isinstance(tmp, (int, float)):
+ 226                    if tmp < 0:
+ 227                        raise ValueError(kwarg_name + ' has to be larger or equal to 0.')
+ 228                    for e, e_name in enumerate(self.e_names):
+ 229                        getattr(self, kwarg_name)[e_name] = tmp
+ 230                else:
+ 231                    raise TypeError(kwarg_name + ' is not in proper format.')
+ 232            else:
+ 233                for e, e_name in enumerate(self.e_names):
+ 234                    if e_name in getattr(Obs, kwarg_name + '_dict'):
+ 235                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name]
+ 236                    else:
+ 237                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global')
+ 238
+ 239        _parse_kwarg('S')
+ 240        _parse_kwarg('tau_exp')
+ 241        _parse_kwarg('N_sigma')
+ 242
+ 243        for e, e_name in enumerate(self.mc_names):
+ 244            gapsize = _determine_gap(self, e_content, e_name)
+ 245
+ 246            r_length = []
+ 247            for r_name in e_content[e_name]:
+ 248                if isinstance(self.idl[r_name], range):
+ 249                    r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize)
+ 250                else:
+ 251                    r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize)
+ 252
+ 253            e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]])
+ 254            w_max = max(r_length) // 2
+ 255            e_gamma[e_name] = np.zeros(w_max)
+ 256            self.e_rho[e_name] = np.zeros(w_max)
+ 257            self.e_drho[e_name] = np.zeros(w_max)
+ 258
+ 259            for r_name in e_content[e_name]:
+ 260                e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
+ 261
+ 262            gamma_div = np.zeros(w_max)
+ 263            for r_name in e_content[e_name]:
+ 264                gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
+ 265            gamma_div[gamma_div < 1] = 1.0
+ 266            e_gamma[e_name] /= gamma_div[:w_max]
+ 267
+ 268            if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny:  # Prevent division by zero
+ 269                self.e_tauint[e_name] = 0.5
+ 270                self.e_dtauint[e_name] = 0.0
+ 271                self.e_dvalue[e_name] = 0.0
+ 272                self.e_ddvalue[e_name] = 0.0
+ 273                self.e_windowsize[e_name] = 0
+ 274                continue
+ 275
+ 276            self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
+ 277            self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:])))
+ 278            # Make sure no entry of tauint is smaller than 0.5
+ 279            self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps
+ 280            # hep-lat/0306017 eq. (42)
+ 281            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
+ 282            self.e_n_dtauint[e_name][0] = 0.0
+ 283
+ 284            def _compute_drho(i):
+ 285                tmp = (self.e_rho[e_name][i + 1:w_max]
+ 286                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
+ 287                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
+ 288                       - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i])
+ 289                self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N)
+ 290
+ 291            if self.tau_exp[e_name] > 0:
+ 292                _compute_drho(1)
+ 293                texp = self.tau_exp[e_name]
+ 294                # Critical slowing down analysis
+ 295                if w_max // 2 <= 1:
+ 296                    raise ValueError("Need at least 8 samples for tau_exp error analysis")
+ 297                for n in range(1, w_max // 2):
+ 298                    _compute_drho(n + 1)
+ 299                    if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2:
+ 300                        # Bias correction hep-lat/0306017 eq. (49) included
+ 301                        self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1])  # The absolute makes sure, that the tail contribution is always positive
+ 302                        self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2)
+ 303                        # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2
+ 304                        self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+ 305                        self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
+ 306                        self.e_windowsize[e_name] = n
+ 307                        break
+ 308            else:
+ 309                if self.S[e_name] == 0.0:
+ 310                    self.e_tauint[e_name] = 0.5
+ 311                    self.e_dtauint[e_name] = 0.0
+ 312                    self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1))
+ 313                    self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N)
+ 314                    self.e_windowsize[e_name] = 0
+ 315                else:
+ 316                    # Standard automatic windowing procedure
+ 317                    tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1))
+ 318                    g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N)
+ 319                    for n in range(1, w_max):
+ 320                        if g_w[n - 1] < 0 or n >= w_max - 1:
+ 321                            _compute_drho(n)
+ 322                            self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N)  # Bias correction hep-lat/0306017 eq. (49)
+ 323                            self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n]
+ 324                            self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+ 325                            self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
+ 326                            self.e_windowsize[e_name] = n
+ 327                            break
+ 328
+ 329            self._dvalue += self.e_dvalue[e_name] ** 2
+ 330            self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2
+ 331
+ 332        for e_name in self.cov_names:
+ 333            self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq())
+ 334            self.e_ddvalue[e_name] = 0
+ 335            self._dvalue += self.e_dvalue[e_name]**2
+ 336
+ 337        self._dvalue = np.sqrt(self._dvalue)
+ 338        if self._dvalue == 0.0:
+ 339            self.ddvalue = 0.0
+ 340        else:
+ 341            self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue
+ 342        return
  343
- 344    def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize):
- 345        """Calculate Gamma_{AA} from the deltas, which are defined on idx.
- 346           idx is assumed to be a contiguous range (possibly with a stepsize != 1)
- 347
- 348        Parameters
- 349        ----------
- 350        deltas : list
- 351            List of fluctuations
- 352        idx : list
- 353            List or range of configurations on which the deltas are defined.
- 354        shape : int
- 355            Number of configurations in idx.
- 356        w_max : int
- 357            Upper bound for the summation window.
- 358        fft : bool
- 359            determines whether the fft algorithm is used for the computation
- 360            of the autocorrelation function.
- 361        gapsize : int
- 362            The target distance between two configurations. If longer distances
- 363            are found in idx, the data is expanded.
- 364        """
- 365        gamma = np.zeros(w_max)
- 366        deltas = _expand_deltas(deltas, idx, shape, gapsize)
- 367        new_shape = len(deltas)
- 368        if fft:
- 369            max_gamma = min(new_shape, w_max)
- 370            # The padding for the fft has to be even
- 371            padding = new_shape + max_gamma + (new_shape + max_gamma) % 2
- 372            gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma]
- 373        else:
- 374            for n in range(w_max):
- 375                if new_shape - n >= 0:
- 376                    gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape])
- 377
- 378        return gamma
+ 344    gm = gamma_method
+ 345
+ 346    def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize):
+ 347        """Calculate Gamma_{AA} from the deltas, which are defined on idx.
+ 348           idx is assumed to be a contiguous range (possibly with a stepsize != 1)
+ 349
+ 350        Parameters
+ 351        ----------
+ 352        deltas : list
+ 353            List of fluctuations
+ 354        idx : list
+ 355            List or range of configurations on which the deltas are defined.
+ 356        shape : int
+ 357            Number of configurations in idx.
+ 358        w_max : int
+ 359            Upper bound for the summation window.
+ 360        fft : bool
+ 361            determines whether the fft algorithm is used for the computation
+ 362            of the autocorrelation function.
+ 363        gapsize : int
+ 364            The target distance between two configurations. If longer distances
+ 365            are found in idx, the data is expanded.
+ 366        """
+ 367        gamma = np.zeros(w_max)
+ 368        deltas = _expand_deltas(deltas, idx, shape, gapsize)
+ 369        new_shape = len(deltas)
+ 370        if fft:
+ 371            max_gamma = min(new_shape, w_max)
+ 372            # The padding for the fft has to be even
+ 373            padding = new_shape + max_gamma + (new_shape + max_gamma) % 2
+ 374            gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma]
+ 375        else:
+ 376            for n in range(w_max):
+ 377                if new_shape - n >= 0:
+ 378                    gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape])
  379
- 380    def details(self, ens_content=True):
- 381        """Output detailed properties of the Obs.
- 382
- 383        Parameters
- 384        ----------
- 385        ens_content : bool
- 386            print details about the ensembles and replica if true.
- 387        """
- 388        if self.tag is not None:
- 389            print("Description:", self.tag)
- 390        if not hasattr(self, 'e_dvalue'):
- 391            print('Result\t %3.8e' % (self.value))
- 392        else:
- 393            if self.value == 0.0:
- 394                percentage = np.nan
- 395            else:
- 396                percentage = np.abs(self._dvalue / self.value) * 100
- 397            print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage))
- 398            if len(self.e_names) > 1:
- 399                print(' Ensemble errors:')
- 400            e_content = self.e_content
- 401            for e_name in self.mc_names:
- 402                gap = _determine_gap(self, e_content, e_name)
- 403
- 404                if len(self.e_names) > 1:
- 405                    print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name]))
- 406                tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name])
- 407                tau_string += f" in units of {gap} config"
- 408                if gap > 1:
- 409                    tau_string += "s"
- 410                if self.tau_exp[e_name] > 0:
- 411                    tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name])
- 412                else:
- 413                    tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name])
- 414                print(tau_string)
- 415            for e_name in self.cov_names:
- 416                print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name]))
- 417        if ens_content is True:
- 418            if len(self.e_names) == 1:
- 419                print(self.N, 'samples in', len(self.e_names), 'ensemble:')
- 420            else:
- 421                print(self.N, 'samples in', len(self.e_names), 'ensembles:')
- 422            my_string_list = []
- 423            for key, value in sorted(self.e_content.items()):
- 424                if key not in self.covobs:
- 425                    my_string = '  ' + "\u00B7 Ensemble '" + key + "' "
- 426                    if len(value) == 1:
- 427                        my_string += f': {self.shape[value[0]]} configurations'
- 428                        if isinstance(self.idl[value[0]], range):
- 429                            my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')'
- 430                        else:
- 431                            my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})'
- 432                    else:
- 433                        sublist = []
- 434                        for v in value:
- 435                            my_substring = '    ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' "
- 436                            my_substring += f': {self.shape[v]} configurations'
- 437                            if isinstance(self.idl[v], range):
- 438                                my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')'
- 439                            else:
- 440                                my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})'
- 441                            sublist.append(my_substring)
- 442
- 443                        my_string += '\n' + '\n'.join(sublist)
- 444                else:
- 445                    my_string = '  ' + "\u00B7 Covobs   '" + key + "' "
- 446                my_string_list.append(my_string)
- 447            print('\n'.join(my_string_list))
- 448
- 449    def reweight(self, weight):
- 450        """Reweight the obs with given rewighting factors.
- 451
- 452        Parameters
- 453        ----------
- 454        weight : Obs
- 455            Reweighting factor. An Observable that has to be defined on a superset of the
- 456            configurations in obs[i].idl for all i.
- 457        all_configs : bool
- 458            if True, the reweighted observables are normalized by the average of
- 459            the reweighting factor on all configurations in weight.idl and not
- 460            on the configurations in obs[i].idl. Default False.
- 461        """
- 462        return reweight(weight, [self])[0]
- 463
- 464    def is_zero_within_error(self, sigma=1):
- 465        """Checks whether the observable is zero within 'sigma' standard errors.
- 466
- 467        Parameters
- 468        ----------
- 469        sigma : int
- 470            Number of standard errors used for the check.
- 471
- 472        Works only properly when the gamma method was run.
- 473        """
- 474        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
- 475
- 476    def is_zero(self, atol=1e-10):
- 477        """Checks whether the observable is zero within a given tolerance.
- 478
- 479        Parameters
- 480        ----------
- 481        atol : float
- 482            Absolute tolerance (for details see numpy documentation).
- 483        """
- 484        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
- 485
- 486    def plot_tauint(self, save=None):
- 487        """Plot integrated autocorrelation time for each ensemble.
- 488
- 489        Parameters
- 490        ----------
- 491        save : str
- 492            saves the figure to a file named 'save' if.
- 493        """
- 494        if not hasattr(self, 'e_dvalue'):
- 495            raise Exception('Run the gamma method first.')
- 496
- 497        for e, e_name in enumerate(self.mc_names):
- 498            fig = plt.figure()
- 499            plt.xlabel(r'$W$')
- 500            plt.ylabel(r'$\tau_\mathrm{int}$')
- 501            length = int(len(self.e_n_tauint[e_name]))
- 502            if self.tau_exp[e_name] > 0:
- 503                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
- 504                x_help = np.arange(2 * self.tau_exp[e_name])
- 505                y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base
- 506                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
- 507                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
- 508                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
- 509                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
- 510                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
- 511                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
- 512            else:
- 513                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
- 514                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
- 515
- 516            plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label)
- 517            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
- 518            plt.legend()
- 519            plt.xlim(-0.5, xmax)
- 520            ylim = plt.ylim()
- 521            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
- 522            plt.draw()
- 523            if save:
- 524                fig.savefig(save + "_" + str(e))
- 525
- 526    def plot_rho(self, save=None):
- 527        """Plot normalized autocorrelation function time for each ensemble.
- 528
- 529        Parameters
- 530        ----------
- 531        save : str
- 532            saves the figure to a file named 'save' if.
- 533        """
- 534        if not hasattr(self, 'e_dvalue'):
- 535            raise Exception('Run the gamma method first.')
- 536        for e, e_name in enumerate(self.mc_names):
- 537            fig = plt.figure()
- 538            plt.xlabel('W')
- 539            plt.ylabel('rho')
- 540            length = int(len(self.e_drho[e_name]))
- 541            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
- 542            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
- 543            if self.tau_exp[e_name] > 0:
- 544                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
- 545                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
- 546                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
- 547                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
- 548            else:
- 549                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
- 550                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
- 551            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
- 552            plt.xlim(-0.5, xmax)
- 553            plt.draw()
- 554            if save:
- 555                fig.savefig(save + "_" + str(e))
- 556
- 557    def plot_rep_dist(self):
- 558        """Plot replica distribution for each ensemble with more than one replicum."""
- 559        if not hasattr(self, 'e_dvalue'):
- 560            raise Exception('Run the gamma method first.')
- 561        for e, e_name in enumerate(self.mc_names):
- 562            if len(self.e_content[e_name]) == 1:
- 563                print('No replica distribution for a single replicum (', e_name, ')')
- 564                continue
- 565            r_length = []
- 566            sub_r_mean = 0
- 567            for r, r_name in enumerate(self.e_content[e_name]):
- 568                r_length.append(len(self.deltas[r_name]))
- 569                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
- 570            e_N = np.sum(r_length)
- 571            sub_r_mean /= e_N
- 572            arr = np.zeros(len(self.e_content[e_name]))
- 573            for r, r_name in enumerate(self.e_content[e_name]):
- 574                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
- 575            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
- 576            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
- 577            plt.draw()
- 578
- 579    def plot_history(self, expand=True):
- 580        """Plot derived Monte Carlo history for each ensemble
- 581
- 582        Parameters
- 583        ----------
- 584        expand : bool
- 585            show expanded history for irregular Monte Carlo chains (default: True).
- 586        """
- 587        for e, e_name in enumerate(self.mc_names):
- 588            plt.figure()
- 589            r_length = []
- 590            tmp = []
- 591            tmp_expanded = []
- 592            for r, r_name in enumerate(self.e_content[e_name]):
- 593                tmp.append(self.deltas[r_name] + self.r_values[r_name])
- 594                if expand:
- 595                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name], 1) + self.r_values[r_name])
- 596                    r_length.append(len(tmp_expanded[-1]))
- 597                else:
- 598                    r_length.append(len(tmp[-1]))
- 599            e_N = np.sum(r_length)
- 600            x = np.arange(e_N)
- 601            y_test = np.concatenate(tmp, axis=0)
- 602            if expand:
- 603                y = np.concatenate(tmp_expanded, axis=0)
- 604            else:
- 605                y = y_test
- 606            plt.errorbar(x, y, fmt='.', markersize=3)
- 607            plt.xlim(-0.5, e_N - 0.5)
- 608            plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})')
- 609            plt.draw()
- 610
- 611    def plot_piechart(self, save=None):
- 612        """Plot piechart which shows the fractional contribution of each
- 613        ensemble to the error and returns a dictionary containing the fractions.
- 614
- 615        Parameters
- 616        ----------
- 617        save : str
- 618            saves the figure to a file named 'save' if.
- 619        """
- 620        if not hasattr(self, 'e_dvalue'):
- 621            raise Exception('Run the gamma method first.')
- 622        if np.isclose(0.0, self._dvalue, atol=1e-15):
- 623            raise ValueError('Error is 0.0')
- 624        labels = self.e_names
- 625        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
- 626        fig1, ax1 = plt.subplots()
- 627        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
- 628        ax1.axis('equal')
- 629        plt.draw()
- 630        if save:
- 631            fig1.savefig(save)
- 632
- 633        return dict(zip(labels, sizes))
+ 380        return gamma
+ 381
+ 382    def details(self, ens_content=True):
+ 383        """Output detailed properties of the Obs.
+ 384
+ 385        Parameters
+ 386        ----------
+ 387        ens_content : bool
+ 388            print details about the ensembles and replica if true.
+ 389        """
+ 390        if self.tag is not None:
+ 391            print("Description:", self.tag)
+ 392        if not hasattr(self, 'e_dvalue'):
+ 393            print('Result\t %3.8e' % (self.value))
+ 394        else:
+ 395            if self.value == 0.0:
+ 396                percentage = np.nan
+ 397            else:
+ 398                percentage = np.abs(self._dvalue / self.value) * 100
+ 399            print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage))
+ 400            if len(self.e_names) > 1:
+ 401                print(' Ensemble errors:')
+ 402            e_content = self.e_content
+ 403            for e_name in self.mc_names:
+ 404                gap = _determine_gap(self, e_content, e_name)
+ 405
+ 406                if len(self.e_names) > 1:
+ 407                    print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name]))
+ 408                tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name])
+ 409                tau_string += f" in units of {gap} config"
+ 410                if gap > 1:
+ 411                    tau_string += "s"
+ 412                if self.tau_exp[e_name] > 0:
+ 413                    tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name])
+ 414                else:
+ 415                    tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name])
+ 416                print(tau_string)
+ 417            for e_name in self.cov_names:
+ 418                print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name]))
+ 419        if ens_content is True:
+ 420            if len(self.e_names) == 1:
+ 421                print(self.N, 'samples in', len(self.e_names), 'ensemble:')
+ 422            else:
+ 423                print(self.N, 'samples in', len(self.e_names), 'ensembles:')
+ 424            my_string_list = []
+ 425            for key, value in sorted(self.e_content.items()):
+ 426                if key not in self.covobs:
+ 427                    my_string = '  ' + "\u00B7 Ensemble '" + key + "' "
+ 428                    if len(value) == 1:
+ 429                        my_string += f': {self.shape[value[0]]} configurations'
+ 430                        if isinstance(self.idl[value[0]], range):
+ 431                            my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')'
+ 432                        else:
+ 433                            my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})'
+ 434                    else:
+ 435                        sublist = []
+ 436                        for v in value:
+ 437                            my_substring = '    ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' "
+ 438                            my_substring += f': {self.shape[v]} configurations'
+ 439                            if isinstance(self.idl[v], range):
+ 440                                my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')'
+ 441                            else:
+ 442                                my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})'
+ 443                            sublist.append(my_substring)
+ 444
+ 445                        my_string += '\n' + '\n'.join(sublist)
+ 446                else:
+ 447                    my_string = '  ' + "\u00B7 Covobs   '" + key + "' "
+ 448                my_string_list.append(my_string)
+ 449            print('\n'.join(my_string_list))
+ 450
+ 451    def reweight(self, weight):
+ 452        """Reweight the obs with given rewighting factors.
+ 453
+ 454        Parameters
+ 455        ----------
+ 456        weight : Obs
+ 457            Reweighting factor. An Observable that has to be defined on a superset of the
+ 458            configurations in obs[i].idl for all i.
+ 459        all_configs : bool
+ 460            if True, the reweighted observables are normalized by the average of
+ 461            the reweighting factor on all configurations in weight.idl and not
+ 462            on the configurations in obs[i].idl. Default False.
+ 463        """
+ 464        return reweight(weight, [self])[0]
+ 465
+ 466    def is_zero_within_error(self, sigma=1):
+ 467        """Checks whether the observable is zero within 'sigma' standard errors.
+ 468
+ 469        Parameters
+ 470        ----------
+ 471        sigma : int
+ 472            Number of standard errors used for the check.
+ 473
+ 474        Works only properly when the gamma method was run.
+ 475        """
+ 476        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
+ 477
+ 478    def is_zero(self, atol=1e-10):
+ 479        """Checks whether the observable is zero within a given tolerance.
+ 480
+ 481        Parameters
+ 482        ----------
+ 483        atol : float
+ 484            Absolute tolerance (for details see numpy documentation).
+ 485        """
+ 486        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
+ 487
+ 488    def plot_tauint(self, save=None):
+ 489        """Plot integrated autocorrelation time for each ensemble.
+ 490
+ 491        Parameters
+ 492        ----------
+ 493        save : str
+ 494            saves the figure to a file named 'save' if.
+ 495        """
+ 496        if not hasattr(self, 'e_dvalue'):
+ 497            raise Exception('Run the gamma method first.')
+ 498
+ 499        for e, e_name in enumerate(self.mc_names):
+ 500            fig = plt.figure()
+ 501            plt.xlabel(r'$W$')
+ 502            plt.ylabel(r'$\tau_\mathrm{int}$')
+ 503            length = int(len(self.e_n_tauint[e_name]))
+ 504            if self.tau_exp[e_name] > 0:
+ 505                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
+ 506                x_help = np.arange(2 * self.tau_exp[e_name])
+ 507                y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base
+ 508                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
+ 509                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
+ 510                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
+ 511                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
+ 512                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+ 513                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
+ 514            else:
+ 515                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
+ 516                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+ 517
+ 518            plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label)
+ 519            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
+ 520            plt.legend()
+ 521            plt.xlim(-0.5, xmax)
+ 522            ylim = plt.ylim()
+ 523            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
+ 524            plt.draw()
+ 525            if save:
+ 526                fig.savefig(save + "_" + str(e))
+ 527
+ 528    def plot_rho(self, save=None):
+ 529        """Plot normalized autocorrelation function time for each ensemble.
+ 530
+ 531        Parameters
+ 532        ----------
+ 533        save : str
+ 534            saves the figure to a file named 'save' if.
+ 535        """
+ 536        if not hasattr(self, 'e_dvalue'):
+ 537            raise Exception('Run the gamma method first.')
+ 538        for e, e_name in enumerate(self.mc_names):
+ 539            fig = plt.figure()
+ 540            plt.xlabel('W')
+ 541            plt.ylabel('rho')
+ 542            length = int(len(self.e_drho[e_name]))
+ 543            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
+ 544            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
+ 545            if self.tau_exp[e_name] > 0:
+ 546                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
+ 547                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
+ 548                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+ 549                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
+ 550            else:
+ 551                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+ 552                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
+ 553            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
+ 554            plt.xlim(-0.5, xmax)
+ 555            plt.draw()
+ 556            if save:
+ 557                fig.savefig(save + "_" + str(e))
+ 558
+ 559    def plot_rep_dist(self):
+ 560        """Plot replica distribution for each ensemble with more than one replicum."""
+ 561        if not hasattr(self, 'e_dvalue'):
+ 562            raise Exception('Run the gamma method first.')
+ 563        for e, e_name in enumerate(self.mc_names):
+ 564            if len(self.e_content[e_name]) == 1:
+ 565                print('No replica distribution for a single replicum (', e_name, ')')
+ 566                continue
+ 567            r_length = []
+ 568            sub_r_mean = 0
+ 569            for r, r_name in enumerate(self.e_content[e_name]):
+ 570                r_length.append(len(self.deltas[r_name]))
+ 571                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
+ 572            e_N = np.sum(r_length)
+ 573            sub_r_mean /= e_N
+ 574            arr = np.zeros(len(self.e_content[e_name]))
+ 575            for r, r_name in enumerate(self.e_content[e_name]):
+ 576                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
+ 577            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
+ 578            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
+ 579            plt.draw()
+ 580
+ 581    def plot_history(self, expand=True):
+ 582        """Plot derived Monte Carlo history for each ensemble
+ 583
+ 584        Parameters
+ 585        ----------
+ 586        expand : bool
+ 587            show expanded history for irregular Monte Carlo chains (default: True).
+ 588        """
+ 589        for e, e_name in enumerate(self.mc_names):
+ 590            plt.figure()
+ 591            r_length = []
+ 592            tmp = []
+ 593            tmp_expanded = []
+ 594            for r, r_name in enumerate(self.e_content[e_name]):
+ 595                tmp.append(self.deltas[r_name] + self.r_values[r_name])
+ 596                if expand:
+ 597                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name], 1) + self.r_values[r_name])
+ 598                    r_length.append(len(tmp_expanded[-1]))
+ 599                else:
+ 600                    r_length.append(len(tmp[-1]))
+ 601            e_N = np.sum(r_length)
+ 602            x = np.arange(e_N)
+ 603            y_test = np.concatenate(tmp, axis=0)
+ 604            if expand:
+ 605                y = np.concatenate(tmp_expanded, axis=0)
+ 606            else:
+ 607                y = y_test
+ 608            plt.errorbar(x, y, fmt='.', markersize=3)
+ 609            plt.xlim(-0.5, e_N - 0.5)
+ 610            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})')
+ 611            plt.draw()
+ 612
+ 613    def plot_piechart(self, save=None):
+ 614        """Plot piechart which shows the fractional contribution of each
+ 615        ensemble to the error and returns a dictionary containing the fractions.
+ 616
+ 617        Parameters
+ 618        ----------
+ 619        save : str
+ 620            saves the figure to a file named 'save' if.
+ 621        """
+ 622        if not hasattr(self, 'e_dvalue'):
+ 623            raise Exception('Run the gamma method first.')
+ 624        if np.isclose(0.0, self._dvalue, atol=1e-15):
+ 625            raise ValueError('Error is 0.0')
+ 626        labels = self.e_names
+ 627        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
+ 628        fig1, ax1 = plt.subplots()
+ 629        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
+ 630        ax1.axis('equal')
+ 631        plt.draw()
+ 632        if save:
+ 633            fig1.savefig(save)
  634
- 635    def dump(self, filename, datatype="json.gz", description="", **kwargs):
- 636        """Dump the Obs to a file 'name' of chosen format.
- 637
- 638        Parameters
- 639        ----------
- 640        filename : str
- 641            name of the file to be saved.
- 642        datatype : str
- 643            Format of the exported file. Supported formats include
- 644            "json.gz" and "pickle"
- 645        description : str
- 646            Description for output file, only relevant for json.gz format.
- 647        path : str
- 648            specifies a custom path for the file (default '.')
- 649        """
- 650        if 'path' in kwargs:
- 651            file_name = kwargs.get('path') + '/' + filename
- 652        else:
- 653            file_name = filename
- 654
- 655        if datatype == "json.gz":
- 656            from .input.json import dump_to_json
- 657            dump_to_json([self], file_name, description=description)
- 658        elif datatype == "pickle":
- 659            with open(file_name + '.p', 'wb') as fb:
- 660                pickle.dump(self, fb)
- 661        else:
- 662            raise TypeError("Unknown datatype " + str(datatype))
- 663
- 664    def export_jackknife(self):
- 665        """Export jackknife samples from the Obs
- 666
- 667        Returns
- 668        -------
- 669        numpy.ndarray
- 670            Returns a numpy array of length N + 1 where N is the number of samples
- 671            for the given ensemble and replicum. The zeroth entry of the array contains
- 672            the mean value of the Obs, entries 1 to N contain the N jackknife samples
- 673            derived from the Obs. The current implementation only works for observables
- 674            defined on exactly one ensemble and replicum. The derived jackknife samples
- 675            should agree with samples from a full jackknife analysis up to O(1/N).
- 676        """
- 677
- 678        if len(self.names) != 1:
- 679            raise ValueError("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
- 680
- 681        name = self.names[0]
- 682        full_data = self.deltas[name] + self.r_values[name]
- 683        n = full_data.size
- 684        mean = self.value
- 685        tmp_jacks = np.zeros(n + 1)
- 686        tmp_jacks[0] = mean
- 687        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
- 688        return tmp_jacks
- 689
- 690    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
- 691        """Export bootstrap samples from the Obs
- 692
- 693        Parameters
- 694        ----------
- 695        samples : int
- 696            Number of bootstrap samples to generate.
- 697        random_numbers : np.ndarray
- 698            Array of shape (samples, length) containing the random numbers to generate the bootstrap samples.
- 699            If not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
- 700        save_rng : str
- 701            Save the random numbers to a file if a path is specified.
- 702
- 703        Returns
- 704        -------
- 705        numpy.ndarray
- 706            Returns a numpy array of length N + 1 where N is the number of samples
- 707            for the given ensemble and replicum. The zeroth entry of the array contains
- 708            the mean value of the Obs, entries 1 to N contain the N import_bootstrap samples
- 709            derived from the Obs. The current implementation only works for observables
- 710            defined on exactly one ensemble and replicum. The derived bootstrap samples
- 711            should agree with samples from a full bootstrap analysis up to O(1/N).
- 712        """
- 713        if len(self.names) != 1:
- 714            raise ValueError("'export_boostrap' is only implemented for Obs defined on one ensemble and replicum.")
- 715
- 716        name = self.names[0]
- 717        length = self.N
- 718
- 719        if random_numbers is None:
- 720            seed = int(hashlib.md5(name.encode()).hexdigest(), 16) & 0xFFFFFFFF
- 721            rng = np.random.default_rng(seed)
- 722            random_numbers = rng.integers(0, length, size=(samples, length))
- 723
- 724        if save_rng is not None:
- 725            np.savetxt(save_rng, random_numbers, fmt='%i')
- 726
- 727        proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
- 728        ret = np.zeros(samples + 1)
- 729        ret[0] = self.value
- 730        ret[1:] = proj @ (self.deltas[name] + self.r_values[name])
- 731        return ret
- 732
- 733    def __float__(self):
- 734        return float(self.value)
- 735
- 736    def __repr__(self):
- 737        return 'Obs[' + str(self) + ']'
- 738
- 739    def __str__(self):
- 740        return _format_uncertainty(self.value, self._dvalue)
- 741
- 742    def __format__(self, format_type):
- 743        if format_type == "":
- 744            significance = 2
- 745        else:
- 746            significance = int(float(format_type.replace("+", "").replace("-", "")))
- 747        my_str = _format_uncertainty(self.value, self._dvalue,
- 748                                     significance=significance)
- 749        for char in ["+", " "]:
- 750            if format_type.startswith(char):
- 751                if my_str[0] != "-":
- 752                    my_str = char + my_str
- 753        return my_str
- 754
- 755    def __hash__(self):
- 756        hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),)
- 757        hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()])
- 758        hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()])
- 759        hash_tuple += tuple([o.encode() for o in self.names])
- 760        m = hashlib.md5()
- 761        [m.update(o) for o in hash_tuple]
- 762        return int(m.hexdigest(), 16) & 0xFFFFFFFF
- 763
- 764    # Overload comparisons
- 765    def __lt__(self, other):
- 766        return self.value < other
- 767
- 768    def __le__(self, other):
- 769        return self.value <= other
- 770
- 771    def __gt__(self, other):
- 772        return self.value > other
- 773
- 774    def __ge__(self, other):
- 775        return self.value >= other
- 776
- 777    def __eq__(self, other):
- 778        if other is None:
- 779            return False
- 780        return (self - other).is_zero()
- 781
- 782    # Overload math operations
- 783    def __add__(self, y):
- 784        if isinstance(y, Obs):
- 785            return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1])
- 786        else:
- 787            if isinstance(y, np.ndarray):
- 788                return np.array([self + o for o in y])
- 789            elif isinstance(y, complex):
- 790                return CObs(self, 0) + y
- 791            elif y.__class__.__name__ in ['Corr', 'CObs']:
- 792                return NotImplemented
- 793            else:
- 794                return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1])
- 795
- 796    def __radd__(self, y):
- 797        return self + y
- 798
- 799    def __mul__(self, y):
- 800        if isinstance(y, Obs):
- 801            return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value])
- 802        else:
- 803            if isinstance(y, np.ndarray):
- 804                return np.array([self * o for o in y])
- 805            elif isinstance(y, complex):
- 806                return CObs(self * y.real, self * y.imag)
- 807            elif y.__class__.__name__ in ['Corr', 'CObs']:
- 808                return NotImplemented
- 809            else:
- 810                return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y])
- 811
- 812    def __rmul__(self, y):
- 813        return self * y
- 814
- 815    def __sub__(self, y):
- 816        if isinstance(y, Obs):
- 817            return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1])
- 818        else:
- 819            if isinstance(y, np.ndarray):
- 820                return np.array([self - o for o in y])
- 821            elif y.__class__.__name__ in ['Corr', 'CObs']:
- 822                return NotImplemented
- 823            else:
- 824                return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1])
- 825
- 826    def __rsub__(self, y):
- 827        return -1 * (self - y)
- 828
- 829    def __pos__(self):
- 830        return self
- 831
- 832    def __neg__(self):
- 833        return -1 * self
- 834
- 835    def __truediv__(self, y):
- 836        if isinstance(y, Obs):
- 837            return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2])
- 838        else:
- 839            if isinstance(y, np.ndarray):
- 840                return np.array([self / o for o in y])
- 841            elif y.__class__.__name__ in ['Corr', 'CObs']:
- 842                return NotImplemented
- 843            else:
- 844                return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y])
- 845
- 846    def __rtruediv__(self, y):
- 847        if isinstance(y, Obs):
- 848            return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2])
- 849        else:
- 850            if isinstance(y, np.ndarray):
- 851                return np.array([o / self for o in y])
- 852            elif y.__class__.__name__ in ['Corr', 'CObs']:
- 853                return NotImplemented
- 854            else:
- 855                return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2])
- 856
- 857    def __pow__(self, y):
- 858        if isinstance(y, Obs):
- 859            return derived_observable(lambda x, **kwargs: x[0] ** x[1], [self, y], man_grad=[y.value * self.value ** (y.value - 1), self.value ** y.value * np.log(self.value)])
- 860        else:
- 861            return derived_observable(lambda x, **kwargs: x[0] ** y, [self], man_grad=[y * self.value ** (y - 1)])
- 862
- 863    def __rpow__(self, y):
- 864        return derived_observable(lambda x, **kwargs: y ** x[0], [self], man_grad=[y ** self.value * np.log(y)])
- 865
- 866    def __abs__(self):
- 867        return derived_observable(lambda x: anp.abs(x[0]), [self])
- 868
- 869    # Overload numpy functions
- 870    def sqrt(self):
- 871        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
- 872
- 873    def log(self):
- 874        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
- 875
- 876    def exp(self):
- 877        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
- 878
- 879    def sin(self):
- 880        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
- 881
- 882    def cos(self):
- 883        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
- 884
- 885    def tan(self):
- 886        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
- 887
- 888    def arcsin(self):
- 889        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
- 890
- 891    def arccos(self):
- 892        return derived_observable(lambda x: anp.arccos(x[0]), [self])
- 893
- 894    def arctan(self):
- 895        return derived_observable(lambda x: anp.arctan(x[0]), [self])
- 896
- 897    def sinh(self):
- 898        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
- 899
- 900    def cosh(self):
- 901        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
- 902
- 903    def tanh(self):
- 904        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
- 905
- 906    def arcsinh(self):
- 907        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
- 908
- 909    def arccosh(self):
- 910        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
- 911
- 912    def arctanh(self):
- 913        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
- 914
- 915
- 916class CObs:
- 917    """Class for a complex valued observable."""
- 918    __slots__ = ['_real', '_imag', 'tag']
- 919
- 920    def __init__(self, real, imag=0.0):
- 921        self._real = real
- 922        self._imag = imag
- 923        self.tag = None
- 924
- 925    @property
- 926    def real(self):
- 927        return self._real
- 928
- 929    @property
- 930    def imag(self):
- 931        return self._imag
- 932
- 933    def gamma_method(self, **kwargs):
- 934        """Executes the gamma_method for the real and the imaginary part."""
- 935        if isinstance(self.real, Obs):
- 936            self.real.gamma_method(**kwargs)
- 937        if isinstance(self.imag, Obs):
- 938            self.imag.gamma_method(**kwargs)
- 939
- 940    def is_zero(self):
- 941        """Checks whether both real and imaginary part are zero within machine precision."""
- 942        return self.real == 0.0 and self.imag == 0.0
- 943
- 944    def conjugate(self):
- 945        return CObs(self.real, -self.imag)
- 946
- 947    def __add__(self, other):
- 948        if isinstance(other, np.ndarray):
- 949            return other + self
- 950        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 951            return CObs(self.real + other.real,
- 952                        self.imag + other.imag)
- 953        else:
- 954            return CObs(self.real + other, self.imag)
- 955
- 956    def __radd__(self, y):
- 957        return self + y
- 958
- 959    def __sub__(self, other):
- 960        if isinstance(other, np.ndarray):
- 961            return -1 * (other - self)
- 962        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 963            return CObs(self.real - other.real, self.imag - other.imag)
- 964        else:
- 965            return CObs(self.real - other, self.imag)
- 966
- 967    def __rsub__(self, other):
- 968        return -1 * (self - other)
- 969
- 970    def __mul__(self, other):
- 971        if isinstance(other, np.ndarray):
- 972            return other * self
- 973        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 974            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
- 975                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
- 976                                               [self.real, other.real, self.imag, other.imag],
- 977                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
- 978                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
- 979                                               [self.real, other.real, self.imag, other.imag],
- 980                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
- 981            elif getattr(other, 'imag', 0) != 0:
- 982                return CObs(self.real * other.real - self.imag * other.imag,
- 983                            self.imag * other.real + self.real * other.imag)
- 984            else:
- 985                return CObs(self.real * other.real, self.imag * other.real)
- 986        else:
- 987            return CObs(self.real * other, self.imag * other)
- 988
- 989    def __rmul__(self, other):
- 990        return self * other
- 991
- 992    def __truediv__(self, other):
- 993        if isinstance(other, np.ndarray):
- 994            return 1 / (other / self)
- 995        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 996            r = other.real ** 2 + other.imag ** 2
- 997            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
- 998        else:
- 999            return CObs(self.real / other, self.imag / other)
-1000
-1001    def __rtruediv__(self, other):
-1002        r = self.real ** 2 + self.imag ** 2
-1003        if hasattr(other, 'real') and hasattr(other, 'imag'):
-1004            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
-1005        else:
-1006            return CObs(self.real * other / r, -self.imag * other / r)
-1007
-1008    def __abs__(self):
-1009        return np.sqrt(self.real**2 + self.imag**2)
-1010
-1011    def __pos__(self):
-1012        return self
-1013
-1014    def __neg__(self):
-1015        return -1 * self
-1016
-1017    def __eq__(self, other):
-1018        return self.real == other.real and self.imag == other.imag
-1019
-1020    def __str__(self):
-1021        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
-1022
-1023    def __repr__(self):
-1024        return 'CObs[' + str(self) + ']'
-1025
-1026    def __format__(self, format_type):
-1027        if format_type == "":
-1028            significance = 2
-1029            format_type = "2"
-1030        else:
-1031            significance = int(float(format_type.replace("+", "").replace("-", "")))
-1032        return f"({self.real:{format_type}}{self.imag:+{significance}}j)"
-1033
-1034
-1035def gamma_method(x, **kwargs):
-1036    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
-1037
-1038    See docstring of pe.Obs.gamma_method for details.
-1039    """
-1040    return np.vectorize(lambda o: o.gm(**kwargs))(x)
-1041
-1042
-1043gm = gamma_method
+ 635        return dict(zip(labels, sizes))
+ 636
+ 637    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+ 638        """Dump the Obs to a file 'name' of chosen format.
+ 639
+ 640        Parameters
+ 641        ----------
+ 642        filename : str
+ 643            name of the file to be saved.
+ 644        datatype : str
+ 645            Format of the exported file. Supported formats include
+ 646            "json.gz" and "pickle"
+ 647        description : str
+ 648            Description for output file, only relevant for json.gz format.
+ 649        path : str
+ 650            specifies a custom path for the file (default '.')
+ 651        """
+ 652        if 'path' in kwargs:
+ 653            file_name = kwargs.get('path') + '/' + filename
+ 654        else:
+ 655            file_name = filename
+ 656
+ 657        if datatype == "json.gz":
+ 658            from .input.json import dump_to_json
+ 659            dump_to_json([self], file_name, description=description)
+ 660        elif datatype == "pickle":
+ 661            with open(file_name + '.p', 'wb') as fb:
+ 662                pickle.dump(self, fb)
+ 663        else:
+ 664            raise TypeError("Unknown datatype " + str(datatype))
+ 665
+ 666    def export_jackknife(self):
+ 667        """Export jackknife samples from the Obs
+ 668
+ 669        Returns
+ 670        -------
+ 671        numpy.ndarray
+ 672            Returns a numpy array of length N + 1 where N is the number of samples
+ 673            for the given ensemble and replicum. The zeroth entry of the array contains
+ 674            the mean value of the Obs, entries 1 to N contain the N jackknife samples
+ 675            derived from the Obs. The current implementation only works for observables
+ 676            defined on exactly one ensemble and replicum. The derived jackknife samples
+ 677            should agree with samples from a full jackknife analysis up to O(1/N).
+ 678        """
+ 679
+ 680        if len(self.names) != 1:
+ 681            raise ValueError("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
+ 682
+ 683        name = self.names[0]
+ 684        full_data = self.deltas[name] + self.r_values[name]
+ 685        n = full_data.size
+ 686        mean = self.value
+ 687        tmp_jacks = np.zeros(n + 1)
+ 688        tmp_jacks[0] = mean
+ 689        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
+ 690        return tmp_jacks
+ 691
+ 692    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
+ 693        """Export bootstrap samples from the Obs
+ 694
+ 695        Parameters
+ 696        ----------
+ 697        samples : int
+ 698            Number of bootstrap samples to generate.
+ 699        random_numbers : np.ndarray
+ 700            Array of shape (samples, length) containing the random numbers to generate the bootstrap samples.
+ 701            If not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
+ 702        save_rng : str
+ 703            Save the random numbers to a file if a path is specified.
+ 704
+ 705        Returns
+ 706        -------
+ 707        numpy.ndarray
+ 708            Returns a numpy array of length N + 1 where N is the number of samples
+ 709            for the given ensemble and replicum. The zeroth entry of the array contains
+ 710            the mean value of the Obs, entries 1 to N contain the N import_bootstrap samples
+ 711            derived from the Obs. The current implementation only works for observables
+ 712            defined on exactly one ensemble and replicum. The derived bootstrap samples
+ 713            should agree with samples from a full bootstrap analysis up to O(1/N).
+ 714        """
+ 715        if len(self.names) != 1:
+ 716            raise ValueError("'export_boostrap' is only implemented for Obs defined on one ensemble and replicum.")
+ 717
+ 718        name = self.names[0]
+ 719        length = self.N
+ 720
+ 721        if random_numbers is None:
+ 722            seed = int(hashlib.md5(name.encode()).hexdigest(), 16) & 0xFFFFFFFF
+ 723            rng = np.random.default_rng(seed)
+ 724            random_numbers = rng.integers(0, length, size=(samples, length))
+ 725
+ 726        if save_rng is not None:
+ 727            np.savetxt(save_rng, random_numbers, fmt='%i')
+ 728
+ 729        proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
+ 730        ret = np.zeros(samples + 1)
+ 731        ret[0] = self.value
+ 732        ret[1:] = proj @ (self.deltas[name] + self.r_values[name])
+ 733        return ret
+ 734
+ 735    def __float__(self):
+ 736        return float(self.value)
+ 737
+ 738    def __repr__(self):
+ 739        return 'Obs[' + str(self) + ']'
+ 740
+ 741    def __str__(self):
+ 742        return _format_uncertainty(self.value, self._dvalue)
+ 743
+ 744    def __format__(self, format_type):
+ 745        if format_type == "":
+ 746            significance = 2
+ 747        else:
+ 748            significance = int(float(format_type.replace("+", "").replace("-", "")))
+ 749        my_str = _format_uncertainty(self.value, self._dvalue,
+ 750                                     significance=significance)
+ 751        for char in ["+", " "]:
+ 752            if format_type.startswith(char):
+ 753                if my_str[0] != "-":
+ 754                    my_str = char + my_str
+ 755        return my_str
+ 756
+ 757    def __hash__(self):
+ 758        hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),)
+ 759        hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()])
+ 760        hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()])
+ 761        hash_tuple += tuple([o.encode() for o in self.names])
+ 762        m = hashlib.md5()
+ 763        [m.update(o) for o in hash_tuple]
+ 764        return int(m.hexdigest(), 16) & 0xFFFFFFFF
+ 765
+ 766    # Overload comparisons
+ 767    def __lt__(self, other):
+ 768        return self.value < other
+ 769
+ 770    def __le__(self, other):
+ 771        return self.value <= other
+ 772
+ 773    def __gt__(self, other):
+ 774        return self.value > other
+ 775
+ 776    def __ge__(self, other):
+ 777        return self.value >= other
+ 778
+ 779    def __eq__(self, other):
+ 780        if other is None:
+ 781            return False
+ 782        return (self - other).is_zero()
+ 783
+ 784    # Overload math operations
+ 785    def __add__(self, y):
+ 786        if isinstance(y, Obs):
+ 787            return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1])
+ 788        else:
+ 789            if isinstance(y, np.ndarray):
+ 790                return np.array([self + o for o in y])
+ 791            elif isinstance(y, complex):
+ 792                return CObs(self, 0) + y
+ 793            elif y.__class__.__name__ in ['Corr', 'CObs']:
+ 794                return NotImplemented
+ 795            else:
+ 796                return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1])
+ 797
+ 798    def __radd__(self, y):
+ 799        return self + y
+ 800
+ 801    def __mul__(self, y):
+ 802        if isinstance(y, Obs):
+ 803            return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value])
+ 804        else:
+ 805            if isinstance(y, np.ndarray):
+ 806                return np.array([self * o for o in y])
+ 807            elif isinstance(y, complex):
+ 808                return CObs(self * y.real, self * y.imag)
+ 809            elif y.__class__.__name__ in ['Corr', 'CObs']:
+ 810                return NotImplemented
+ 811            else:
+ 812                return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y])
+ 813
+ 814    def __rmul__(self, y):
+ 815        return self * y
+ 816
+ 817    def __sub__(self, y):
+ 818        if isinstance(y, Obs):
+ 819            return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1])
+ 820        else:
+ 821            if isinstance(y, np.ndarray):
+ 822                return np.array([self - o for o in y])
+ 823            elif y.__class__.__name__ in ['Corr', 'CObs']:
+ 824                return NotImplemented
+ 825            else:
+ 826                return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1])
+ 827
+ 828    def __rsub__(self, y):
+ 829        return -1 * (self - y)
+ 830
+ 831    def __pos__(self):
+ 832        return self
+ 833
+ 834    def __neg__(self):
+ 835        return -1 * self
+ 836
+ 837    def __truediv__(self, y):
+ 838        if isinstance(y, Obs):
+ 839            return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2])
+ 840        else:
+ 841            if isinstance(y, np.ndarray):
+ 842                return np.array([self / o for o in y])
+ 843            elif y.__class__.__name__ in ['Corr', 'CObs']:
+ 844                return NotImplemented
+ 845            else:
+ 846                return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y])
+ 847
+ 848    def __rtruediv__(self, y):
+ 849        if isinstance(y, Obs):
+ 850            return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2])
+ 851        else:
+ 852            if isinstance(y, np.ndarray):
+ 853                return np.array([o / self for o in y])
+ 854            elif y.__class__.__name__ in ['Corr', 'CObs']:
+ 855                return NotImplemented
+ 856            else:
+ 857                return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2])
+ 858
+ 859    def __pow__(self, y):
+ 860        if isinstance(y, Obs):
+ 861            return derived_observable(lambda x, **kwargs: x[0] ** x[1], [self, y], man_grad=[y.value * self.value ** (y.value - 1), self.value ** y.value * np.log(self.value)])
+ 862        else:
+ 863            return derived_observable(lambda x, **kwargs: x[0] ** y, [self], man_grad=[y * self.value ** (y - 1)])
+ 864
+ 865    def __rpow__(self, y):
+ 866        return derived_observable(lambda x, **kwargs: y ** x[0], [self], man_grad=[y ** self.value * np.log(y)])
+ 867
+ 868    def __abs__(self):
+ 869        return derived_observable(lambda x: anp.abs(x[0]), [self])
+ 870
+ 871    # Overload numpy functions
+ 872    def sqrt(self):
+ 873        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
+ 874
+ 875    def log(self):
+ 876        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
+ 877
+ 878    def exp(self):
+ 879        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
+ 880
+ 881    def sin(self):
+ 882        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
+ 883
+ 884    def cos(self):
+ 885        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
+ 886
+ 887    def tan(self):
+ 888        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
+ 889
+ 890    def arcsin(self):
+ 891        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
+ 892
+ 893    def arccos(self):
+ 894        return derived_observable(lambda x: anp.arccos(x[0]), [self])
+ 895
+ 896    def arctan(self):
+ 897        return derived_observable(lambda x: anp.arctan(x[0]), [self])
+ 898
+ 899    def sinh(self):
+ 900        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
+ 901
+ 902    def cosh(self):
+ 903        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
+ 904
+ 905    def tanh(self):
+ 906        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
+ 907
+ 908    def arcsinh(self):
+ 909        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
+ 910
+ 911    def arccosh(self):
+ 912        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
+ 913
+ 914    def arctanh(self):
+ 915        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
+ 916
+ 917
+ 918class CObs:
+ 919    """Class for a complex valued observable."""
+ 920    __slots__ = ['_real', '_imag', 'tag']
+ 921
+ 922    def __init__(self, real, imag=0.0):
+ 923        self._real = real
+ 924        self._imag = imag
+ 925        self.tag = None
+ 926
+ 927    @property
+ 928    def real(self):
+ 929        return self._real
+ 930
+ 931    @property
+ 932    def imag(self):
+ 933        return self._imag
+ 934
+ 935    def gamma_method(self, **kwargs):
+ 936        """Executes the gamma_method for the real and the imaginary part."""
+ 937        if isinstance(self.real, Obs):
+ 938            self.real.gamma_method(**kwargs)
+ 939        if isinstance(self.imag, Obs):
+ 940            self.imag.gamma_method(**kwargs)
+ 941
+ 942    def is_zero(self):
+ 943        """Checks whether both real and imaginary part are zero within machine precision."""
+ 944        return self.real == 0.0 and self.imag == 0.0
+ 945
+ 946    def conjugate(self):
+ 947        return CObs(self.real, -self.imag)
+ 948
+ 949    def __add__(self, other):
+ 950        if isinstance(other, np.ndarray):
+ 951            return other + self
+ 952        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 953            return CObs(self.real + other.real,
+ 954                        self.imag + other.imag)
+ 955        else:
+ 956            return CObs(self.real + other, self.imag)
+ 957
+ 958    def __radd__(self, y):
+ 959        return self + y
+ 960
+ 961    def __sub__(self, other):
+ 962        if isinstance(other, np.ndarray):
+ 963            return -1 * (other - self)
+ 964        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 965            return CObs(self.real - other.real, self.imag - other.imag)
+ 966        else:
+ 967            return CObs(self.real - other, self.imag)
+ 968
+ 969    def __rsub__(self, other):
+ 970        return -1 * (self - other)
+ 971
+ 972    def __mul__(self, other):
+ 973        if isinstance(other, np.ndarray):
+ 974            return other * self
+ 975        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 976            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
+ 977                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
+ 978                                               [self.real, other.real, self.imag, other.imag],
+ 979                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
+ 980                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
+ 981                                               [self.real, other.real, self.imag, other.imag],
+ 982                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
+ 983            elif getattr(other, 'imag', 0) != 0:
+ 984                return CObs(self.real * other.real - self.imag * other.imag,
+ 985                            self.imag * other.real + self.real * other.imag)
+ 986            else:
+ 987                return CObs(self.real * other.real, self.imag * other.real)
+ 988        else:
+ 989            return CObs(self.real * other, self.imag * other)
+ 990
+ 991    def __rmul__(self, other):
+ 992        return self * other
+ 993
+ 994    def __truediv__(self, other):
+ 995        if isinstance(other, np.ndarray):
+ 996            return 1 / (other / self)
+ 997        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 998            r = other.real ** 2 + other.imag ** 2
+ 999            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
+1000        else:
+1001            return CObs(self.real / other, self.imag / other)
+1002
+1003    def __rtruediv__(self, other):
+1004        r = self.real ** 2 + self.imag ** 2
+1005        if hasattr(other, 'real') and hasattr(other, 'imag'):
+1006            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
+1007        else:
+1008            return CObs(self.real * other / r, -self.imag * other / r)
+1009
+1010    def __abs__(self):
+1011        return np.sqrt(self.real**2 + self.imag**2)
+1012
+1013    def __pos__(self):
+1014        return self
+1015
+1016    def __neg__(self):
+1017        return -1 * self
+1018
+1019    def __eq__(self, other):
+1020        return self.real == other.real and self.imag == other.imag
+1021
+1022    def __str__(self):
+1023        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
+1024
+1025    def __repr__(self):
+1026        return 'CObs[' + str(self) + ']'
+1027
+1028    def __format__(self, format_type):
+1029        if format_type == "":
+1030            significance = 2
+1031            format_type = "2"
+1032        else:
+1033            significance = int(float(format_type.replace("+", "").replace("-", "")))
+1034        return f"({self.real:{format_type}}{self.imag:+{significance}}j)"
+1035
+1036
+1037def gamma_method(x, **kwargs):
+1038    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
+1039
+1040    See docstring of pe.Obs.gamma_method for details.
+1041    """
+1042    return np.vectorize(lambda o: o.gm(**kwargs))(x)
+1043
 1044
-1045
-1046def _format_uncertainty(value, dvalue, significance=2):
-1047    """Creates a string of a value and its error in paranthesis notation, e.g., 13.02(45)"""
-1048    if dvalue == 0.0 or (not np.isfinite(dvalue)):
-1049        return str(value)
-1050    if not isinstance(significance, int):
-1051        raise TypeError("significance needs to be an integer.")
-1052    if significance < 1:
-1053        raise ValueError("significance needs to be larger than zero.")
-1054    fexp = np.floor(np.log10(dvalue))
-1055    if fexp < 0.0:
-1056        return '{:{form}}({:1.0f})'.format(value, dvalue * 10 ** (-fexp + significance - 1), form='.' + str(-int(fexp) + significance - 1) + 'f')
-1057    elif fexp == 0.0:
-1058        return f"{value:.{significance - 1}f}({dvalue:1.{significance - 1}f})"
-1059    else:
-1060        return f"{value:.{max(0, int(significance - fexp - 1))}f}({dvalue:2.{max(0, int(significance - fexp - 1))}f})"
-1061
-1062
-1063def _expand_deltas(deltas, idx, shape, gapsize):
-1064    """Expand deltas defined on idx to a regular range with spacing gapsize between two
-1065       configurations and where holes are filled by 0.
-1066       If idx is of type range, the deltas are not changed if the idx.step == gapsize.
-1067
-1068    Parameters
-1069    ----------
-1070    deltas : list
-1071        List of fluctuations
-1072    idx : list
-1073        List or range of configs on which the deltas are defined, has to be sorted in ascending order.
-1074    shape : int
-1075        Number of configs in idx.
-1076    gapsize : int
-1077        The target distance between two configurations. If longer distances
-1078        are found in idx, the data is expanded.
-1079    """
-1080    if isinstance(idx, range):
-1081        if (idx.step == gapsize):
-1082            return deltas
-1083    ret = np.zeros((idx[-1] - idx[0] + gapsize) // gapsize)
-1084    for i in range(shape):
-1085        ret[(idx[i] - idx[0]) // gapsize] = deltas[i]
-1086    return ret
-1087
-1088
-1089def _merge_idx(idl):
-1090    """Returns the union of all lists in idl as range or sorted list
-1091
-1092    Parameters
-1093    ----------
-1094    idl : list
-1095        List of lists or ranges.
-1096    """
-1097
-1098    if _check_lists_equal(idl):
-1099        return idl[0]
-1100
-1101    idunion = sorted(set().union(*idl))
+1045gm = gamma_method
+1046
+1047
+1048def _format_uncertainty(value, dvalue, significance=2):
+1049    """Creates a string of a value and its error in paranthesis notation, e.g., 13.02(45)"""
+1050    if dvalue == 0.0 or (not np.isfinite(dvalue)):
+1051        return str(value)
+1052    if not isinstance(significance, int):
+1053        raise TypeError("significance needs to be an integer.")
+1054    if significance < 1:
+1055        raise ValueError("significance needs to be larger than zero.")
+1056    fexp = np.floor(np.log10(dvalue))
+1057    if fexp < 0.0:
+1058        return '{:{form}}({:1.0f})'.format(value, dvalue * 10 ** (-fexp + significance - 1), form='.' + str(-int(fexp) + significance - 1) + 'f')
+1059    elif fexp == 0.0:
+1060        return f"{value:.{significance - 1}f}({dvalue:1.{significance - 1}f})"
+1061    else:
+1062        return f"{value:.{max(0, int(significance - fexp - 1))}f}({dvalue:2.{max(0, int(significance - fexp - 1))}f})"
+1063
+1064
+1065def _expand_deltas(deltas, idx, shape, gapsize):
+1066    """Expand deltas defined on idx to a regular range with spacing gapsize between two
+1067       configurations and where holes are filled by 0.
+1068       If idx is of type range, the deltas are not changed if the idx.step == gapsize.
+1069
+1070    Parameters
+1071    ----------
+1072    deltas : list
+1073        List of fluctuations
+1074    idx : list
+1075        List or range of configs on which the deltas are defined, has to be sorted in ascending order.
+1076    shape : int
+1077        Number of configs in idx.
+1078    gapsize : int
+1079        The target distance between two configurations. If longer distances
+1080        are found in idx, the data is expanded.
+1081    """
+1082    if isinstance(idx, range):
+1083        if (idx.step == gapsize):
+1084            return deltas
+1085    ret = np.zeros((idx[-1] - idx[0] + gapsize) // gapsize)
+1086    for i in range(shape):
+1087        ret[(idx[i] - idx[0]) // gapsize] = deltas[i]
+1088    return ret
+1089
+1090
+1091def _merge_idx(idl):
+1092    """Returns the union of all lists in idl as range or sorted list
+1093
+1094    Parameters
+1095    ----------
+1096    idl : list
+1097        List of lists or ranges.
+1098    """
+1099
+1100    if _check_lists_equal(idl):
+1101        return idl[0]
 1102
-1103    # Check whether idunion can be expressed as range
-1104    idrange = range(idunion[0], idunion[-1] + 1, idunion[1] - idunion[0])
-1105    idtest = [list(idrange), idunion]
-1106    if _check_lists_equal(idtest):
-1107        return idrange
-1108
-1109    return idunion
+1103    idunion = sorted(set().union(*idl))
+1104
+1105    # Check whether idunion can be expressed as range
+1106    idrange = range(idunion[0], idunion[-1] + 1, idunion[1] - idunion[0])
+1107    idtest = [list(idrange), idunion]
+1108    if _check_lists_equal(idtest):
+1109        return idrange
 1110
-1111
-1112def _intersection_idx(idl):
-1113    """Returns the intersection of all lists in idl as range or sorted list
-1114
-1115    Parameters
-1116    ----------
-1117    idl : list
-1118        List of lists or ranges.
-1119    """
-1120
-1121    if _check_lists_equal(idl):
-1122        return idl[0]
-1123
-1124    idinter = sorted(set.intersection(*[set(o) for o in idl]))
+1111    return idunion
+1112
+1113
+1114def _intersection_idx(idl):
+1115    """Returns the intersection of all lists in idl as range or sorted list
+1116
+1117    Parameters
+1118    ----------
+1119    idl : list
+1120        List of lists or ranges.
+1121    """
+1122
+1123    if _check_lists_equal(idl):
+1124        return idl[0]
 1125
-1126    # Check whether idinter can be expressed as range
-1127    try:
-1128        idrange = range(idinter[0], idinter[-1] + 1, idinter[1] - idinter[0])
-1129        idtest = [list(idrange), idinter]
-1130        if _check_lists_equal(idtest):
-1131            return idrange
-1132    except IndexError:
-1133        pass
-1134
-1135    return idinter
+1126    idinter = sorted(set.intersection(*[set(o) for o in idl]))
+1127
+1128    # Check whether idinter can be expressed as range
+1129    try:
+1130        idrange = range(idinter[0], idinter[-1] + 1, idinter[1] - idinter[0])
+1131        idtest = [list(idrange), idinter]
+1132        if _check_lists_equal(idtest):
+1133            return idrange
+1134    except IndexError:
+1135        pass
 1136
-1137
-1138def _expand_deltas_for_merge(deltas, idx, shape, new_idx, scalefactor):
-1139    """Expand deltas defined on idx to the list of configs that is defined by new_idx.
-1140       New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest
-1141       common divisor of the step sizes is used as new step size.
-1142
-1143    Parameters
-1144    ----------
-1145    deltas : list
-1146        List of fluctuations
-1147    idx : list
-1148        List or range of configs on which the deltas are defined.
-1149        Has to be a subset of new_idx and has to be sorted in ascending order.
-1150    shape : list
-1151        Number of configs in idx.
-1152    new_idx : list
-1153        List of configs that defines the new range, has to be sorted in ascending order.
-1154    scalefactor : float
-1155        An additional scaling factor that can be applied to scale the fluctuations,
-1156        e.g., when Obs with differing numbers of replica are merged.
-1157    """
-1158    if type(idx) is range and type(new_idx) is range:
-1159        if idx == new_idx:
-1160            if scalefactor == 1:
-1161                return deltas
-1162            else:
-1163                return deltas * scalefactor
-1164    ret = np.zeros(new_idx[-1] - new_idx[0] + 1)
-1165    for i in range(shape):
-1166        ret[idx[i] - new_idx[0]] = deltas[i]
-1167    return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) * len(new_idx) / len(idx) * scalefactor
-1168
-1169
-1170def derived_observable(func, data, array_mode=False, **kwargs):
-1171    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
-1172
-1173    Parameters
-1174    ----------
-1175    func : object
-1176        arbitrary function of the form func(data, **kwargs). For the
-1177        automatic differentiation to work, all numpy functions have to have
-1178        the autograd wrapper (use 'import autograd.numpy as anp').
-1179    data : list
-1180        list of Obs, e.g. [obs1, obs2, obs3].
-1181    num_grad : bool
-1182        if True, numerical derivatives are used instead of autograd
-1183        (default False). To control the numerical differentiation the
-1184        kwargs of numdifftools.step_generators.MaxStepGenerator
-1185        can be used.
-1186    man_grad : list
-1187        manually supply a list or an array which contains the jacobian
-1188        of func. Use cautiously, supplying the wrong derivative will
-1189        not be intercepted.
-1190
-1191    Notes
-1192    -----
-1193    For simple mathematical operations it can be practical to use anonymous
-1194    functions. For the ratio of two observables one can e.g. use
-1195
-1196    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
-1197    """
-1198
-1199    data = np.asarray(data)
-1200    raveled_data = data.ravel()
-1201
-1202    # Workaround for matrix operations containing non Obs data
-1203    if not all(isinstance(x, Obs) for x in raveled_data):
-1204        for i in range(len(raveled_data)):
-1205            if isinstance(raveled_data[i], (int, float)):
-1206                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
-1207
-1208    allcov = {}
-1209    for o in raveled_data:
-1210        for name in o.cov_names:
-1211            if name in allcov:
-1212                if not np.allclose(allcov[name], o.covobs[name].cov):
-1213                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
-1214            else:
-1215                allcov[name] = o.covobs[name].cov
-1216
-1217    n_obs = len(raveled_data)
-1218    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
-1219    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
-1220    new_sample_names = sorted(set(new_names) - set(new_cov_names))
-1221
-1222    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1137    return idinter
+1138
+1139
+1140def _expand_deltas_for_merge(deltas, idx, shape, new_idx, scalefactor):
+1141    """Expand deltas defined on idx to the list of configs that is defined by new_idx.
+1142       New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest
+1143       common divisor of the step sizes is used as new step size.
+1144
+1145    Parameters
+1146    ----------
+1147    deltas : list
+1148        List of fluctuations
+1149    idx : list
+1150        List or range of configs on which the deltas are defined.
+1151        Has to be a subset of new_idx and has to be sorted in ascending order.
+1152    shape : list
+1153        Number of configs in idx.
+1154    new_idx : list
+1155        List of configs that defines the new range, has to be sorted in ascending order.
+1156    scalefactor : float
+1157        An additional scaling factor that can be applied to scale the fluctuations,
+1158        e.g., when Obs with differing numbers of replica are merged.
+1159    """
+1160    if type(idx) is range and type(new_idx) is range:
+1161        if idx == new_idx:
+1162            if scalefactor == 1:
+1163                return deltas
+1164            else:
+1165                return deltas * scalefactor
+1166    ret = np.zeros(new_idx[-1] - new_idx[0] + 1)
+1167    for i in range(shape):
+1168        ret[idx[i] - new_idx[0]] = deltas[i]
+1169    return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) * len(new_idx) / len(idx) * scalefactor
+1170
+1171
+1172def derived_observable(func, data, array_mode=False, **kwargs):
+1173    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
+1174
+1175    Parameters
+1176    ----------
+1177    func : object
+1178        arbitrary function of the form func(data, **kwargs). For the
+1179        automatic differentiation to work, all numpy functions have to have
+1180        the autograd wrapper (use 'import autograd.numpy as anp').
+1181    data : list
+1182        list of Obs, e.g. [obs1, obs2, obs3].
+1183    num_grad : bool
+1184        if True, numerical derivatives are used instead of autograd
+1185        (default False). To control the numerical differentiation the
+1186        kwargs of numdifftools.step_generators.MaxStepGenerator
+1187        can be used.
+1188    man_grad : list
+1189        manually supply a list or an array which contains the jacobian
+1190        of func. Use cautiously, supplying the wrong derivative will
+1191        not be intercepted.
+1192
+1193    Notes
+1194    -----
+1195    For simple mathematical operations it can be practical to use anonymous
+1196    functions. For the ratio of two observables one can e.g. use
+1197
+1198    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
+1199    """
+1200
+1201    data = np.asarray(data)
+1202    raveled_data = data.ravel()
+1203
+1204    # Workaround for matrix operations containing non Obs data
+1205    if not all(isinstance(x, Obs) for x in raveled_data):
+1206        for i in range(len(raveled_data)):
+1207            if isinstance(raveled_data[i], (int, float)):
+1208                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
+1209
+1210    allcov = {}
+1211    for o in raveled_data:
+1212        for name in o.cov_names:
+1213            if name in allcov:
+1214                if not np.allclose(allcov[name], o.covobs[name].cov):
+1215                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
+1216            else:
+1217                allcov[name] = o.covobs[name].cov
+1218
+1219    n_obs = len(raveled_data)
+1220    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
+1221    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
+1222    new_sample_names = sorted(set(new_names) - set(new_cov_names))
 1223
-1224    if data.ndim == 1:
-1225        values = np.array([o.value for o in data])
-1226    else:
-1227        values = np.vectorize(lambda x: x.value)(data)
-1228
-1229    new_values = func(values, **kwargs)
+1224    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1225
+1226    if data.ndim == 1:
+1227        values = np.array([o.value for o in data])
+1228    else:
+1229        values = np.vectorize(lambda x: x.value)(data)
 1230
-1231    multi = int(isinstance(new_values, np.ndarray))
+1231    new_values = func(values, **kwargs)
 1232
-1233    new_r_values = {}
-1234    new_idl_d = {}
-1235    for name in new_sample_names:
-1236        idl = []
-1237        tmp_values = np.zeros(n_obs)
-1238        for i, item in enumerate(raveled_data):
-1239            tmp_values[i] = item.r_values.get(name, item.value)
-1240            tmp_idl = item.idl.get(name)
-1241            if tmp_idl is not None:
-1242                idl.append(tmp_idl)
-1243        if multi > 0:
-1244            tmp_values = np.array(tmp_values).reshape(data.shape)
-1245        new_r_values[name] = func(tmp_values, **kwargs)
-1246        new_idl_d[name] = _merge_idx(idl)
-1247
-1248    def _compute_scalefactor_missing_rep(obs):
-1249        """
-1250        Computes the scale factor that is to be multiplied with the deltas
-1251        in the case where Obs with different subsets of replica are merged.
-1252        Returns a dictionary with the scale factor for each Monte Carlo name.
-1253
-1254        Parameters
-1255        ----------
-1256        obs : Obs
-1257            The observable corresponding to the deltas that are to be scaled
-1258        """
-1259        scalef_d = {}
-1260        for mc_name in obs.mc_names:
-1261            mc_idl_d = [name for name in obs.idl if name.startswith(mc_name + '|')]
-1262            new_mc_idl_d = [name for name in new_idl_d if name.startswith(mc_name + '|')]
-1263            if len(mc_idl_d) > 0 and len(mc_idl_d) < len(new_mc_idl_d):
-1264                scalef_d[mc_name] = sum([len(new_idl_d[name]) for name in new_mc_idl_d]) / sum([len(new_idl_d[name]) for name in mc_idl_d])
-1265        return scalef_d
-1266
-1267    if 'man_grad' in kwargs:
-1268        deriv = np.asarray(kwargs.get('man_grad'))
-1269        if new_values.shape + data.shape != deriv.shape:
-1270            raise ValueError('Manual derivative does not have correct shape.')
-1271    elif kwargs.get('num_grad') is True:
-1272        if multi > 0:
-1273            raise Exception('Multi mode currently not supported for numerical derivative')
-1274        options = {
-1275            'base_step': 0.1,
-1276            'step_ratio': 2.5}
-1277        for key in options.keys():
-1278            kwarg = kwargs.get(key)
-1279            if kwarg is not None:
-1280                options[key] = kwarg
-1281        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
-1282        if tmp_df.size == 1:
-1283            deriv = np.array([tmp_df.real])
-1284        else:
-1285            deriv = tmp_df.real
-1286    else:
-1287        deriv = jacobian(func)(values, **kwargs)
-1288
-1289    final_result = np.zeros(new_values.shape, dtype=object)
+1233    multi = int(isinstance(new_values, np.ndarray))
+1234
+1235    new_r_values = {}
+1236    new_idl_d = {}
+1237    for name in new_sample_names:
+1238        idl = []
+1239        tmp_values = np.zeros(n_obs)
+1240        for i, item in enumerate(raveled_data):
+1241            tmp_values[i] = item.r_values.get(name, item.value)
+1242            tmp_idl = item.idl.get(name)
+1243            if tmp_idl is not None:
+1244                idl.append(tmp_idl)
+1245        if multi > 0:
+1246            tmp_values = np.array(tmp_values).reshape(data.shape)
+1247        new_r_values[name] = func(tmp_values, **kwargs)
+1248        new_idl_d[name] = _merge_idx(idl)
+1249
+1250    def _compute_scalefactor_missing_rep(obs):
+1251        """
+1252        Computes the scale factor that is to be multiplied with the deltas
+1253        in the case where Obs with different subsets of replica are merged.
+1254        Returns a dictionary with the scale factor for each Monte Carlo name.
+1255
+1256        Parameters
+1257        ----------
+1258        obs : Obs
+1259            The observable corresponding to the deltas that are to be scaled
+1260        """
+1261        scalef_d = {}
+1262        for mc_name in obs.mc_names:
+1263            mc_idl_d = [name for name in obs.idl if name.startswith(mc_name + '|')]
+1264            new_mc_idl_d = [name for name in new_idl_d if name.startswith(mc_name + '|')]
+1265            if len(mc_idl_d) > 0 and len(mc_idl_d) < len(new_mc_idl_d):
+1266                scalef_d[mc_name] = sum([len(new_idl_d[name]) for name in new_mc_idl_d]) / sum([len(new_idl_d[name]) for name in mc_idl_d])
+1267        return scalef_d
+1268
+1269    if 'man_grad' in kwargs:
+1270        deriv = np.asarray(kwargs.get('man_grad'))
+1271        if new_values.shape + data.shape != deriv.shape:
+1272            raise ValueError('Manual derivative does not have correct shape.')
+1273    elif kwargs.get('num_grad') is True:
+1274        if multi > 0:
+1275            raise Exception('Multi mode currently not supported for numerical derivative')
+1276        options = {
+1277            'base_step': 0.1,
+1278            'step_ratio': 2.5}
+1279        for key in options.keys():
+1280            kwarg = kwargs.get(key)
+1281            if kwarg is not None:
+1282                options[key] = kwarg
+1283        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
+1284        if tmp_df.size == 1:
+1285            deriv = np.array([tmp_df.real])
+1286        else:
+1287            deriv = tmp_df.real
+1288    else:
+1289        deriv = jacobian(func)(values, **kwargs)
 1290
-1291    if array_mode is True:
+1291    final_result = np.zeros(new_values.shape, dtype=object)
 1292
-1293        class _Zero_grad():
-1294            def __init__(self, N):
-1295                self.grad = np.zeros((N, 1))
-1296
-1297        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
-1298        d_extracted = {}
-1299        g_extracted = {}
-1300        for name in new_sample_names:
-1301            d_extracted[name] = []
-1302            ens_length = len(new_idl_d[name])
-1303            for i_dat, dat in enumerate(data):
-1304                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], _compute_scalefactor_missing_rep(o).get(name.split('|')[0], 1)) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
-1305        for name in new_cov_names:
-1306            g_extracted[name] = []
-1307            zero_grad = _Zero_grad(new_covobs_lengths[name])
-1308            for i_dat, dat in enumerate(data):
-1309                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)))
-1310
-1311    for i_val, new_val in np.ndenumerate(new_values):
-1312        new_deltas = {}
-1313        new_grad = {}
-1314        if array_mode is True:
-1315            for name in new_sample_names:
-1316                ens_length = d_extracted[name][0].shape[-1]
-1317                new_deltas[name] = np.zeros(ens_length)
-1318                for i_dat, dat in enumerate(d_extracted[name]):
-1319                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1320            for name in new_cov_names:
-1321                new_grad[name] = 0
-1322                for i_dat, dat in enumerate(g_extracted[name]):
-1323                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1324        else:
-1325            for j_obs, obs in np.ndenumerate(data):
-1326                scalef_d = _compute_scalefactor_missing_rep(obs)
-1327                for name in obs.names:
-1328                    if name in obs.cov_names:
-1329                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
-1330                    else:
-1331                        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], scalef_d.get(name.split('|')[0], 1))
-1332
-1333        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1293    if array_mode is True:
+1294
+1295        class _Zero_grad():
+1296            def __init__(self, N):
+1297                self.grad = np.zeros((N, 1))
+1298
+1299        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]))
+1300        d_extracted = {}
+1301        g_extracted = {}
+1302        for name in new_sample_names:
+1303            d_extracted[name] = []
+1304            ens_length = len(new_idl_d[name])
+1305            for i_dat, dat in enumerate(data):
+1306                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], _compute_scalefactor_missing_rep(o).get(name.split('|')[0], 1)) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
+1307        for name in new_cov_names:
+1308            g_extracted[name] = []
+1309            zero_grad = _Zero_grad(new_covobs_lengths[name])
+1310            for i_dat, dat in enumerate(data):
+1311                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)))
+1312
+1313    for i_val, new_val in np.ndenumerate(new_values):
+1314        new_deltas = {}
+1315        new_grad = {}
+1316        if array_mode is True:
+1317            for name in new_sample_names:
+1318                ens_length = d_extracted[name][0].shape[-1]
+1319                new_deltas[name] = np.zeros(ens_length)
+1320                for i_dat, dat in enumerate(d_extracted[name]):
+1321                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1322            for name in new_cov_names:
+1323                new_grad[name] = 0
+1324                for i_dat, dat in enumerate(g_extracted[name]):
+1325                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1326        else:
+1327            for j_obs, obs in np.ndenumerate(data):
+1328                scalef_d = _compute_scalefactor_missing_rep(obs)
+1329                for name in obs.names:
+1330                    if name in obs.cov_names:
+1331                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
+1332                    else:
+1333                        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], scalef_d.get(name.split('|')[0], 1))
 1334
-1335        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
-1336            raise ValueError('The same name has been used for deltas and covobs!')
-1337        new_samples = []
-1338        new_means = []
-1339        new_idl = []
-1340        new_names_obs = []
-1341        for name in new_names:
-1342            if name not in new_covobs:
-1343                new_samples.append(new_deltas[name])
-1344                new_idl.append(new_idl_d[name])
-1345                new_means.append(new_r_values[name][i_val])
-1346                new_names_obs.append(name)
-1347        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
-1348        for name in new_covobs:
-1349            final_result[i_val].names.append(name)
-1350        final_result[i_val]._covobs = new_covobs
-1351        final_result[i_val]._value = new_val
-1352        final_result[i_val].reweighted = reweighted
-1353
-1354    if multi == 0:
-1355        final_result = final_result.item()
-1356
-1357    return final_result
+1335        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1336
+1337        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
+1338            raise ValueError('The same name has been used for deltas and covobs!')
+1339        new_samples = []
+1340        new_means = []
+1341        new_idl = []
+1342        new_names_obs = []
+1343        for name in new_names:
+1344            if name not in new_covobs:
+1345                new_samples.append(new_deltas[name])
+1346                new_idl.append(new_idl_d[name])
+1347                new_means.append(new_r_values[name][i_val])
+1348                new_names_obs.append(name)
+1349        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
+1350        for name in new_covobs:
+1351            final_result[i_val].names.append(name)
+1352        final_result[i_val]._covobs = new_covobs
+1353        final_result[i_val]._value = new_val
+1354        final_result[i_val].reweighted = reweighted
+1355
+1356    if multi == 0:
+1357        final_result = final_result.item()
 1358
-1359
-1360def _reduce_deltas(deltas, idx_old, idx_new):
-1361    """Extract deltas defined on idx_old on all configs of idx_new.
-1362
-1363    Assumes, that idx_old and idx_new are correctly defined idl, i.e., they
-1364    are ordered in an ascending order.
-1365
-1366    Parameters
-1367    ----------
-1368    deltas : list
-1369        List of fluctuations
-1370    idx_old : list
-1371        List or range of configs on which the deltas are defined
-1372    idx_new : list
-1373        List of configs for which we want to extract the deltas.
-1374        Has to be a subset of idx_old.
-1375    """
-1376    if not len(deltas) == len(idx_old):
-1377        raise ValueError('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old)))
-1378    if type(idx_old) is range and type(idx_new) is range:
-1379        if idx_old == idx_new:
-1380            return deltas
-1381    if _check_lists_equal([idx_old, idx_new]):
-1382        return deltas
-1383    indices = np.intersect1d(idx_old, idx_new, assume_unique=True, return_indices=True)[1]
-1384    if len(indices) < len(idx_new):
-1385        raise ValueError('Error in _reduce_deltas: Config of idx_new not in idx_old')
-1386    return np.array(deltas)[indices]
-1387
-1388
-1389def reweight(weight, obs, **kwargs):
-1390    """Reweight a list of observables.
-1391
-1392    Parameters
-1393    ----------
-1394    weight : Obs
-1395        Reweighting factor. An Observable that has to be defined on a superset of the
-1396        configurations in obs[i].idl for all i.
-1397    obs : list
-1398        list of Obs, e.g. [obs1, obs2, obs3].
-1399    all_configs : bool
-1400        if True, the reweighted observables are normalized by the average of
-1401        the reweighting factor on all configurations in weight.idl and not
-1402        on the configurations in obs[i].idl. Default False.
-1403    """
-1404    result = []
-1405    for i in range(len(obs)):
-1406        if len(obs[i].cov_names):
-1407            raise ValueError('Error: Not possible to reweight an Obs that contains covobs!')
-1408        if not set(obs[i].names).issubset(weight.names):
-1409            raise ValueError('Error: Ensembles do not fit')
-1410        for name in obs[i].names:
-1411            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
-1412                raise ValueError('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
-1413        new_samples = []
-1414        w_deltas = {}
-1415        for name in sorted(obs[i].names):
-1416            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
-1417            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
-1418        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1419
-1420        if kwargs.get('all_configs'):
-1421            new_weight = weight
-1422        else:
-1423            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)])
-1424
-1425        result.append(tmp_obs / new_weight)
-1426        result[-1].reweighted = True
-1427
-1428    return result
-1429
-1430
-1431def correlate(obs_a, obs_b):
-1432    """Correlate two observables.
+1359    return final_result
+1360
+1361
+1362def _reduce_deltas(deltas, idx_old, idx_new):
+1363    """Extract deltas defined on idx_old on all configs of idx_new.
+1364
+1365    Assumes, that idx_old and idx_new are correctly defined idl, i.e., they
+1366    are ordered in an ascending order.
+1367
+1368    Parameters
+1369    ----------
+1370    deltas : list
+1371        List of fluctuations
+1372    idx_old : list
+1373        List or range of configs on which the deltas are defined
+1374    idx_new : list
+1375        List of configs for which we want to extract the deltas.
+1376        Has to be a subset of idx_old.
+1377    """
+1378    if not len(deltas) == len(idx_old):
+1379        raise ValueError('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old)))
+1380    if type(idx_old) is range and type(idx_new) is range:
+1381        if idx_old == idx_new:
+1382            return deltas
+1383    if _check_lists_equal([idx_old, idx_new]):
+1384        return deltas
+1385    indices = np.intersect1d(idx_old, idx_new, assume_unique=True, return_indices=True)[1]
+1386    if len(indices) < len(idx_new):
+1387        raise ValueError('Error in _reduce_deltas: Config of idx_new not in idx_old')
+1388    return np.array(deltas)[indices]
+1389
+1390
+1391def reweight(weight, obs, **kwargs):
+1392    """Reweight a list of observables.
+1393
+1394    Parameters
+1395    ----------
+1396    weight : Obs
+1397        Reweighting factor. An Observable that has to be defined on a superset of the
+1398        configurations in obs[i].idl for all i.
+1399    obs : list
+1400        list of Obs, e.g. [obs1, obs2, obs3].
+1401    all_configs : bool
+1402        if True, the reweighted observables are normalized by the average of
+1403        the reweighting factor on all configurations in weight.idl and not
+1404        on the configurations in obs[i].idl. Default False.
+1405    """
+1406    result = []
+1407    for i in range(len(obs)):
+1408        if len(obs[i].cov_names):
+1409            raise ValueError('Error: Not possible to reweight an Obs that contains covobs!')
+1410        if not set(obs[i].names).issubset(weight.names):
+1411            raise ValueError('Error: Ensembles do not fit')
+1412        if len(obs[i].mc_names) > 1 or len(weight.mc_names) > 1:
+1413            raise ValueError('Error: Cannot reweight an Obs that contains multiple ensembles.')
+1414        for name in obs[i].names:
+1415            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
+1416                raise ValueError('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
+1417        new_samples = []
+1418        w_deltas = {}
+1419        for name in sorted(obs[i].names):
+1420            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
+1421            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
+1422        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1423
+1424        if kwargs.get('all_configs'):
+1425            new_weight = weight
+1426        else:
+1427            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)])
+1428
+1429        result.append(tmp_obs / new_weight)
+1430        result[-1].reweighted = True
+1431
+1432    return result
 1433
-1434    Parameters
-1435    ----------
-1436    obs_a : Obs
-1437        First observable
-1438    obs_b : Obs
-1439        Second observable
-1440
-1441    Notes
-1442    -----
-1443    Keep in mind to only correlate primary observables which have not been reweighted
-1444    yet. The reweighting has to be applied after correlating the observables.
-1445    Currently only works if ensembles are identical (this is not strictly necessary).
-1446    """
-1447
-1448    if sorted(obs_a.names) != sorted(obs_b.names):
-1449        raise ValueError(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
-1450    if len(obs_a.cov_names) or len(obs_b.cov_names):
-1451        raise ValueError('Error: Not possible to correlate Obs that contain covobs!')
-1452    for name in obs_a.names:
-1453        if obs_a.shape[name] != obs_b.shape[name]:
-1454            raise ValueError('Shapes of ensemble', name, 'do not fit')
-1455        if obs_a.idl[name] != obs_b.idl[name]:
-1456            raise ValueError('idl of ensemble', name, 'do not fit')
-1457
-1458    if obs_a.reweighted is True:
-1459        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
-1460    if obs_b.reweighted is True:
-1461        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
-1462
-1463    new_samples = []
-1464    new_idl = []
-1465    for name in sorted(obs_a.names):
-1466        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
-1467        new_idl.append(obs_a.idl[name])
-1468
-1469    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
-1470    o.reweighted = obs_a.reweighted or obs_b.reweighted
-1471    return o
-1472
-1473
-1474def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
-1475    r'''Calculates the error covariance matrix of a set of observables.
-1476
-1477    WARNING: This function should be used with care, especially for observables with support on multiple
-1478             ensembles with differing autocorrelations. See the notes below for details.
+1434
+1435def correlate(obs_a, obs_b):
+1436    """Correlate two observables.
+1437
+1438    Parameters
+1439    ----------
+1440    obs_a : Obs
+1441        First observable
+1442    obs_b : Obs
+1443        Second observable
+1444
+1445    Notes
+1446    -----
+1447    Keep in mind to only correlate primary observables which have not been reweighted
+1448    yet. The reweighting has to be applied after correlating the observables.
+1449    Only works if a single ensemble is present in the Obs.
+1450    Currently only works if ensemble content is identical (this is not strictly necessary).
+1451    """
+1452
+1453    if len(obs_a.mc_names) > 1 or len(obs_b.mc_names) > 1:
+1454        raise ValueError('Error: Cannot correlate Obs that contain multiple ensembles.')
+1455    if sorted(obs_a.names) != sorted(obs_b.names):
+1456        raise ValueError(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
+1457    if len(obs_a.cov_names) or len(obs_b.cov_names):
+1458        raise ValueError('Error: Not possible to correlate Obs that contain covobs!')
+1459    for name in obs_a.names:
+1460        if obs_a.shape[name] != obs_b.shape[name]:
+1461            raise ValueError('Shapes of ensemble', name, 'do not fit')
+1462        if obs_a.idl[name] != obs_b.idl[name]:
+1463            raise ValueError('idl of ensemble', name, 'do not fit')
+1464
+1465    if obs_a.reweighted is True:
+1466        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
+1467    if obs_b.reweighted is True:
+1468        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
+1469
+1470    new_samples = []
+1471    new_idl = []
+1472    for name in sorted(obs_a.names):
+1473        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
+1474        new_idl.append(obs_a.idl[name])
+1475
+1476    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
+1477    o.reweighted = obs_a.reweighted or obs_b.reweighted
+1478    return o
 1479
-1480    The gamma method has to be applied first to all observables.
-1481
-1482    Parameters
-1483    ----------
-1484    obs : list or numpy.ndarray
-1485        List or one dimensional array of Obs
-1486    visualize : bool
-1487        If True plots the corresponding normalized correlation matrix (default False).
-1488    correlation : bool
-1489        If True the correlation matrix instead of the error covariance matrix is returned (default False).
-1490    smooth : None or int
-1491        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
-1492        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
-1493        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
-1494        small ones.
-1495
-1496    Notes
-1497    -----
-1498    The error covariance is defined such that it agrees with the squared standard error for two identical observables
-1499    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
-1500    in the absence of autocorrelation.
-1501    The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite
-1502    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
-1503    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.
-1504    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
-1505    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
-1506    '''
-1507
-1508    length = len(obs)
-1509
-1510    max_samples = np.max([o.N for o in obs])
-1511    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
-1512        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)
-1513
-1514    cov = np.zeros((length, length))
-1515    for i in range(length):
-1516        for j in range(i, length):
-1517            cov[i, j] = _covariance_element(obs[i], obs[j])
-1518    cov = cov + cov.T - np.diag(np.diag(cov))
-1519
-1520    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
-1521
-1522    if isinstance(smooth, int):
-1523        corr = _smooth_eigenvalues(corr, smooth)
-1524
-1525    if visualize:
-1526        plt.matshow(corr, vmin=-1, vmax=1)
-1527        plt.set_cmap('RdBu')
-1528        plt.colorbar()
-1529        plt.draw()
-1530
-1531    if correlation is True:
-1532        return corr
-1533
-1534    errors = [o.dvalue for o in obs]
-1535    cov = np.diag(errors) @ corr @ np.diag(errors)
-1536
-1537    eigenvalues = np.linalg.eigh(cov)[0]
-1538    if not np.all(eigenvalues >= 0):
-1539        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
+1480
+1481def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+1482    r'''Calculates the error covariance matrix of a set of observables.
+1483
+1484    WARNING: This function should be used with care, especially for observables with support on multiple
+1485             ensembles with differing autocorrelations. See the notes below for details.
+1486
+1487    The gamma method has to be applied first to all observables.
+1488
+1489    Parameters
+1490    ----------
+1491    obs : list or numpy.ndarray
+1492        List or one dimensional array of Obs
+1493    visualize : bool
+1494        If True plots the corresponding normalized correlation matrix (default False).
+1495    correlation : bool
+1496        If True the correlation matrix instead of the error covariance matrix is returned (default False).
+1497    smooth : None or int
+1498        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
+1499        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
+1500        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
+1501        small ones.
+1502
+1503    Notes
+1504    -----
+1505    The error covariance is defined such that it agrees with the squared standard error for two identical observables
+1506    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
+1507    in the absence of autocorrelation.
+1508    The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite
+1509    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
+1510    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.
+1511    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
+1512    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
+1513    '''
+1514
+1515    length = len(obs)
+1516
+1517    max_samples = np.max([o.N for o in obs])
+1518    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
+1519        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)
+1520
+1521    cov = np.zeros((length, length))
+1522    for i in range(length):
+1523        for j in range(i, length):
+1524            cov[i, j] = _covariance_element(obs[i], obs[j])
+1525    cov = cov + cov.T - np.diag(np.diag(cov))
+1526
+1527    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
+1528
+1529    if isinstance(smooth, int):
+1530        corr = _smooth_eigenvalues(corr, smooth)
+1531
+1532    if visualize:
+1533        plt.matshow(corr, vmin=-1, vmax=1)
+1534        plt.set_cmap('RdBu')
+1535        plt.colorbar()
+1536        plt.draw()
+1537
+1538    if correlation is True:
+1539        return corr
 1540
-1541    return cov
-1542
+1541    errors = [o.dvalue for o in obs]
+1542    cov = np.diag(errors) @ corr @ np.diag(errors)
 1543
-1544def invert_corr_cov_cholesky(corr, inverrdiag):
-1545    """Constructs a lower triangular matrix `chol` via the Cholesky decomposition of the correlation matrix `corr`
-1546       and then returns the inverse covariance matrix `chol_inv` as a lower triangular matrix by solving `chol * x = inverrdiag`.
+1544    eigenvalues = np.linalg.eigh(cov)[0]
+1545    if not np.all(eigenvalues >= 0):
+1546        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
 1547
-1548    Parameters
-1549    ----------
-1550    corr : np.ndarray
-1551           correlation matrix
-1552    inverrdiag : np.ndarray
-1553              diagonal matrix, the entries are the inverse errors of the data points considered
-1554    """
-1555
-1556    condn = np.linalg.cond(corr)
-1557    if condn > 0.1 / np.finfo(float).eps:
-1558        raise ValueError(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
-1559    if condn > 1e13:
-1560        warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
-1561    chol = np.linalg.cholesky(corr)
-1562    chol_inv = scipy.linalg.solve_triangular(chol, inverrdiag, lower=True)
-1563
-1564    return chol_inv
-1565
-1566
-1567def sort_corr(corr, kl, yd):
-1568    """ Reorders a correlation matrix to match the alphabetical order of its underlying y data.
-1569
-1570    The ordering of the input correlation matrix `corr` is given by the list of keys `kl`.
-1571    The input dictionary `yd` (with the same keys `kl`) must contain the corresponding y data
-1572    that the correlation matrix is based on.
-1573    This function sorts the list of keys `kl` alphabetically and sorts the matrix `corr`
-1574    according to this alphabetical order such that the sorted matrix `corr_sorted` corresponds
-1575    to the y data `yd` when arranged in an alphabetical order by its keys.
+1548    return cov
+1549
+1550
+1551def invert_corr_cov_cholesky(corr, inverrdiag):
+1552    """Constructs a lower triangular matrix `chol` via the Cholesky decomposition of the correlation matrix `corr`
+1553       and then returns the inverse covariance matrix `chol_inv` as a lower triangular matrix by solving `chol * x = inverrdiag`.
+1554
+1555    Parameters
+1556    ----------
+1557    corr : np.ndarray
+1558           correlation matrix
+1559    inverrdiag : np.ndarray
+1560              diagonal matrix, the entries are the inverse errors of the data points considered
+1561    """
+1562
+1563    condn = np.linalg.cond(corr)
+1564    if condn > 0.1 / np.finfo(float).eps:
+1565        raise ValueError(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
+1566    if condn > 1e13:
+1567        warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
+1568    chol = np.linalg.cholesky(corr)
+1569    chol_inv = scipy.linalg.solve_triangular(chol, inverrdiag, lower=True)
+1570
+1571    return chol_inv
+1572
+1573
+1574def sort_corr(corr, kl, yd):
+1575    """ Reorders a correlation matrix to match the alphabetical order of its underlying y data.
 1576
-1577    Parameters
-1578    ----------
-1579    corr : np.ndarray
-1580        A square correlation matrix constructed using the order of the y data specified by `kl`.
-1581        The dimensions of `corr` should match the total number of y data points in `yd` combined.
-1582    kl : list of str
-1583        A list of keys that denotes the order in which the y data from `yd` was used to build the
-1584        input correlation matrix `corr`.
-1585    yd : dict of list
-1586        A dictionary where each key corresponds to a unique identifier, and its value is a list of
-1587        y data points. The total number of y data points across all keys must match the dimensions
-1588        of `corr`. The lists in the dictionary can be lists of Obs.
-1589
-1590    Returns
-1591    -------
-1592    np.ndarray
-1593        A new, sorted correlation matrix that corresponds to the y data from `yd` when arranged alphabetically by its keys.
-1594
-1595    Example
-1596    -------
-1597    >>> import numpy as np
-1598    >>> import pyerrors as pe
-1599    >>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])
-1600    >>> kl = ['b', 'a']
-1601    >>> yd = {'a': [1, 2], 'b': [3]}
-1602    >>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)
-1603    >>> print(sorted_corr)
-1604    array([[1. , 0.3, 0.4],
-1605           [0.3, 1. , 0.2],
-1606           [0.4, 0.2, 1. ]])
-1607
-1608    """
-1609    kl_sorted = sorted(kl)
-1610
-1611    posd = {}
-1612    ofs = 0
-1613    for ki, k in enumerate(kl):
-1614        posd[k] = [i + ofs for i in range(len(yd[k]))]
-1615        ofs += len(posd[k])
-1616
-1617    mapping = []
-1618    for k in kl_sorted:
-1619        for i in range(len(yd[k])):
-1620            mapping.append(posd[k][i])
-1621
-1622    corr_sorted = np.zeros_like(corr)
-1623    for i in range(corr.shape[0]):
-1624        for j in range(corr.shape[0]):
-1625            corr_sorted[i][j] = corr[mapping[i]][mapping[j]]
-1626
-1627    return corr_sorted
+1577    The ordering of the input correlation matrix `corr` is given by the list of keys `kl`.
+1578    The input dictionary `yd` (with the same keys `kl`) must contain the corresponding y data
+1579    that the correlation matrix is based on.
+1580    This function sorts the list of keys `kl` alphabetically and sorts the matrix `corr`
+1581    according to this alphabetical order such that the sorted matrix `corr_sorted` corresponds
+1582    to the y data `yd` when arranged in an alphabetical order by its keys.
+1583
+1584    Parameters
+1585    ----------
+1586    corr : np.ndarray
+1587        A square correlation matrix constructed using the order of the y data specified by `kl`.
+1588        The dimensions of `corr` should match the total number of y data points in `yd` combined.
+1589    kl : list of str
+1590        A list of keys that denotes the order in which the y data from `yd` was used to build the
+1591        input correlation matrix `corr`.
+1592    yd : dict of list
+1593        A dictionary where each key corresponds to a unique identifier, and its value is a list of
+1594        y data points. The total number of y data points across all keys must match the dimensions
+1595        of `corr`. The lists in the dictionary can be lists of Obs.
+1596
+1597    Returns
+1598    -------
+1599    np.ndarray
+1600        A new, sorted correlation matrix that corresponds to the y data from `yd` when arranged alphabetically by its keys.
+1601
+1602    Example
+1603    -------
+1604    >>> import numpy as np
+1605    >>> import pyerrors as pe
+1606    >>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])
+1607    >>> kl = ['b', 'a']
+1608    >>> yd = {'a': [1, 2], 'b': [3]}
+1609    >>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)
+1610    >>> print(sorted_corr)
+1611    array([[1. , 0.3, 0.4],
+1612           [0.3, 1. , 0.2],
+1613           [0.4, 0.2, 1. ]])
+1614
+1615    """
+1616    kl_sorted = sorted(kl)
+1617
+1618    posd = {}
+1619    ofs = 0
+1620    for ki, k in enumerate(kl):
+1621        posd[k] = [i + ofs for i in range(len(yd[k]))]
+1622        ofs += len(posd[k])
+1623
+1624    mapping = []
+1625    for k in kl_sorted:
+1626        for i in range(len(yd[k])):
+1627            mapping.append(posd[k][i])
 1628
-1629
-1630def _smooth_eigenvalues(corr, E):
-1631    """Eigenvalue smoothing as described in hep-lat/9412087
-1632
-1633    corr : np.ndarray
-1634        correlation matrix
-1635    E : integer
-1636        Number of eigenvalues to be left substantially unchanged
-1637    """
-1638    if not (2 < E < corr.shape[0] - 1):
-1639        raise ValueError(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).")
-1640    vals, vec = np.linalg.eigh(corr)
-1641    lambda_min = np.mean(vals[:-E])
-1642    vals[vals < lambda_min] = lambda_min
-1643    vals /= np.mean(vals)
-1644    return vec @ np.diag(vals) @ vec.T
-1645
-1646
-1647def _covariance_element(obs1, obs2):
-1648    """Estimates the covariance of two Obs objects, neglecting autocorrelations."""
-1649
-1650    def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx):
-1651        deltas1 = _reduce_deltas(deltas1, idx1, new_idx)
-1652        deltas2 = _reduce_deltas(deltas2, idx2, new_idx)
-1653        return np.sum(deltas1 * deltas2)
-1654
-1655    if set(obs1.names).isdisjoint(set(obs2.names)):
-1656        return 0.0
-1657
-1658    if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'):
-1659        raise Exception('The gamma method has to be applied to both Obs first.')
-1660
-1661    dvalue = 0.0
-1662
-1663    for e_name in obs1.mc_names:
+1629    corr_sorted = np.zeros_like(corr)
+1630    for i in range(corr.shape[0]):
+1631        for j in range(corr.shape[0]):
+1632            corr_sorted[i][j] = corr[mapping[i]][mapping[j]]
+1633
+1634    return corr_sorted
+1635
+1636
+1637def _smooth_eigenvalues(corr, E):
+1638    """Eigenvalue smoothing as described in hep-lat/9412087
+1639
+1640    corr : np.ndarray
+1641        correlation matrix
+1642    E : integer
+1643        Number of eigenvalues to be left substantially unchanged
+1644    """
+1645    if not (2 < E < corr.shape[0] - 1):
+1646        raise ValueError(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).")
+1647    vals, vec = np.linalg.eigh(corr)
+1648    lambda_min = np.mean(vals[:-E])
+1649    vals[vals < lambda_min] = lambda_min
+1650    vals /= np.mean(vals)
+1651    return vec @ np.diag(vals) @ vec.T
+1652
+1653
+1654def _covariance_element(obs1, obs2):
+1655    """Estimates the covariance of two Obs objects, neglecting autocorrelations."""
+1656
+1657    def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx):
+1658        deltas1 = _reduce_deltas(deltas1, idx1, new_idx)
+1659        deltas2 = _reduce_deltas(deltas2, idx2, new_idx)
+1660        return np.sum(deltas1 * deltas2)
+1661
+1662    if set(obs1.names).isdisjoint(set(obs2.names)):
+1663        return 0.0
 1664
-1665        if e_name not in obs2.mc_names:
-1666            continue
+1665    if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'):
+1666        raise Exception('The gamma method has to be applied to both Obs first.')
 1667
-1668        idl_d = {}
-1669        for r_name in obs1.e_content[e_name]:
-1670            if r_name not in obs2.e_content[e_name]:
-1671                continue
-1672            idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]])
-1673
-1674        gamma = 0.0
-1675
+1668    dvalue = 0.0
+1669
+1670    for e_name in obs1.mc_names:
+1671
+1672        if e_name not in obs2.mc_names:
+1673            continue
+1674
+1675        idl_d = {}
 1676        for r_name in obs1.e_content[e_name]:
 1677            if r_name not in obs2.e_content[e_name]:
 1678                continue
-1679            if len(idl_d[r_name]) == 0:
-1680                continue
-1681            gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name])
+1679            idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]])
+1680
+1681        gamma = 0.0
 1682
-1683        if gamma == 0.0:
-1684            continue
-1685
-1686        gamma_div = 0.0
-1687        for r_name in obs1.e_content[e_name]:
-1688            if r_name not in obs2.e_content[e_name]:
-1689                continue
-1690            if len(idl_d[r_name]) == 0:
-1691                continue
-1692            gamma_div += np.sqrt(calc_gamma(obs1.deltas[r_name], obs1.deltas[r_name], obs1.idl[r_name], obs1.idl[r_name], idl_d[r_name]) * calc_gamma(obs2.deltas[r_name], obs2.deltas[r_name], obs2.idl[r_name], obs2.idl[r_name], idl_d[r_name]))
-1693        gamma /= gamma_div
-1694
-1695        dvalue += gamma
-1696
-1697    for e_name in obs1.cov_names:
-1698
-1699        if e_name not in obs2.cov_names:
-1700            continue
+1683        for r_name in obs1.e_content[e_name]:
+1684            if r_name not in obs2.e_content[e_name]:
+1685                continue
+1686            if len(idl_d[r_name]) == 0:
+1687                continue
+1688            gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name])
+1689
+1690        if gamma == 0.0:
+1691            continue
+1692
+1693        gamma_div = 0.0
+1694        for r_name in obs1.e_content[e_name]:
+1695            if r_name not in obs2.e_content[e_name]:
+1696                continue
+1697            if len(idl_d[r_name]) == 0:
+1698                continue
+1699            gamma_div += np.sqrt(calc_gamma(obs1.deltas[r_name], obs1.deltas[r_name], obs1.idl[r_name], obs1.idl[r_name], idl_d[r_name]) * calc_gamma(obs2.deltas[r_name], obs2.deltas[r_name], obs2.idl[r_name], obs2.idl[r_name], idl_d[r_name]))
+1700        gamma /= gamma_div
 1701
-1702        dvalue += np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad)).item()
+1702        dvalue += gamma
 1703
-1704    return dvalue
+1704    for e_name in obs1.cov_names:
 1705
-1706
-1707def import_jackknife(jacks, name, idl=None):
-1708    """Imports jackknife samples and returns an Obs
-1709
-1710    Parameters
-1711    ----------
-1712    jacks : numpy.ndarray
-1713        numpy array containing the mean value as zeroth entry and
-1714        the N jackknife samples as first to Nth entry.
-1715    name : str
-1716        name of the ensemble the samples are defined on.
-1717    """
-1718    length = len(jacks) - 1
-1719    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
-1720    samples = jacks[1:] @ prj
-1721    mean = np.mean(samples)
-1722    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
-1723    new_obs._value = jacks[0]
-1724    return new_obs
-1725
-1726
-1727def import_bootstrap(boots, name, random_numbers):
-1728    """Imports bootstrap samples and returns an Obs
-1729
-1730    Parameters
-1731    ----------
-1732    boots : numpy.ndarray
-1733        numpy array containing the mean value as zeroth entry and
-1734        the N bootstrap samples as first to Nth entry.
-1735    name : str
-1736        name of the ensemble the samples are defined on.
-1737    random_numbers : np.ndarray
-1738        Array of shape (samples, length) containing the random numbers to generate the bootstrap samples,
-1739        where samples is the number of bootstrap samples and length is the length of the original Monte Carlo
-1740        chain to be reconstructed.
-1741    """
-1742    samples, length = random_numbers.shape
-1743    if samples != len(boots) - 1:
-1744        raise ValueError("Random numbers do not have the correct shape.")
-1745
-1746    if samples < length:
-1747        raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.")
-1748
-1749    proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
-1750
-1751    samples = scipy.linalg.lstsq(proj, boots[1:])[0]
-1752    ret = Obs([samples], [name])
-1753    ret._value = boots[0]
-1754    return ret
+1706        if e_name not in obs2.cov_names:
+1707            continue
+1708
+1709        dvalue += np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad)).item()
+1710
+1711    return dvalue
+1712
+1713
+1714def import_jackknife(jacks, name, idl=None):
+1715    """Imports jackknife samples and returns an Obs
+1716
+1717    Parameters
+1718    ----------
+1719    jacks : numpy.ndarray
+1720        numpy array containing the mean value as zeroth entry and
+1721        the N jackknife samples as first to Nth entry.
+1722    name : str
+1723        name of the ensemble the samples are defined on.
+1724    """
+1725    length = len(jacks) - 1
+1726    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
+1727    samples = jacks[1:] @ prj
+1728    mean = np.mean(samples)
+1729    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
+1730    new_obs._value = jacks[0]
+1731    return new_obs
+1732
+1733
+1734def import_bootstrap(boots, name, random_numbers):
+1735    """Imports bootstrap samples and returns an Obs
+1736
+1737    Parameters
+1738    ----------
+1739    boots : numpy.ndarray
+1740        numpy array containing the mean value as zeroth entry and
+1741        the N bootstrap samples as first to Nth entry.
+1742    name : str
+1743        name of the ensemble the samples are defined on.
+1744    random_numbers : np.ndarray
+1745        Array of shape (samples, length) containing the random numbers to generate the bootstrap samples,
+1746        where samples is the number of bootstrap samples and length is the length of the original Monte Carlo
+1747        chain to be reconstructed.
+1748    """
+1749    samples, length = random_numbers.shape
+1750    if samples != len(boots) - 1:
+1751        raise ValueError("Random numbers do not have the correct shape.")
+1752
+1753    if samples < length:
+1754        raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.")
 1755
-1756
-1757def merge_obs(list_of_obs):
-1758    """Combine all observables in list_of_obs into one new observable
-1759
-1760    Parameters
-1761    ----------
-1762    list_of_obs : list
-1763        list of the Obs object to be combined
-1764
-1765    Notes
-1766    -----
-1767    It is not possible to combine obs which are based on the same replicum
-1768    """
-1769    replist = [item for obs in list_of_obs for item in obs.names]
-1770    if (len(replist) == len(set(replist))) is False:
-1771        raise ValueError('list_of_obs contains duplicate replica: %s' % (str(replist)))
-1772    if any([len(o.cov_names) for o in list_of_obs]):
-1773        raise ValueError('Not possible to merge data that contains covobs!')
-1774    new_dict = {}
-1775    idl_dict = {}
-1776    for o in list_of_obs:
-1777        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
-1778                        for key in set(o.deltas) | set(o.r_values)})
-1779        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
-1780
-1781    names = sorted(new_dict.keys())
-1782    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
-1783    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
-1784    return o
-1785
-1786
-1787def cov_Obs(means, cov, name, grad=None):
-1788    """Create an Obs based on mean(s) and a covariance matrix
-1789
-1790    Parameters
-1791    ----------
-1792    mean : list of floats or float
-1793        N mean value(s) of the new Obs
-1794    cov : list or array
-1795        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
-1796    name : str
-1797        identifier for the covariance matrix
-1798    grad : list or array
-1799        Gradient of the Covobs wrt. the means belonging to cov.
-1800    """
-1801
-1802    def covobs_to_obs(co):
-1803        """Make an Obs out of a Covobs
-1804
-1805        Parameters
-1806        ----------
-1807        co : Covobs
-1808            Covobs to be embedded into the Obs
-1809        """
-1810        o = Obs([], [], means=[])
-1811        o._value = co.value
-1812        o.names.append(co.name)
-1813        o._covobs[co.name] = co
-1814        o._dvalue = np.sqrt(co.errsq())
-1815        return o
-1816
-1817    ol = []
-1818    if isinstance(means, (float, int)):
-1819        means = [means]
-1820
-1821    for i in range(len(means)):
-1822        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
-1823    if ol[0].covobs[name].N != len(means):
-1824        raise ValueError('You have to provide %d mean values!' % (ol[0].N))
-1825    if len(ol) == 1:
-1826        return ol[0]
-1827    return ol
-1828
-1829
-1830def _determine_gap(o, e_content, e_name):
-1831    gaps = []
-1832    for r_name in e_content[e_name]:
-1833        if isinstance(o.idl[r_name], range):
-1834            gaps.append(o.idl[r_name].step)
-1835        else:
-1836            gaps.append(np.min(np.diff(o.idl[r_name])))
-1837
-1838    gap = min(gaps)
-1839    if not np.all([gi % gap == 0 for gi in gaps]):
-1840        raise ValueError(f"Replica for ensemble {e_name} do not have a common spacing.", gaps)
-1841
-1842    return gap
-1843
-1844
-1845def _check_lists_equal(idl):
-1846    '''
-1847    Use groupby to efficiently check whether all elements of idl are identical.
-1848    Returns True if all elements are equal, otherwise False.
-1849
-1850    Parameters
-1851    ----------
-1852    idl : list of lists, ranges or np.ndarrays
-1853    '''
-1854    g = groupby([np.nditer(el) if isinstance(el, np.ndarray) else el for el in idl])
-1855    if next(g, True) and not next(g, False):
-1856        return True
-1857    return False
+1756    proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
+1757
+1758    samples = scipy.linalg.lstsq(proj, boots[1:])[0]
+1759    ret = Obs([samples], [name])
+1760    ret._value = boots[0]
+1761    return ret
+1762
+1763
+1764def merge_obs(list_of_obs):
+1765    """Combine all observables in list_of_obs into one new observable.
+1766    This allows to merge Obs that have been computed on multiple replica
+1767    of the same ensemble.
+1768    If you like to merge Obs that are based on several ensembles, please
+1769    average them yourself.
+1770
+1771    Parameters
+1772    ----------
+1773    list_of_obs : list
+1774        list of the Obs object to be combined
+1775
+1776    Notes
+1777    -----
+1778    It is not possible to combine obs which are based on the same replicum
+1779    """
+1780    replist = [item for obs in list_of_obs for item in obs.names]
+1781    if (len(replist) == len(set(replist))) is False:
+1782        raise ValueError('list_of_obs contains duplicate replica: %s' % (str(replist)))
+1783    if any([len(o.cov_names) for o in list_of_obs]):
+1784        raise ValueError('Not possible to merge data that contains covobs!')
+1785    new_dict = {}
+1786    idl_dict = {}
+1787    for o in list_of_obs:
+1788        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
+1789                        for key in set(o.deltas) | set(o.r_values)})
+1790        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
+1791
+1792    names = sorted(new_dict.keys())
+1793    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
+1794    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
+1795    return o
+1796
+1797
+1798def cov_Obs(means, cov, name, grad=None):
+1799    """Create an Obs based on mean(s) and a covariance matrix
+1800
+1801    Parameters
+1802    ----------
+1803    mean : list of floats or float
+1804        N mean value(s) of the new Obs
+1805    cov : list or array
+1806        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
+1807    name : str
+1808        identifier for the covariance matrix
+1809    grad : list or array
+1810        Gradient of the Covobs wrt. the means belonging to cov.
+1811    """
+1812
+1813    def covobs_to_obs(co):
+1814        """Make an Obs out of a Covobs
+1815
+1816        Parameters
+1817        ----------
+1818        co : Covobs
+1819            Covobs to be embedded into the Obs
+1820        """
+1821        o = Obs([], [], means=[])
+1822        o._value = co.value
+1823        o.names.append(co.name)
+1824        o._covobs[co.name] = co
+1825        o._dvalue = np.sqrt(co.errsq())
+1826        return o
+1827
+1828    ol = []
+1829    if isinstance(means, (float, int)):
+1830        means = [means]
+1831
+1832    for i in range(len(means)):
+1833        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
+1834    if ol[0].covobs[name].N != len(means):
+1835        raise ValueError('You have to provide %d mean values!' % (ol[0].N))
+1836    if len(ol) == 1:
+1837        return ol[0]
+1838    return ol
+1839
+1840
+1841def _determine_gap(o, e_content, e_name):
+1842    gaps = []
+1843    for r_name in e_content[e_name]:
+1844        if isinstance(o.idl[r_name], range):
+1845            gaps.append(o.idl[r_name].step)
+1846        else:
+1847            gaps.append(np.min(np.diff(o.idl[r_name])))
+1848
+1849    gap = min(gaps)
+1850    if not np.all([gi % gap == 0 for gi in gaps]):
+1851        raise ValueError(f"Replica for ensemble {e_name} do not have a common spacing.", gaps)
+1852
+1853    return gap
+1854
+1855
+1856def _check_lists_equal(idl):
+1857    '''
+1858    Use groupby to efficiently check whether all elements of idl are identical.
+1859    Returns True if all elements are equal, otherwise False.
+1860
+1861    Parameters
+1862    ----------
+1863    idl : list of lists, ranges or np.ndarrays
+1864    '''
+1865    g = groupby([np.nditer(el) if isinstance(el, np.ndarray) else el for el in idl])
+1866    if next(g, True) and not next(g, False):
+1867        return True
+1868    return False
@@ -2273,835 +2284,837 @@ 83 raise ValueError('Names are not unique.') 84 if not all(isinstance(x, str) for x in names): 85 raise TypeError('All names have to be strings.') - 86 else: - 87 if not isinstance(names[0], str): - 88 raise TypeError('All names have to be strings.') - 89 if min(len(x) for x in samples) <= 4: - 90 raise ValueError('Samples have to have at least 5 entries.') - 91 - 92 self.names = sorted(names) - 93 self.shape = {} - 94 self.r_values = {} - 95 self.deltas = {} - 96 self._covobs = {} - 97 - 98 self._value = 0 - 99 self.N = 0 -100 self.idl = {} -101 if idl is not None: -102 for name, idx in sorted(zip(names, idl)): -103 if isinstance(idx, range): -104 self.idl[name] = idx -105 elif isinstance(idx, (list, np.ndarray)): -106 dc = np.unique(np.diff(idx)) -107 if np.any(dc < 0): -108 raise ValueError("Unsorted idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) < 0)[0]]))) -109 elif np.any(dc == 0): -110 raise ValueError("Duplicate entries in idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) == 0)[0]]))) -111 if len(dc) == 1: -112 self.idl[name] = range(idx[0], idx[-1] + dc[0], dc[0]) -113 else: -114 self.idl[name] = list(idx) -115 else: -116 raise TypeError('incompatible type for idl[%s].' % (name)) -117 else: -118 for name, sample in sorted(zip(names, samples)): -119 self.idl[name] = range(1, len(sample) + 1) -120 -121 if kwargs.get("means") is not None: -122 for name, sample, mean in sorted(zip(names, samples, kwargs.get("means"))): -123 self.shape[name] = len(self.idl[name]) -124 self.N += self.shape[name] -125 self.r_values[name] = mean -126 self.deltas[name] = sample -127 else: -128 for name, sample in sorted(zip(names, samples)): -129 self.shape[name] = len(self.idl[name]) -130 self.N += self.shape[name] -131 if len(sample) != self.shape[name]: -132 raise ValueError('Incompatible samples and idx for %s: %d vs. %d' % (name, len(sample), self.shape[name])) -133 self.r_values[name] = np.mean(sample) -134 self.deltas[name] = sample - self.r_values[name] -135 self._value += self.shape[name] * self.r_values[name] -136 self._value /= self.N -137 -138 self._dvalue = 0.0 -139 self.ddvalue = 0.0 -140 self.reweighted = False -141 -142 self.tag = None + 86 if len(set([o.split('|')[0] for o in names])) > 1: + 87 raise ValueError('Cannot initialize Obs based on multiple ensembles. Please average separate Obs from each ensemble.') + 88 else: + 89 if not isinstance(names[0], str): + 90 raise TypeError('All names have to be strings.') + 91 if min(len(x) for x in samples) <= 4: + 92 raise ValueError('Samples have to have at least 5 entries.') + 93 + 94 self.names = sorted(names) + 95 self.shape = {} + 96 self.r_values = {} + 97 self.deltas = {} + 98 self._covobs = {} + 99 +100 self._value = 0 +101 self.N = 0 +102 self.idl = {} +103 if idl is not None: +104 for name, idx in sorted(zip(names, idl)): +105 if isinstance(idx, range): +106 self.idl[name] = idx +107 elif isinstance(idx, (list, np.ndarray)): +108 dc = np.unique(np.diff(idx)) +109 if np.any(dc < 0): +110 raise ValueError("Unsorted idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) < 0)[0]]))) +111 elif np.any(dc == 0): +112 raise ValueError("Duplicate entries in idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) == 0)[0]]))) +113 if len(dc) == 1: +114 self.idl[name] = range(idx[0], idx[-1] + dc[0], dc[0]) +115 else: +116 self.idl[name] = list(idx) +117 else: +118 raise TypeError('incompatible type for idl[%s].' % (name)) +119 else: +120 for name, sample in sorted(zip(names, samples)): +121 self.idl[name] = range(1, len(sample) + 1) +122 +123 if kwargs.get("means") is not None: +124 for name, sample, mean in sorted(zip(names, samples, kwargs.get("means"))): +125 self.shape[name] = len(self.idl[name]) +126 self.N += self.shape[name] +127 self.r_values[name] = mean +128 self.deltas[name] = sample +129 else: +130 for name, sample in sorted(zip(names, samples)): +131 self.shape[name] = len(self.idl[name]) +132 self.N += self.shape[name] +133 if len(sample) != self.shape[name]: +134 raise ValueError('Incompatible samples and idx for %s: %d vs. %d' % (name, len(sample), self.shape[name])) +135 self.r_values[name] = np.mean(sample) +136 self.deltas[name] = sample - self.r_values[name] +137 self._value += self.shape[name] * self.r_values[name] +138 self._value /= self.N +139 +140 self._dvalue = 0.0 +141 self.ddvalue = 0.0 +142 self.reweighted = False 143 -144 @property -145 def value(self): -146 return self._value -147 -148 @property -149 def dvalue(self): -150 return self._dvalue -151 -152 @property -153 def e_names(self): -154 return sorted(set([o.split('|')[0] for o in self.names])) -155 -156 @property -157 def cov_names(self): -158 return sorted(set([o for o in self.covobs.keys()])) -159 -160 @property -161 def mc_names(self): -162 return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names])) -163 -164 @property -165 def e_content(self): -166 res = {} -167 for e, e_name in enumerate(self.e_names): -168 res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names)) -169 if e_name in self.names: -170 res[e_name].append(e_name) -171 return res -172 -173 @property -174 def covobs(self): -175 return self._covobs -176 -177 def gamma_method(self, **kwargs): -178 """Estimate the error and related properties of the Obs. -179 -180 Parameters -181 ---------- -182 S : float -183 specifies a custom value for the parameter S (default 2.0). -184 If set to 0 it is assumed that the data exhibits no -185 autocorrelation. In this case the error estimates coincides -186 with the sample standard error. -187 tau_exp : float -188 positive value triggers the critical slowing down analysis -189 (default 0.0). -190 N_sigma : float -191 number of standard deviations from zero until the tail is -192 attached to the autocorrelation function (default 1). -193 fft : bool -194 determines whether the fft algorithm is used for the computation -195 of the autocorrelation function (default True) -196 """ -197 -198 e_content = self.e_content -199 self.e_dvalue = {} -200 self.e_ddvalue = {} -201 self.e_tauint = {} -202 self.e_dtauint = {} -203 self.e_windowsize = {} -204 self.e_n_tauint = {} -205 self.e_n_dtauint = {} -206 e_gamma = {} -207 self.e_rho = {} -208 self.e_drho = {} -209 self._dvalue = 0 -210 self.ddvalue = 0 -211 -212 self.S = {} -213 self.tau_exp = {} -214 self.N_sigma = {} -215 -216 if kwargs.get('fft') is False: -217 fft = False -218 else: -219 fft = True -220 -221 def _parse_kwarg(kwarg_name): -222 if kwarg_name in kwargs: -223 tmp = kwargs.get(kwarg_name) -224 if isinstance(tmp, (int, float)): -225 if tmp < 0: -226 raise ValueError(kwarg_name + ' has to be larger or equal to 0.') -227 for e, e_name in enumerate(self.e_names): -228 getattr(self, kwarg_name)[e_name] = tmp -229 else: -230 raise TypeError(kwarg_name + ' is not in proper format.') -231 else: -232 for e, e_name in enumerate(self.e_names): -233 if e_name in getattr(Obs, kwarg_name + '_dict'): -234 getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name] -235 else: -236 getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global') -237 -238 _parse_kwarg('S') -239 _parse_kwarg('tau_exp') -240 _parse_kwarg('N_sigma') -241 -242 for e, e_name in enumerate(self.mc_names): -243 gapsize = _determine_gap(self, e_content, e_name) -244 -245 r_length = [] -246 for r_name in e_content[e_name]: -247 if isinstance(self.idl[r_name], range): -248 r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize) -249 else: -250 r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize) -251 -252 e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]]) -253 w_max = max(r_length) // 2 -254 e_gamma[e_name] = np.zeros(w_max) -255 self.e_rho[e_name] = np.zeros(w_max) -256 self.e_drho[e_name] = np.zeros(w_max) -257 -258 for r_name in e_content[e_name]: -259 e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize) -260 -261 gamma_div = np.zeros(w_max) -262 for r_name in e_content[e_name]: -263 gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize) -264 gamma_div[gamma_div < 1] = 1.0 -265 e_gamma[e_name] /= gamma_div[:w_max] -266 -267 if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny: # Prevent division by zero -268 self.e_tauint[e_name] = 0.5 -269 self.e_dtauint[e_name] = 0.0 -270 self.e_dvalue[e_name] = 0.0 -271 self.e_ddvalue[e_name] = 0.0 -272 self.e_windowsize[e_name] = 0 -273 continue -274 -275 self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0] -276 self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:]))) -277 # Make sure no entry of tauint is smaller than 0.5 -278 self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps -279 # hep-lat/0306017 eq. (42) -280 self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N) -281 self.e_n_dtauint[e_name][0] = 0.0 -282 -283 def _compute_drho(i): -284 tmp = (self.e_rho[e_name][i + 1:w_max] -285 + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1], -286 self.e_rho[e_name][1:max(1, w_max - 2 * i)]]) -287 - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i]) -288 self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N) -289 -290 if self.tau_exp[e_name] > 0: -291 _compute_drho(1) -292 texp = self.tau_exp[e_name] -293 # Critical slowing down analysis -294 if w_max // 2 <= 1: -295 raise ValueError("Need at least 8 samples for tau_exp error analysis") -296 for n in range(1, w_max // 2): -297 _compute_drho(n + 1) -298 if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2: -299 # Bias correction hep-lat/0306017 eq. (49) included -300 self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1]) # The absolute makes sure, that the tail contribution is always positive -301 self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2) -302 # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2 -303 self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N) -304 self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N) -305 self.e_windowsize[e_name] = n -306 break -307 else: -308 if self.S[e_name] == 0.0: -309 self.e_tauint[e_name] = 0.5 -310 self.e_dtauint[e_name] = 0.0 -311 self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1)) -312 self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N) -313 self.e_windowsize[e_name] = 0 -314 else: -315 # Standard automatic windowing procedure -316 tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1)) -317 g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N) -318 for n in range(1, w_max): -319 if g_w[n - 1] < 0 or n >= w_max - 1: -320 _compute_drho(n) -321 self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) # Bias correction hep-lat/0306017 eq. (49) -322 self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n] -323 self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N) -324 self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N) -325 self.e_windowsize[e_name] = n -326 break -327 -328 self._dvalue += self.e_dvalue[e_name] ** 2 -329 self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2 -330 -331 for e_name in self.cov_names: -332 self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq()) -333 self.e_ddvalue[e_name] = 0 -334 self._dvalue += self.e_dvalue[e_name]**2 -335 -336 self._dvalue = np.sqrt(self._dvalue) -337 if self._dvalue == 0.0: -338 self.ddvalue = 0.0 -339 else: -340 self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue -341 return -342 -343 gm = gamma_method +144 self.tag = None +145 +146 @property +147 def value(self): +148 return self._value +149 +150 @property +151 def dvalue(self): +152 return self._dvalue +153 +154 @property +155 def e_names(self): +156 return sorted(set([o.split('|')[0] for o in self.names])) +157 +158 @property +159 def cov_names(self): +160 return sorted(set([o for o in self.covobs.keys()])) +161 +162 @property +163 def mc_names(self): +164 return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names])) +165 +166 @property +167 def e_content(self): +168 res = {} +169 for e, e_name in enumerate(self.e_names): +170 res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names)) +171 if e_name in self.names: +172 res[e_name].append(e_name) +173 return res +174 +175 @property +176 def covobs(self): +177 return self._covobs +178 +179 def gamma_method(self, **kwargs): +180 """Estimate the error and related properties of the Obs. +181 +182 Parameters +183 ---------- +184 S : float +185 specifies a custom value for the parameter S (default 2.0). +186 If set to 0 it is assumed that the data exhibits no +187 autocorrelation. In this case the error estimates coincides +188 with the sample standard error. +189 tau_exp : float +190 positive value triggers the critical slowing down analysis +191 (default 0.0). +192 N_sigma : float +193 number of standard deviations from zero until the tail is +194 attached to the autocorrelation function (default 1). +195 fft : bool +196 determines whether the fft algorithm is used for the computation +197 of the autocorrelation function (default True) +198 """ +199 +200 e_content = self.e_content +201 self.e_dvalue = {} +202 self.e_ddvalue = {} +203 self.e_tauint = {} +204 self.e_dtauint = {} +205 self.e_windowsize = {} +206 self.e_n_tauint = {} +207 self.e_n_dtauint = {} +208 e_gamma = {} +209 self.e_rho = {} +210 self.e_drho = {} +211 self._dvalue = 0 +212 self.ddvalue = 0 +213 +214 self.S = {} +215 self.tau_exp = {} +216 self.N_sigma = {} +217 +218 if kwargs.get('fft') is False: +219 fft = False +220 else: +221 fft = True +222 +223 def _parse_kwarg(kwarg_name): +224 if kwarg_name in kwargs: +225 tmp = kwargs.get(kwarg_name) +226 if isinstance(tmp, (int, float)): +227 if tmp < 0: +228 raise ValueError(kwarg_name + ' has to be larger or equal to 0.') +229 for e, e_name in enumerate(self.e_names): +230 getattr(self, kwarg_name)[e_name] = tmp +231 else: +232 raise TypeError(kwarg_name + ' is not in proper format.') +233 else: +234 for e, e_name in enumerate(self.e_names): +235 if e_name in getattr(Obs, kwarg_name + '_dict'): +236 getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name] +237 else: +238 getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global') +239 +240 _parse_kwarg('S') +241 _parse_kwarg('tau_exp') +242 _parse_kwarg('N_sigma') +243 +244 for e, e_name in enumerate(self.mc_names): +245 gapsize = _determine_gap(self, e_content, e_name) +246 +247 r_length = [] +248 for r_name in e_content[e_name]: +249 if isinstance(self.idl[r_name], range): +250 r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize) +251 else: +252 r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize) +253 +254 e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]]) +255 w_max = max(r_length) // 2 +256 e_gamma[e_name] = np.zeros(w_max) +257 self.e_rho[e_name] = np.zeros(w_max) +258 self.e_drho[e_name] = np.zeros(w_max) +259 +260 for r_name in e_content[e_name]: +261 e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize) +262 +263 gamma_div = np.zeros(w_max) +264 for r_name in e_content[e_name]: +265 gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize) +266 gamma_div[gamma_div < 1] = 1.0 +267 e_gamma[e_name] /= gamma_div[:w_max] +268 +269 if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny: # Prevent division by zero +270 self.e_tauint[e_name] = 0.5 +271 self.e_dtauint[e_name] = 0.0 +272 self.e_dvalue[e_name] = 0.0 +273 self.e_ddvalue[e_name] = 0.0 +274 self.e_windowsize[e_name] = 0 +275 continue +276 +277 self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0] +278 self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:]))) +279 # Make sure no entry of tauint is smaller than 0.5 +280 self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps +281 # hep-lat/0306017 eq. (42) +282 self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N) +283 self.e_n_dtauint[e_name][0] = 0.0 +284 +285 def _compute_drho(i): +286 tmp = (self.e_rho[e_name][i + 1:w_max] +287 + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1], +288 self.e_rho[e_name][1:max(1, w_max - 2 * i)]]) +289 - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i]) +290 self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N) +291 +292 if self.tau_exp[e_name] > 0: +293 _compute_drho(1) +294 texp = self.tau_exp[e_name] +295 # Critical slowing down analysis +296 if w_max // 2 <= 1: +297 raise ValueError("Need at least 8 samples for tau_exp error analysis") +298 for n in range(1, w_max // 2): +299 _compute_drho(n + 1) +300 if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2: +301 # Bias correction hep-lat/0306017 eq. (49) included +302 self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1]) # The absolute makes sure, that the tail contribution is always positive +303 self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2) +304 # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2 +305 self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N) +306 self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N) +307 self.e_windowsize[e_name] = n +308 break +309 else: +310 if self.S[e_name] == 0.0: +311 self.e_tauint[e_name] = 0.5 +312 self.e_dtauint[e_name] = 0.0 +313 self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1)) +314 self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N) +315 self.e_windowsize[e_name] = 0 +316 else: +317 # Standard automatic windowing procedure +318 tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1)) +319 g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N) +320 for n in range(1, w_max): +321 if g_w[n - 1] < 0 or n >= w_max - 1: +322 _compute_drho(n) +323 self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) # Bias correction hep-lat/0306017 eq. (49) +324 self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n] +325 self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N) +326 self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N) +327 self.e_windowsize[e_name] = n +328 break +329 +330 self._dvalue += self.e_dvalue[e_name] ** 2 +331 self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2 +332 +333 for e_name in self.cov_names: +334 self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq()) +335 self.e_ddvalue[e_name] = 0 +336 self._dvalue += self.e_dvalue[e_name]**2 +337 +338 self._dvalue = np.sqrt(self._dvalue) +339 if self._dvalue == 0.0: +340 self.ddvalue = 0.0 +341 else: +342 self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue +343 return 344 -345 def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize): -346 """Calculate Gamma_{AA} from the deltas, which are defined on idx. -347 idx is assumed to be a contiguous range (possibly with a stepsize != 1) -348 -349 Parameters -350 ---------- -351 deltas : list -352 List of fluctuations -353 idx : list -354 List or range of configurations on which the deltas are defined. -355 shape : int -356 Number of configurations in idx. -357 w_max : int -358 Upper bound for the summation window. -359 fft : bool -360 determines whether the fft algorithm is used for the computation -361 of the autocorrelation function. -362 gapsize : int -363 The target distance between two configurations. If longer distances -364 are found in idx, the data is expanded. -365 """ -366 gamma = np.zeros(w_max) -367 deltas = _expand_deltas(deltas, idx, shape, gapsize) -368 new_shape = len(deltas) -369 if fft: -370 max_gamma = min(new_shape, w_max) -371 # The padding for the fft has to be even -372 padding = new_shape + max_gamma + (new_shape + max_gamma) % 2 -373 gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma] -374 else: -375 for n in range(w_max): -376 if new_shape - n >= 0: -377 gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape]) -378 -379 return gamma +345 gm = gamma_method +346 +347 def _calc_gamma(self, deltas, idx, shape, w_max, fft, gapsize): +348 """Calculate Gamma_{AA} from the deltas, which are defined on idx. +349 idx is assumed to be a contiguous range (possibly with a stepsize != 1) +350 +351 Parameters +352 ---------- +353 deltas : list +354 List of fluctuations +355 idx : list +356 List or range of configurations on which the deltas are defined. +357 shape : int +358 Number of configurations in idx. +359 w_max : int +360 Upper bound for the summation window. +361 fft : bool +362 determines whether the fft algorithm is used for the computation +363 of the autocorrelation function. +364 gapsize : int +365 The target distance between two configurations. If longer distances +366 are found in idx, the data is expanded. +367 """ +368 gamma = np.zeros(w_max) +369 deltas = _expand_deltas(deltas, idx, shape, gapsize) +370 new_shape = len(deltas) +371 if fft: +372 max_gamma = min(new_shape, w_max) +373 # The padding for the fft has to be even +374 padding = new_shape + max_gamma + (new_shape + max_gamma) % 2 +375 gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma] +376 else: +377 for n in range(w_max): +378 if new_shape - n >= 0: +379 gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape]) 380 -381 def details(self, ens_content=True): -382 """Output detailed properties of the Obs. -383 -384 Parameters -385 ---------- -386 ens_content : bool -387 print details about the ensembles and replica if true. -388 """ -389 if self.tag is not None: -390 print("Description:", self.tag) -391 if not hasattr(self, 'e_dvalue'): -392 print('Result\t %3.8e' % (self.value)) -393 else: -394 if self.value == 0.0: -395 percentage = np.nan -396 else: -397 percentage = np.abs(self._dvalue / self.value) * 100 -398 print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage)) -399 if len(self.e_names) > 1: -400 print(' Ensemble errors:') -401 e_content = self.e_content -402 for e_name in self.mc_names: -403 gap = _determine_gap(self, e_content, e_name) -404 -405 if len(self.e_names) > 1: -406 print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name])) -407 tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name]) -408 tau_string += f" in units of {gap} config" -409 if gap > 1: -410 tau_string += "s" -411 if self.tau_exp[e_name] > 0: -412 tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name]) -413 else: -414 tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name]) -415 print(tau_string) -416 for e_name in self.cov_names: -417 print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name])) -418 if ens_content is True: -419 if len(self.e_names) == 1: -420 print(self.N, 'samples in', len(self.e_names), 'ensemble:') -421 else: -422 print(self.N, 'samples in', len(self.e_names), 'ensembles:') -423 my_string_list = [] -424 for key, value in sorted(self.e_content.items()): -425 if key not in self.covobs: -426 my_string = ' ' + "\u00B7 Ensemble '" + key + "' " -427 if len(value) == 1: -428 my_string += f': {self.shape[value[0]]} configurations' -429 if isinstance(self.idl[value[0]], range): -430 my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')' -431 else: -432 my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})' -433 else: -434 sublist = [] -435 for v in value: -436 my_substring = ' ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' " -437 my_substring += f': {self.shape[v]} configurations' -438 if isinstance(self.idl[v], range): -439 my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')' -440 else: -441 my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})' -442 sublist.append(my_substring) -443 -444 my_string += '\n' + '\n'.join(sublist) -445 else: -446 my_string = ' ' + "\u00B7 Covobs '" + key + "' " -447 my_string_list.append(my_string) -448 print('\n'.join(my_string_list)) -449 -450 def reweight(self, weight): -451 """Reweight the obs with given rewighting factors. -452 -453 Parameters -454 ---------- -455 weight : Obs -456 Reweighting factor. An Observable that has to be defined on a superset of the -457 configurations in obs[i].idl for all i. -458 all_configs : bool -459 if True, the reweighted observables are normalized by the average of -460 the reweighting factor on all configurations in weight.idl and not -461 on the configurations in obs[i].idl. Default False. -462 """ -463 return reweight(weight, [self])[0] -464 -465 def is_zero_within_error(self, sigma=1): -466 """Checks whether the observable is zero within 'sigma' standard errors. -467 -468 Parameters -469 ---------- -470 sigma : int -471 Number of standard errors used for the check. -472 -473 Works only properly when the gamma method was run. -474 """ -475 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue -476 -477 def is_zero(self, atol=1e-10): -478 """Checks whether the observable is zero within a given tolerance. -479 -480 Parameters -481 ---------- -482 atol : float -483 Absolute tolerance (for details see numpy documentation). -484 """ -485 return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values()) -486 -487 def plot_tauint(self, save=None): -488 """Plot integrated autocorrelation time for each ensemble. -489 -490 Parameters -491 ---------- -492 save : str -493 saves the figure to a file named 'save' if. -494 """ -495 if not hasattr(self, 'e_dvalue'): -496 raise Exception('Run the gamma method first.') -497 -498 for e, e_name in enumerate(self.mc_names): -499 fig = plt.figure() -500 plt.xlabel(r'$W$') -501 plt.ylabel(r'$\tau_\mathrm{int}$') -502 length = int(len(self.e_n_tauint[e_name])) -503 if self.tau_exp[e_name] > 0: -504 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] -505 x_help = np.arange(2 * self.tau_exp[e_name]) -506 y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base -507 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) -508 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') -509 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], -510 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) -511 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 -512 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) -513 else: -514 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) -515 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) -516 -517 plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label) -518 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') -519 plt.legend() -520 plt.xlim(-0.5, xmax) -521 ylim = plt.ylim() -522 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) -523 plt.draw() -524 if save: -525 fig.savefig(save + "_" + str(e)) -526 -527 def plot_rho(self, save=None): -528 """Plot normalized autocorrelation function time for each ensemble. -529 -530 Parameters -531 ---------- -532 save : str -533 saves the figure to a file named 'save' if. -534 """ -535 if not hasattr(self, 'e_dvalue'): -536 raise Exception('Run the gamma method first.') -537 for e, e_name in enumerate(self.mc_names): -538 fig = plt.figure() -539 plt.xlabel('W') -540 plt.ylabel('rho') -541 length = int(len(self.e_drho[e_name])) -542 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) -543 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') -544 if self.tau_exp[e_name] > 0: -545 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], -546 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) -547 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 -548 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) -549 else: -550 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) -551 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) -552 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) -553 plt.xlim(-0.5, xmax) -554 plt.draw() -555 if save: -556 fig.savefig(save + "_" + str(e)) -557 -558 def plot_rep_dist(self): -559 """Plot replica distribution for each ensemble with more than one replicum.""" -560 if not hasattr(self, 'e_dvalue'): -561 raise Exception('Run the gamma method first.') -562 for e, e_name in enumerate(self.mc_names): -563 if len(self.e_content[e_name]) == 1: -564 print('No replica distribution for a single replicum (', e_name, ')') -565 continue -566 r_length = [] -567 sub_r_mean = 0 -568 for r, r_name in enumerate(self.e_content[e_name]): -569 r_length.append(len(self.deltas[r_name])) -570 sub_r_mean += self.shape[r_name] * self.r_values[r_name] -571 e_N = np.sum(r_length) -572 sub_r_mean /= e_N -573 arr = np.zeros(len(self.e_content[e_name])) -574 for r, r_name in enumerate(self.e_content[e_name]): -575 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) -576 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) -577 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') -578 plt.draw() -579 -580 def plot_history(self, expand=True): -581 """Plot derived Monte Carlo history for each ensemble -582 -583 Parameters -584 ---------- -585 expand : bool -586 show expanded history for irregular Monte Carlo chains (default: True). -587 """ -588 for e, e_name in enumerate(self.mc_names): -589 plt.figure() -590 r_length = [] -591 tmp = [] -592 tmp_expanded = [] -593 for r, r_name in enumerate(self.e_content[e_name]): -594 tmp.append(self.deltas[r_name] + self.r_values[r_name]) -595 if expand: -596 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name], 1) + self.r_values[r_name]) -597 r_length.append(len(tmp_expanded[-1])) -598 else: -599 r_length.append(len(tmp[-1])) -600 e_N = np.sum(r_length) -601 x = np.arange(e_N) -602 y_test = np.concatenate(tmp, axis=0) -603 if expand: -604 y = np.concatenate(tmp_expanded, axis=0) -605 else: -606 y = y_test -607 plt.errorbar(x, y, fmt='.', markersize=3) -608 plt.xlim(-0.5, e_N - 0.5) -609 plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})') -610 plt.draw() -611 -612 def plot_piechart(self, save=None): -613 """Plot piechart which shows the fractional contribution of each -614 ensemble to the error and returns a dictionary containing the fractions. -615 -616 Parameters -617 ---------- -618 save : str -619 saves the figure to a file named 'save' if. -620 """ -621 if not hasattr(self, 'e_dvalue'): -622 raise Exception('Run the gamma method first.') -623 if np.isclose(0.0, self._dvalue, atol=1e-15): -624 raise ValueError('Error is 0.0') -625 labels = self.e_names -626 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 -627 fig1, ax1 = plt.subplots() -628 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) -629 ax1.axis('equal') -630 plt.draw() -631 if save: -632 fig1.savefig(save) -633 -634 return dict(zip(labels, sizes)) +381 return gamma +382 +383 def details(self, ens_content=True): +384 """Output detailed properties of the Obs. +385 +386 Parameters +387 ---------- +388 ens_content : bool +389 print details about the ensembles and replica if true. +390 """ +391 if self.tag is not None: +392 print("Description:", self.tag) +393 if not hasattr(self, 'e_dvalue'): +394 print('Result\t %3.8e' % (self.value)) +395 else: +396 if self.value == 0.0: +397 percentage = np.nan +398 else: +399 percentage = np.abs(self._dvalue / self.value) * 100 +400 print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage)) +401 if len(self.e_names) > 1: +402 print(' Ensemble errors:') +403 e_content = self.e_content +404 for e_name in self.mc_names: +405 gap = _determine_gap(self, e_content, e_name) +406 +407 if len(self.e_names) > 1: +408 print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name])) +409 tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name]) +410 tau_string += f" in units of {gap} config" +411 if gap > 1: +412 tau_string += "s" +413 if self.tau_exp[e_name] > 0: +414 tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name]) +415 else: +416 tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name]) +417 print(tau_string) +418 for e_name in self.cov_names: +419 print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name])) +420 if ens_content is True: +421 if len(self.e_names) == 1: +422 print(self.N, 'samples in', len(self.e_names), 'ensemble:') +423 else: +424 print(self.N, 'samples in', len(self.e_names), 'ensembles:') +425 my_string_list = [] +426 for key, value in sorted(self.e_content.items()): +427 if key not in self.covobs: +428 my_string = ' ' + "\u00B7 Ensemble '" + key + "' " +429 if len(value) == 1: +430 my_string += f': {self.shape[value[0]]} configurations' +431 if isinstance(self.idl[value[0]], range): +432 my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')' +433 else: +434 my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})' +435 else: +436 sublist = [] +437 for v in value: +438 my_substring = ' ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' " +439 my_substring += f': {self.shape[v]} configurations' +440 if isinstance(self.idl[v], range): +441 my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')' +442 else: +443 my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})' +444 sublist.append(my_substring) +445 +446 my_string += '\n' + '\n'.join(sublist) +447 else: +448 my_string = ' ' + "\u00B7 Covobs '" + key + "' " +449 my_string_list.append(my_string) +450 print('\n'.join(my_string_list)) +451 +452 def reweight(self, weight): +453 """Reweight the obs with given rewighting factors. +454 +455 Parameters +456 ---------- +457 weight : Obs +458 Reweighting factor. An Observable that has to be defined on a superset of the +459 configurations in obs[i].idl for all i. +460 all_configs : bool +461 if True, the reweighted observables are normalized by the average of +462 the reweighting factor on all configurations in weight.idl and not +463 on the configurations in obs[i].idl. Default False. +464 """ +465 return reweight(weight, [self])[0] +466 +467 def is_zero_within_error(self, sigma=1): +468 """Checks whether the observable is zero within 'sigma' standard errors. +469 +470 Parameters +471 ---------- +472 sigma : int +473 Number of standard errors used for the check. +474 +475 Works only properly when the gamma method was run. +476 """ +477 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue +478 +479 def is_zero(self, atol=1e-10): +480 """Checks whether the observable is zero within a given tolerance. +481 +482 Parameters +483 ---------- +484 atol : float +485 Absolute tolerance (for details see numpy documentation). +486 """ +487 return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values()) +488 +489 def plot_tauint(self, save=None): +490 """Plot integrated autocorrelation time for each ensemble. +491 +492 Parameters +493 ---------- +494 save : str +495 saves the figure to a file named 'save' if. +496 """ +497 if not hasattr(self, 'e_dvalue'): +498 raise Exception('Run the gamma method first.') +499 +500 for e, e_name in enumerate(self.mc_names): +501 fig = plt.figure() +502 plt.xlabel(r'$W$') +503 plt.ylabel(r'$\tau_\mathrm{int}$') +504 length = int(len(self.e_n_tauint[e_name])) +505 if self.tau_exp[e_name] > 0: +506 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] +507 x_help = np.arange(2 * self.tau_exp[e_name]) +508 y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base +509 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) +510 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') +511 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], +512 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) +513 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 +514 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) +515 else: +516 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) +517 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) +518 +519 plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label) +520 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') +521 plt.legend() +522 plt.xlim(-0.5, xmax) +523 ylim = plt.ylim() +524 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) +525 plt.draw() +526 if save: +527 fig.savefig(save + "_" + str(e)) +528 +529 def plot_rho(self, save=None): +530 """Plot normalized autocorrelation function time for each ensemble. +531 +532 Parameters +533 ---------- +534 save : str +535 saves the figure to a file named 'save' if. +536 """ +537 if not hasattr(self, 'e_dvalue'): +538 raise Exception('Run the gamma method first.') +539 for e, e_name in enumerate(self.mc_names): +540 fig = plt.figure() +541 plt.xlabel('W') +542 plt.ylabel('rho') +543 length = int(len(self.e_drho[e_name])) +544 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) +545 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') +546 if self.tau_exp[e_name] > 0: +547 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], +548 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) +549 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 +550 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) +551 else: +552 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) +553 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) +554 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) +555 plt.xlim(-0.5, xmax) +556 plt.draw() +557 if save: +558 fig.savefig(save + "_" + str(e)) +559 +560 def plot_rep_dist(self): +561 """Plot replica distribution for each ensemble with more than one replicum.""" +562 if not hasattr(self, 'e_dvalue'): +563 raise Exception('Run the gamma method first.') +564 for e, e_name in enumerate(self.mc_names): +565 if len(self.e_content[e_name]) == 1: +566 print('No replica distribution for a single replicum (', e_name, ')') +567 continue +568 r_length = [] +569 sub_r_mean = 0 +570 for r, r_name in enumerate(self.e_content[e_name]): +571 r_length.append(len(self.deltas[r_name])) +572 sub_r_mean += self.shape[r_name] * self.r_values[r_name] +573 e_N = np.sum(r_length) +574 sub_r_mean /= e_N +575 arr = np.zeros(len(self.e_content[e_name])) +576 for r, r_name in enumerate(self.e_content[e_name]): +577 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) +578 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) +579 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') +580 plt.draw() +581 +582 def plot_history(self, expand=True): +583 """Plot derived Monte Carlo history for each ensemble +584 +585 Parameters +586 ---------- +587 expand : bool +588 show expanded history for irregular Monte Carlo chains (default: True). +589 """ +590 for e, e_name in enumerate(self.mc_names): +591 plt.figure() +592 r_length = [] +593 tmp = [] +594 tmp_expanded = [] +595 for r, r_name in enumerate(self.e_content[e_name]): +596 tmp.append(self.deltas[r_name] + self.r_values[r_name]) +597 if expand: +598 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name], 1) + self.r_values[r_name]) +599 r_length.append(len(tmp_expanded[-1])) +600 else: +601 r_length.append(len(tmp[-1])) +602 e_N = np.sum(r_length) +603 x = np.arange(e_N) +604 y_test = np.concatenate(tmp, axis=0) +605 if expand: +606 y = np.concatenate(tmp_expanded, axis=0) +607 else: +608 y = y_test +609 plt.errorbar(x, y, fmt='.', markersize=3) +610 plt.xlim(-0.5, e_N - 0.5) +611 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})') +612 plt.draw() +613 +614 def plot_piechart(self, save=None): +615 """Plot piechart which shows the fractional contribution of each +616 ensemble to the error and returns a dictionary containing the fractions. +617 +618 Parameters +619 ---------- +620 save : str +621 saves the figure to a file named 'save' if. +622 """ +623 if not hasattr(self, 'e_dvalue'): +624 raise Exception('Run the gamma method first.') +625 if np.isclose(0.0, self._dvalue, atol=1e-15): +626 raise ValueError('Error is 0.0') +627 labels = self.e_names +628 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 +629 fig1, ax1 = plt.subplots() +630 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) +631 ax1.axis('equal') +632 plt.draw() +633 if save: +634 fig1.savefig(save) 635 -636 def dump(self, filename, datatype="json.gz", description="", **kwargs): -637 """Dump the Obs to a file 'name' of chosen format. -638 -639 Parameters -640 ---------- -641 filename : str -642 name of the file to be saved. -643 datatype : str -644 Format of the exported file. Supported formats include -645 "json.gz" and "pickle" -646 description : str -647 Description for output file, only relevant for json.gz format. -648 path : str -649 specifies a custom path for the file (default '.') -650 """ -651 if 'path' in kwargs: -652 file_name = kwargs.get('path') + '/' + filename -653 else: -654 file_name = filename -655 -656 if datatype == "json.gz": -657 from .input.json import dump_to_json -658 dump_to_json([self], file_name, description=description) -659 elif datatype == "pickle": -660 with open(file_name + '.p', 'wb') as fb: -661 pickle.dump(self, fb) -662 else: -663 raise TypeError("Unknown datatype " + str(datatype)) -664 -665 def export_jackknife(self): -666 """Export jackknife samples from the Obs -667 -668 Returns -669 ------- -670 numpy.ndarray -671 Returns a numpy array of length N + 1 where N is the number of samples -672 for the given ensemble and replicum. The zeroth entry of the array contains -673 the mean value of the Obs, entries 1 to N contain the N jackknife samples -674 derived from the Obs. The current implementation only works for observables -675 defined on exactly one ensemble and replicum. The derived jackknife samples -676 should agree with samples from a full jackknife analysis up to O(1/N). -677 """ -678 -679 if len(self.names) != 1: -680 raise ValueError("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") -681 -682 name = self.names[0] -683 full_data = self.deltas[name] + self.r_values[name] -684 n = full_data.size -685 mean = self.value -686 tmp_jacks = np.zeros(n + 1) -687 tmp_jacks[0] = mean -688 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) -689 return tmp_jacks -690 -691 def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None): -692 """Export bootstrap samples from the Obs -693 -694 Parameters -695 ---------- -696 samples : int -697 Number of bootstrap samples to generate. -698 random_numbers : np.ndarray -699 Array of shape (samples, length) containing the random numbers to generate the bootstrap samples. -700 If not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name. -701 save_rng : str -702 Save the random numbers to a file if a path is specified. -703 -704 Returns -705 ------- -706 numpy.ndarray -707 Returns a numpy array of length N + 1 where N is the number of samples -708 for the given ensemble and replicum. The zeroth entry of the array contains -709 the mean value of the Obs, entries 1 to N contain the N import_bootstrap samples -710 derived from the Obs. The current implementation only works for observables -711 defined on exactly one ensemble and replicum. The derived bootstrap samples -712 should agree with samples from a full bootstrap analysis up to O(1/N). -713 """ -714 if len(self.names) != 1: -715 raise ValueError("'export_boostrap' is only implemented for Obs defined on one ensemble and replicum.") -716 -717 name = self.names[0] -718 length = self.N -719 -720 if random_numbers is None: -721 seed = int(hashlib.md5(name.encode()).hexdigest(), 16) & 0xFFFFFFFF -722 rng = np.random.default_rng(seed) -723 random_numbers = rng.integers(0, length, size=(samples, length)) -724 -725 if save_rng is not None: -726 np.savetxt(save_rng, random_numbers, fmt='%i') -727 -728 proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length -729 ret = np.zeros(samples + 1) -730 ret[0] = self.value -731 ret[1:] = proj @ (self.deltas[name] + self.r_values[name]) -732 return ret -733 -734 def __float__(self): -735 return float(self.value) -736 -737 def __repr__(self): -738 return 'Obs[' + str(self) + ']' -739 -740 def __str__(self): -741 return _format_uncertainty(self.value, self._dvalue) -742 -743 def __format__(self, format_type): -744 if format_type == "": -745 significance = 2 -746 else: -747 significance = int(float(format_type.replace("+", "").replace("-", ""))) -748 my_str = _format_uncertainty(self.value, self._dvalue, -749 significance=significance) -750 for char in ["+", " "]: -751 if format_type.startswith(char): -752 if my_str[0] != "-": -753 my_str = char + my_str -754 return my_str -755 -756 def __hash__(self): -757 hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),) -758 hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()]) -759 hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()]) -760 hash_tuple += tuple([o.encode() for o in self.names]) -761 m = hashlib.md5() -762 [m.update(o) for o in hash_tuple] -763 return int(m.hexdigest(), 16) & 0xFFFFFFFF -764 -765 # Overload comparisons -766 def __lt__(self, other): -767 return self.value < other -768 -769 def __le__(self, other): -770 return self.value <= other -771 -772 def __gt__(self, other): -773 return self.value > other -774 -775 def __ge__(self, other): -776 return self.value >= other -777 -778 def __eq__(self, other): -779 if other is None: -780 return False -781 return (self - other).is_zero() -782 -783 # Overload math operations -784 def __add__(self, y): -785 if isinstance(y, Obs): -786 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) -787 else: -788 if isinstance(y, np.ndarray): -789 return np.array([self + o for o in y]) -790 elif isinstance(y, complex): -791 return CObs(self, 0) + y -792 elif y.__class__.__name__ in ['Corr', 'CObs']: -793 return NotImplemented -794 else: -795 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) -796 -797 def __radd__(self, y): -798 return self + y -799 -800 def __mul__(self, y): -801 if isinstance(y, Obs): -802 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) -803 else: -804 if isinstance(y, np.ndarray): -805 return np.array([self * o for o in y]) -806 elif isinstance(y, complex): -807 return CObs(self * y.real, self * y.imag) -808 elif y.__class__.__name__ in ['Corr', 'CObs']: -809 return NotImplemented -810 else: -811 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) -812 -813 def __rmul__(self, y): -814 return self * y -815 -816 def __sub__(self, y): -817 if isinstance(y, Obs): -818 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) -819 else: -820 if isinstance(y, np.ndarray): -821 return np.array([self - o for o in y]) -822 elif y.__class__.__name__ in ['Corr', 'CObs']: -823 return NotImplemented -824 else: -825 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) -826 -827 def __rsub__(self, y): -828 return -1 * (self - y) -829 -830 def __pos__(self): -831 return self -832 -833 def __neg__(self): -834 return -1 * self -835 -836 def __truediv__(self, y): -837 if isinstance(y, Obs): -838 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) -839 else: -840 if isinstance(y, np.ndarray): -841 return np.array([self / o for o in y]) -842 elif y.__class__.__name__ in ['Corr', 'CObs']: -843 return NotImplemented -844 else: -845 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) -846 -847 def __rtruediv__(self, y): -848 if isinstance(y, Obs): -849 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) -850 else: -851 if isinstance(y, np.ndarray): -852 return np.array([o / self for o in y]) -853 elif y.__class__.__name__ in ['Corr', 'CObs']: -854 return NotImplemented -855 else: -856 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) -857 -858 def __pow__(self, y): -859 if isinstance(y, Obs): -860 return derived_observable(lambda x, **kwargs: x[0] ** x[1], [self, y], man_grad=[y.value * self.value ** (y.value - 1), self.value ** y.value * np.log(self.value)]) -861 else: -862 return derived_observable(lambda x, **kwargs: x[0] ** y, [self], man_grad=[y * self.value ** (y - 1)]) -863 -864 def __rpow__(self, y): -865 return derived_observable(lambda x, **kwargs: y ** x[0], [self], man_grad=[y ** self.value * np.log(y)]) -866 -867 def __abs__(self): -868 return derived_observable(lambda x: anp.abs(x[0]), [self]) -869 -870 # Overload numpy functions -871 def sqrt(self): -872 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) -873 -874 def log(self): -875 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) -876 -877 def exp(self): -878 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) -879 -880 def sin(self): -881 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) -882 -883 def cos(self): -884 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) -885 -886 def tan(self): -887 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) -888 -889 def arcsin(self): -890 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) -891 -892 def arccos(self): -893 return derived_observable(lambda x: anp.arccos(x[0]), [self]) -894 -895 def arctan(self): -896 return derived_observable(lambda x: anp.arctan(x[0]), [self]) -897 -898 def sinh(self): -899 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) -900 -901 def cosh(self): -902 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) -903 -904 def tanh(self): -905 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) -906 -907 def arcsinh(self): -908 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) -909 -910 def arccosh(self): -911 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) -912 -913 def arctanh(self): -914 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) +636 return dict(zip(labels, sizes)) +637 +638 def dump(self, filename, datatype="json.gz", description="", **kwargs): +639 """Dump the Obs to a file 'name' of chosen format. +640 +641 Parameters +642 ---------- +643 filename : str +644 name of the file to be saved. +645 datatype : str +646 Format of the exported file. Supported formats include +647 "json.gz" and "pickle" +648 description : str +649 Description for output file, only relevant for json.gz format. +650 path : str +651 specifies a custom path for the file (default '.') +652 """ +653 if 'path' in kwargs: +654 file_name = kwargs.get('path') + '/' + filename +655 else: +656 file_name = filename +657 +658 if datatype == "json.gz": +659 from .input.json import dump_to_json +660 dump_to_json([self], file_name, description=description) +661 elif datatype == "pickle": +662 with open(file_name + '.p', 'wb') as fb: +663 pickle.dump(self, fb) +664 else: +665 raise TypeError("Unknown datatype " + str(datatype)) +666 +667 def export_jackknife(self): +668 """Export jackknife samples from the Obs +669 +670 Returns +671 ------- +672 numpy.ndarray +673 Returns a numpy array of length N + 1 where N is the number of samples +674 for the given ensemble and replicum. The zeroth entry of the array contains +675 the mean value of the Obs, entries 1 to N contain the N jackknife samples +676 derived from the Obs. The current implementation only works for observables +677 defined on exactly one ensemble and replicum. The derived jackknife samples +678 should agree with samples from a full jackknife analysis up to O(1/N). +679 """ +680 +681 if len(self.names) != 1: +682 raise ValueError("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") +683 +684 name = self.names[0] +685 full_data = self.deltas[name] + self.r_values[name] +686 n = full_data.size +687 mean = self.value +688 tmp_jacks = np.zeros(n + 1) +689 tmp_jacks[0] = mean +690 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) +691 return tmp_jacks +692 +693 def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None): +694 """Export bootstrap samples from the Obs +695 +696 Parameters +697 ---------- +698 samples : int +699 Number of bootstrap samples to generate. +700 random_numbers : np.ndarray +701 Array of shape (samples, length) containing the random numbers to generate the bootstrap samples. +702 If not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name. +703 save_rng : str +704 Save the random numbers to a file if a path is specified. +705 +706 Returns +707 ------- +708 numpy.ndarray +709 Returns a numpy array of length N + 1 where N is the number of samples +710 for the given ensemble and replicum. The zeroth entry of the array contains +711 the mean value of the Obs, entries 1 to N contain the N import_bootstrap samples +712 derived from the Obs. The current implementation only works for observables +713 defined on exactly one ensemble and replicum. The derived bootstrap samples +714 should agree with samples from a full bootstrap analysis up to O(1/N). +715 """ +716 if len(self.names) != 1: +717 raise ValueError("'export_boostrap' is only implemented for Obs defined on one ensemble and replicum.") +718 +719 name = self.names[0] +720 length = self.N +721 +722 if random_numbers is None: +723 seed = int(hashlib.md5(name.encode()).hexdigest(), 16) & 0xFFFFFFFF +724 rng = np.random.default_rng(seed) +725 random_numbers = rng.integers(0, length, size=(samples, length)) +726 +727 if save_rng is not None: +728 np.savetxt(save_rng, random_numbers, fmt='%i') +729 +730 proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length +731 ret = np.zeros(samples + 1) +732 ret[0] = self.value +733 ret[1:] = proj @ (self.deltas[name] + self.r_values[name]) +734 return ret +735 +736 def __float__(self): +737 return float(self.value) +738 +739 def __repr__(self): +740 return 'Obs[' + str(self) + ']' +741 +742 def __str__(self): +743 return _format_uncertainty(self.value, self._dvalue) +744 +745 def __format__(self, format_type): +746 if format_type == "": +747 significance = 2 +748 else: +749 significance = int(float(format_type.replace("+", "").replace("-", ""))) +750 my_str = _format_uncertainty(self.value, self._dvalue, +751 significance=significance) +752 for char in ["+", " "]: +753 if format_type.startswith(char): +754 if my_str[0] != "-": +755 my_str = char + my_str +756 return my_str +757 +758 def __hash__(self): +759 hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),) +760 hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()]) +761 hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()]) +762 hash_tuple += tuple([o.encode() for o in self.names]) +763 m = hashlib.md5() +764 [m.update(o) for o in hash_tuple] +765 return int(m.hexdigest(), 16) & 0xFFFFFFFF +766 +767 # Overload comparisons +768 def __lt__(self, other): +769 return self.value < other +770 +771 def __le__(self, other): +772 return self.value <= other +773 +774 def __gt__(self, other): +775 return self.value > other +776 +777 def __ge__(self, other): +778 return self.value >= other +779 +780 def __eq__(self, other): +781 if other is None: +782 return False +783 return (self - other).is_zero() +784 +785 # Overload math operations +786 def __add__(self, y): +787 if isinstance(y, Obs): +788 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) +789 else: +790 if isinstance(y, np.ndarray): +791 return np.array([self + o for o in y]) +792 elif isinstance(y, complex): +793 return CObs(self, 0) + y +794 elif y.__class__.__name__ in ['Corr', 'CObs']: +795 return NotImplemented +796 else: +797 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) +798 +799 def __radd__(self, y): +800 return self + y +801 +802 def __mul__(self, y): +803 if isinstance(y, Obs): +804 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) +805 else: +806 if isinstance(y, np.ndarray): +807 return np.array([self * o for o in y]) +808 elif isinstance(y, complex): +809 return CObs(self * y.real, self * y.imag) +810 elif y.__class__.__name__ in ['Corr', 'CObs']: +811 return NotImplemented +812 else: +813 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) +814 +815 def __rmul__(self, y): +816 return self * y +817 +818 def __sub__(self, y): +819 if isinstance(y, Obs): +820 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) +821 else: +822 if isinstance(y, np.ndarray): +823 return np.array([self - o for o in y]) +824 elif y.__class__.__name__ in ['Corr', 'CObs']: +825 return NotImplemented +826 else: +827 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) +828 +829 def __rsub__(self, y): +830 return -1 * (self - y) +831 +832 def __pos__(self): +833 return self +834 +835 def __neg__(self): +836 return -1 * self +837 +838 def __truediv__(self, y): +839 if isinstance(y, Obs): +840 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) +841 else: +842 if isinstance(y, np.ndarray): +843 return np.array([self / o for o in y]) +844 elif y.__class__.__name__ in ['Corr', 'CObs']: +845 return NotImplemented +846 else: +847 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) +848 +849 def __rtruediv__(self, y): +850 if isinstance(y, Obs): +851 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) +852 else: +853 if isinstance(y, np.ndarray): +854 return np.array([o / self for o in y]) +855 elif y.__class__.__name__ in ['Corr', 'CObs']: +856 return NotImplemented +857 else: +858 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) +859 +860 def __pow__(self, y): +861 if isinstance(y, Obs): +862 return derived_observable(lambda x, **kwargs: x[0] ** x[1], [self, y], man_grad=[y.value * self.value ** (y.value - 1), self.value ** y.value * np.log(self.value)]) +863 else: +864 return derived_observable(lambda x, **kwargs: x[0] ** y, [self], man_grad=[y * self.value ** (y - 1)]) +865 +866 def __rpow__(self, y): +867 return derived_observable(lambda x, **kwargs: y ** x[0], [self], man_grad=[y ** self.value * np.log(y)]) +868 +869 def __abs__(self): +870 return derived_observable(lambda x: anp.abs(x[0]), [self]) +871 +872 # Overload numpy functions +873 def sqrt(self): +874 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) +875 +876 def log(self): +877 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) +878 +879 def exp(self): +880 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) +881 +882 def sin(self): +883 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) +884 +885 def cos(self): +886 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) +887 +888 def tan(self): +889 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) +890 +891 def arcsin(self): +892 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) +893 +894 def arccos(self): +895 return derived_observable(lambda x: anp.arccos(x[0]), [self]) +896 +897 def arctan(self): +898 return derived_observable(lambda x: anp.arctan(x[0]), [self]) +899 +900 def sinh(self): +901 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) +902 +903 def cosh(self): +904 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) +905 +906 def tanh(self): +907 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) +908 +909 def arcsinh(self): +910 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) +911 +912 def arccosh(self): +913 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) +914 +915 def arctanh(self): +916 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) @@ -3172,63 +3185,65 @@ this overwrites the standard value for that ensemble. 83 raise ValueError('Names are not unique.') 84 if not all(isinstance(x, str) for x in names): 85 raise TypeError('All names have to be strings.') - 86 else: - 87 if not isinstance(names[0], str): - 88 raise TypeError('All names have to be strings.') - 89 if min(len(x) for x in samples) <= 4: - 90 raise ValueError('Samples have to have at least 5 entries.') - 91 - 92 self.names = sorted(names) - 93 self.shape = {} - 94 self.r_values = {} - 95 self.deltas = {} - 96 self._covobs = {} - 97 - 98 self._value = 0 - 99 self.N = 0 -100 self.idl = {} -101 if idl is not None: -102 for name, idx in sorted(zip(names, idl)): -103 if isinstance(idx, range): -104 self.idl[name] = idx -105 elif isinstance(idx, (list, np.ndarray)): -106 dc = np.unique(np.diff(idx)) -107 if np.any(dc < 0): -108 raise ValueError("Unsorted idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) < 0)[0]]))) -109 elif np.any(dc == 0): -110 raise ValueError("Duplicate entries in idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) == 0)[0]]))) -111 if len(dc) == 1: -112 self.idl[name] = range(idx[0], idx[-1] + dc[0], dc[0]) -113 else: -114 self.idl[name] = list(idx) -115 else: -116 raise TypeError('incompatible type for idl[%s].' % (name)) -117 else: -118 for name, sample in sorted(zip(names, samples)): -119 self.idl[name] = range(1, len(sample) + 1) -120 -121 if kwargs.get("means") is not None: -122 for name, sample, mean in sorted(zip(names, samples, kwargs.get("means"))): -123 self.shape[name] = len(self.idl[name]) -124 self.N += self.shape[name] -125 self.r_values[name] = mean -126 self.deltas[name] = sample -127 else: -128 for name, sample in sorted(zip(names, samples)): -129 self.shape[name] = len(self.idl[name]) -130 self.N += self.shape[name] -131 if len(sample) != self.shape[name]: -132 raise ValueError('Incompatible samples and idx for %s: %d vs. %d' % (name, len(sample), self.shape[name])) -133 self.r_values[name] = np.mean(sample) -134 self.deltas[name] = sample - self.r_values[name] -135 self._value += self.shape[name] * self.r_values[name] -136 self._value /= self.N -137 -138 self._dvalue = 0.0 -139 self.ddvalue = 0.0 -140 self.reweighted = False -141 -142 self.tag = None + 86 if len(set([o.split('|')[0] for o in names])) > 1: + 87 raise ValueError('Cannot initialize Obs based on multiple ensembles. Please average separate Obs from each ensemble.') + 88 else: + 89 if not isinstance(names[0], str): + 90 raise TypeError('All names have to be strings.') + 91 if min(len(x) for x in samples) <= 4: + 92 raise ValueError('Samples have to have at least 5 entries.') + 93 + 94 self.names = sorted(names) + 95 self.shape = {} + 96 self.r_values = {} + 97 self.deltas = {} + 98 self._covobs = {} + 99 +100 self._value = 0 +101 self.N = 0 +102 self.idl = {} +103 if idl is not None: +104 for name, idx in sorted(zip(names, idl)): +105 if isinstance(idx, range): +106 self.idl[name] = idx +107 elif isinstance(idx, (list, np.ndarray)): +108 dc = np.unique(np.diff(idx)) +109 if np.any(dc < 0): +110 raise ValueError("Unsorted idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) < 0)[0]]))) +111 elif np.any(dc == 0): +112 raise ValueError("Duplicate entries in idx for idl[%s] at position %s" % (name, ' '.join(['%s' % (pos + 1) for pos in np.where(np.diff(idx) == 0)[0]]))) +113 if len(dc) == 1: +114 self.idl[name] = range(idx[0], idx[-1] + dc[0], dc[0]) +115 else: +116 self.idl[name] = list(idx) +117 else: +118 raise TypeError('incompatible type for idl[%s].' % (name)) +119 else: +120 for name, sample in sorted(zip(names, samples)): +121 self.idl[name] = range(1, len(sample) + 1) +122 +123 if kwargs.get("means") is not None: +124 for name, sample, mean in sorted(zip(names, samples, kwargs.get("means"))): +125 self.shape[name] = len(self.idl[name]) +126 self.N += self.shape[name] +127 self.r_values[name] = mean +128 self.deltas[name] = sample +129 else: +130 for name, sample in sorted(zip(names, samples)): +131 self.shape[name] = len(self.idl[name]) +132 self.N += self.shape[name] +133 if len(sample) != self.shape[name]: +134 raise ValueError('Incompatible samples and idx for %s: %d vs. %d' % (name, len(sample), self.shape[name])) +135 self.r_values[name] = np.mean(sample) +136 self.deltas[name] = sample - self.r_values[name] +137 self._value += self.shape[name] * self.r_values[name] +138 self._value /= self.N +139 +140 self._dvalue = 0.0 +141 self.ddvalue = 0.0 +142 self.reweighted = False +143 +144 self.tag = None @@ -3428,9 +3443,9 @@ list of ranges or lists on which the samples are defined - 
144    @property
-145    def value(self):
-146        return self._value
+            
146    @property
+147    def value(self):
+148        return self._value
 

 
 
@@ -3446,9 +3461,9 @@ list of ranges or lists on which the samples are defined
- 
148    @property
-149    def dvalue(self):
-150        return self._dvalue
+            
150    @property
+151    def dvalue(self):
+152        return self._dvalue
 

 
 
@@ -3464,9 +3479,9 @@ list of ranges or lists on which the samples are defined
- 
152    @property
-153    def e_names(self):
-154        return sorted(set([o.split('|')[0] for o in self.names]))
+            
154    @property
+155    def e_names(self):
+156        return sorted(set([o.split('|')[0] for o in self.names]))
 

 
 
@@ -3482,9 +3497,9 @@ list of ranges or lists on which the samples are defined
- 
156    @property
-157    def cov_names(self):
-158        return sorted(set([o for o in self.covobs.keys()]))
+            
158    @property
+159    def cov_names(self):
+160        return sorted(set([o for o in self.covobs.keys()]))
 

 
 
@@ -3500,9 +3515,9 @@ list of ranges or lists on which the samples are defined
- 
160    @property
-161    def mc_names(self):
-162        return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names]))
+            
162    @property
+163    def mc_names(self):
+164        return sorted(set([o.split('|')[0] for o in self.names if o not in self.cov_names]))
 

 
 
@@ -3518,14 +3533,14 @@ list of ranges or lists on which the samples are defined
- 
164    @property
-165    def e_content(self):
-166        res = {}
-167        for e, e_name in enumerate(self.e_names):
-168            res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names))
-169            if e_name in self.names:
-170                res[e_name].append(e_name)
-171        return res
+            
166    @property
+167    def e_content(self):
+168        res = {}
+169        for e, e_name in enumerate(self.e_names):
+170            res[e_name] = sorted(filter(lambda x: x.startswith(e_name + '|'), self.names))
+171            if e_name in self.names:
+172                res[e_name].append(e_name)
+173        return res
 

 
 
@@ -3541,9 +3556,9 @@ list of ranges or lists on which the samples are defined
- 
173    @property
-174    def covobs(self):
-175        return self._covobs
+            
175    @property
+176    def covobs(self):
+177        return self._covobs
 

 
 
@@ -3561,171 +3576,171 @@ list of ranges or lists on which the samples are defined
- 
177    def gamma_method(self, **kwargs):
-178        """Estimate the error and related properties of the Obs.
-179
-180        Parameters
-181        ----------
-182        S : float
-183            specifies a custom value for the parameter S (default 2.0).
-184            If set to 0 it is assumed that the data exhibits no
-185            autocorrelation. In this case the error estimates coincides
-186            with the sample standard error.
-187        tau_exp : float
-188            positive value triggers the critical slowing down analysis
-189            (default 0.0).
-190        N_sigma : float
-191            number of standard deviations from zero until the tail is
-192            attached to the autocorrelation function (default 1).
-193        fft : bool
-194            determines whether the fft algorithm is used for the computation
-195            of the autocorrelation function (default True)
-196        """
-197
-198        e_content = self.e_content
-199        self.e_dvalue = {}
-200        self.e_ddvalue = {}
-201        self.e_tauint = {}
-202        self.e_dtauint = {}
-203        self.e_windowsize = {}
-204        self.e_n_tauint = {}
-205        self.e_n_dtauint = {}
-206        e_gamma = {}
-207        self.e_rho = {}
-208        self.e_drho = {}
-209        self._dvalue = 0
-210        self.ddvalue = 0
-211
-212        self.S = {}
-213        self.tau_exp = {}
-214        self.N_sigma = {}
-215
-216        if kwargs.get('fft') is False:
-217            fft = False
-218        else:
-219            fft = True
-220
-221        def _parse_kwarg(kwarg_name):
-222            if kwarg_name in kwargs:
-223                tmp = kwargs.get(kwarg_name)
-224                if isinstance(tmp, (int, float)):
-225                    if tmp < 0:
-226                        raise ValueError(kwarg_name + ' has to be larger or equal to 0.')
-227                    for e, e_name in enumerate(self.e_names):
-228                        getattr(self, kwarg_name)[e_name] = tmp
-229                else:
-230                    raise TypeError(kwarg_name + ' is not in proper format.')
-231            else:
-232                for e, e_name in enumerate(self.e_names):
-233                    if e_name in getattr(Obs, kwarg_name + '_dict'):
-234                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name]
-235                    else:
-236                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global')
-237
-238        _parse_kwarg('S')
-239        _parse_kwarg('tau_exp')
-240        _parse_kwarg('N_sigma')
-241
-242        for e, e_name in enumerate(self.mc_names):
-243            gapsize = _determine_gap(self, e_content, e_name)
-244
-245            r_length = []
-246            for r_name in e_content[e_name]:
-247                if isinstance(self.idl[r_name], range):
-248                    r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize)
-249                else:
-250                    r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize)
-251
-252            e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]])
-253            w_max = max(r_length) // 2
-254            e_gamma[e_name] = np.zeros(w_max)
-255            self.e_rho[e_name] = np.zeros(w_max)
-256            self.e_drho[e_name] = np.zeros(w_max)
-257
-258            for r_name in e_content[e_name]:
-259                e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
-260
-261            gamma_div = np.zeros(w_max)
-262            for r_name in e_content[e_name]:
-263                gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
-264            gamma_div[gamma_div < 1] = 1.0
-265            e_gamma[e_name] /= gamma_div[:w_max]
-266
-267            if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny:  # Prevent division by zero
-268                self.e_tauint[e_name] = 0.5
-269                self.e_dtauint[e_name] = 0.0
-270                self.e_dvalue[e_name] = 0.0
-271                self.e_ddvalue[e_name] = 0.0
-272                self.e_windowsize[e_name] = 0
-273                continue
-274
-275            self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
-276            self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:])))
-277            # Make sure no entry of tauint is smaller than 0.5
-278            self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps
-279            # hep-lat/0306017 eq. (42)
-280            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
-281            self.e_n_dtauint[e_name][0] = 0.0
-282
-283            def _compute_drho(i):
-284                tmp = (self.e_rho[e_name][i + 1:w_max]
-285                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
-286                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
-287                       - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i])
-288                self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N)
-289
-290            if self.tau_exp[e_name] > 0:
-291                _compute_drho(1)
-292                texp = self.tau_exp[e_name]
-293                # Critical slowing down analysis
-294                if w_max // 2 <= 1:
-295                    raise ValueError("Need at least 8 samples for tau_exp error analysis")
-296                for n in range(1, w_max // 2):
-297                    _compute_drho(n + 1)
-298                    if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2:
-299                        # Bias correction hep-lat/0306017 eq. (49) included
-300                        self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1])  # The absolute makes sure, that the tail contribution is always positive
-301                        self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2)
-302                        # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2
-303                        self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
-304                        self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
-305                        self.e_windowsize[e_name] = n
-306                        break
-307            else:
-308                if self.S[e_name] == 0.0:
-309                    self.e_tauint[e_name] = 0.5
-310                    self.e_dtauint[e_name] = 0.0
-311                    self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1))
-312                    self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N)
-313                    self.e_windowsize[e_name] = 0
-314                else:
-315                    # Standard automatic windowing procedure
-316                    tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1))
-317                    g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N)
-318                    for n in range(1, w_max):
-319                        if g_w[n - 1] < 0 or n >= w_max - 1:
-320                            _compute_drho(n)
-321                            self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N)  # Bias correction hep-lat/0306017 eq. (49)
-322                            self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n]
-323                            self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
-324                            self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
-325                            self.e_windowsize[e_name] = n
-326                            break
-327
-328            self._dvalue += self.e_dvalue[e_name] ** 2
-329            self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2
-330
-331        for e_name in self.cov_names:
-332            self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq())
-333            self.e_ddvalue[e_name] = 0
-334            self._dvalue += self.e_dvalue[e_name]**2
-335
-336        self._dvalue = np.sqrt(self._dvalue)
-337        if self._dvalue == 0.0:
-338            self.ddvalue = 0.0
-339        else:
-340            self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue
-341        return
+            
179    def gamma_method(self, **kwargs):
+180        """Estimate the error and related properties of the Obs.
+181
+182        Parameters
+183        ----------
+184        S : float
+185            specifies a custom value for the parameter S (default 2.0).
+186            If set to 0 it is assumed that the data exhibits no
+187            autocorrelation. In this case the error estimates coincides
+188            with the sample standard error.
+189        tau_exp : float
+190            positive value triggers the critical slowing down analysis
+191            (default 0.0).
+192        N_sigma : float
+193            number of standard deviations from zero until the tail is
+194            attached to the autocorrelation function (default 1).
+195        fft : bool
+196            determines whether the fft algorithm is used for the computation
+197            of the autocorrelation function (default True)
+198        """
+199
+200        e_content = self.e_content
+201        self.e_dvalue = {}
+202        self.e_ddvalue = {}
+203        self.e_tauint = {}
+204        self.e_dtauint = {}
+205        self.e_windowsize = {}
+206        self.e_n_tauint = {}
+207        self.e_n_dtauint = {}
+208        e_gamma = {}
+209        self.e_rho = {}
+210        self.e_drho = {}
+211        self._dvalue = 0
+212        self.ddvalue = 0
+213
+214        self.S = {}
+215        self.tau_exp = {}
+216        self.N_sigma = {}
+217
+218        if kwargs.get('fft') is False:
+219            fft = False
+220        else:
+221            fft = True
+222
+223        def _parse_kwarg(kwarg_name):
+224            if kwarg_name in kwargs:
+225                tmp = kwargs.get(kwarg_name)
+226                if isinstance(tmp, (int, float)):
+227                    if tmp < 0:
+228                        raise ValueError(kwarg_name + ' has to be larger or equal to 0.')
+229                    for e, e_name in enumerate(self.e_names):
+230                        getattr(self, kwarg_name)[e_name] = tmp
+231                else:
+232                    raise TypeError(kwarg_name + ' is not in proper format.')
+233            else:
+234                for e, e_name in enumerate(self.e_names):
+235                    if e_name in getattr(Obs, kwarg_name + '_dict'):
+236                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name]
+237                    else:
+238                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global')
+239
+240        _parse_kwarg('S')
+241        _parse_kwarg('tau_exp')
+242        _parse_kwarg('N_sigma')
+243
+244        for e, e_name in enumerate(self.mc_names):
+245            gapsize = _determine_gap(self, e_content, e_name)
+246
+247            r_length = []
+248            for r_name in e_content[e_name]:
+249                if isinstance(self.idl[r_name], range):
+250                    r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize)
+251                else:
+252                    r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize)
+253
+254            e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]])
+255            w_max = max(r_length) // 2
+256            e_gamma[e_name] = np.zeros(w_max)
+257            self.e_rho[e_name] = np.zeros(w_max)
+258            self.e_drho[e_name] = np.zeros(w_max)
+259
+260            for r_name in e_content[e_name]:
+261                e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
+262
+263            gamma_div = np.zeros(w_max)
+264            for r_name in e_content[e_name]:
+265                gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
+266            gamma_div[gamma_div < 1] = 1.0
+267            e_gamma[e_name] /= gamma_div[:w_max]
+268
+269            if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny:  # Prevent division by zero
+270                self.e_tauint[e_name] = 0.5
+271                self.e_dtauint[e_name] = 0.0
+272                self.e_dvalue[e_name] = 0.0
+273                self.e_ddvalue[e_name] = 0.0
+274                self.e_windowsize[e_name] = 0
+275                continue
+276
+277            self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
+278            self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:])))
+279            # Make sure no entry of tauint is smaller than 0.5
+280            self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps
+281            # hep-lat/0306017 eq. (42)
+282            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
+283            self.e_n_dtauint[e_name][0] = 0.0
+284
+285            def _compute_drho(i):
+286                tmp = (self.e_rho[e_name][i + 1:w_max]
+287                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
+288                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
+289                       - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i])
+290                self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N)
+291
+292            if self.tau_exp[e_name] > 0:
+293                _compute_drho(1)
+294                texp = self.tau_exp[e_name]
+295                # Critical slowing down analysis
+296                if w_max // 2 <= 1:
+297                    raise ValueError("Need at least 8 samples for tau_exp error analysis")
+298                for n in range(1, w_max // 2):
+299                    _compute_drho(n + 1)
+300                    if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2:
+301                        # Bias correction hep-lat/0306017 eq. (49) included
+302                        self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1])  # The absolute makes sure, that the tail contribution is always positive
+303                        self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2)
+304                        # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2
+305                        self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+306                        self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
+307                        self.e_windowsize[e_name] = n
+308                        break
+309            else:
+310                if self.S[e_name] == 0.0:
+311                    self.e_tauint[e_name] = 0.5
+312                    self.e_dtauint[e_name] = 0.0
+313                    self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1))
+314                    self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N)
+315                    self.e_windowsize[e_name] = 0
+316                else:
+317                    # Standard automatic windowing procedure
+318                    tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1))
+319                    g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N)
+320                    for n in range(1, w_max):
+321                        if g_w[n - 1] < 0 or n >= w_max - 1:
+322                            _compute_drho(n)
+323                            self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N)  # Bias correction hep-lat/0306017 eq. (49)
+324                            self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n]
+325                            self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+326                            self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
+327                            self.e_windowsize[e_name] = n
+328                            break
+329
+330            self._dvalue += self.e_dvalue[e_name] ** 2
+331            self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2
+332
+333        for e_name in self.cov_names:
+334            self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq())
+335            self.e_ddvalue[e_name] = 0
+336            self._dvalue += self.e_dvalue[e_name]**2
+337
+338        self._dvalue = np.sqrt(self._dvalue)
+339        if self._dvalue == 0.0:
+340            self.ddvalue = 0.0
+341        else:
+342            self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue
+343        return
 

 
 
@@ -3764,171 +3779,171 @@ of the autocorrelation function (default True)
- 
177    def gamma_method(self, **kwargs):
-178        """Estimate the error and related properties of the Obs.
-179
-180        Parameters
-181        ----------
-182        S : float
-183            specifies a custom value for the parameter S (default 2.0).
-184            If set to 0 it is assumed that the data exhibits no
-185            autocorrelation. In this case the error estimates coincides
-186            with the sample standard error.
-187        tau_exp : float
-188            positive value triggers the critical slowing down analysis
-189            (default 0.0).
-190        N_sigma : float
-191            number of standard deviations from zero until the tail is
-192            attached to the autocorrelation function (default 1).
-193        fft : bool
-194            determines whether the fft algorithm is used for the computation
-195            of the autocorrelation function (default True)
-196        """
-197
-198        e_content = self.e_content
-199        self.e_dvalue = {}
-200        self.e_ddvalue = {}
-201        self.e_tauint = {}
-202        self.e_dtauint = {}
-203        self.e_windowsize = {}
-204        self.e_n_tauint = {}
-205        self.e_n_dtauint = {}
-206        e_gamma = {}
-207        self.e_rho = {}
-208        self.e_drho = {}
-209        self._dvalue = 0
-210        self.ddvalue = 0
-211
-212        self.S = {}
-213        self.tau_exp = {}
-214        self.N_sigma = {}
-215
-216        if kwargs.get('fft') is False:
-217            fft = False
-218        else:
-219            fft = True
-220
-221        def _parse_kwarg(kwarg_name):
-222            if kwarg_name in kwargs:
-223                tmp = kwargs.get(kwarg_name)
-224                if isinstance(tmp, (int, float)):
-225                    if tmp < 0:
-226                        raise ValueError(kwarg_name + ' has to be larger or equal to 0.')
-227                    for e, e_name in enumerate(self.e_names):
-228                        getattr(self, kwarg_name)[e_name] = tmp
-229                else:
-230                    raise TypeError(kwarg_name + ' is not in proper format.')
-231            else:
-232                for e, e_name in enumerate(self.e_names):
-233                    if e_name in getattr(Obs, kwarg_name + '_dict'):
-234                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name]
-235                    else:
-236                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global')
-237
-238        _parse_kwarg('S')
-239        _parse_kwarg('tau_exp')
-240        _parse_kwarg('N_sigma')
-241
-242        for e, e_name in enumerate(self.mc_names):
-243            gapsize = _determine_gap(self, e_content, e_name)
-244
-245            r_length = []
-246            for r_name in e_content[e_name]:
-247                if isinstance(self.idl[r_name], range):
-248                    r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize)
-249                else:
-250                    r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize)
-251
-252            e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]])
-253            w_max = max(r_length) // 2
-254            e_gamma[e_name] = np.zeros(w_max)
-255            self.e_rho[e_name] = np.zeros(w_max)
-256            self.e_drho[e_name] = np.zeros(w_max)
-257
-258            for r_name in e_content[e_name]:
-259                e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
-260
-261            gamma_div = np.zeros(w_max)
-262            for r_name in e_content[e_name]:
-263                gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
-264            gamma_div[gamma_div < 1] = 1.0
-265            e_gamma[e_name] /= gamma_div[:w_max]
-266
-267            if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny:  # Prevent division by zero
-268                self.e_tauint[e_name] = 0.5
-269                self.e_dtauint[e_name] = 0.0
-270                self.e_dvalue[e_name] = 0.0
-271                self.e_ddvalue[e_name] = 0.0
-272                self.e_windowsize[e_name] = 0
-273                continue
-274
-275            self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
-276            self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:])))
-277            # Make sure no entry of tauint is smaller than 0.5
-278            self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps
-279            # hep-lat/0306017 eq. (42)
-280            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
-281            self.e_n_dtauint[e_name][0] = 0.0
-282
-283            def _compute_drho(i):
-284                tmp = (self.e_rho[e_name][i + 1:w_max]
-285                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
-286                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
-287                       - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i])
-288                self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N)
-289
-290            if self.tau_exp[e_name] > 0:
-291                _compute_drho(1)
-292                texp = self.tau_exp[e_name]
-293                # Critical slowing down analysis
-294                if w_max // 2 <= 1:
-295                    raise ValueError("Need at least 8 samples for tau_exp error analysis")
-296                for n in range(1, w_max // 2):
-297                    _compute_drho(n + 1)
-298                    if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2:
-299                        # Bias correction hep-lat/0306017 eq. (49) included
-300                        self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1])  # The absolute makes sure, that the tail contribution is always positive
-301                        self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2)
-302                        # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2
-303                        self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
-304                        self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
-305                        self.e_windowsize[e_name] = n
-306                        break
-307            else:
-308                if self.S[e_name] == 0.0:
-309                    self.e_tauint[e_name] = 0.5
-310                    self.e_dtauint[e_name] = 0.0
-311                    self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1))
-312                    self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N)
-313                    self.e_windowsize[e_name] = 0
-314                else:
-315                    # Standard automatic windowing procedure
-316                    tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1))
-317                    g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N)
-318                    for n in range(1, w_max):
-319                        if g_w[n - 1] < 0 or n >= w_max - 1:
-320                            _compute_drho(n)
-321                            self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N)  # Bias correction hep-lat/0306017 eq. (49)
-322                            self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n]
-323                            self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
-324                            self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
-325                            self.e_windowsize[e_name] = n
-326                            break
-327
-328            self._dvalue += self.e_dvalue[e_name] ** 2
-329            self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2
-330
-331        for e_name in self.cov_names:
-332            self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq())
-333            self.e_ddvalue[e_name] = 0
-334            self._dvalue += self.e_dvalue[e_name]**2
-335
-336        self._dvalue = np.sqrt(self._dvalue)
-337        if self._dvalue == 0.0:
-338            self.ddvalue = 0.0
-339        else:
-340            self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue
-341        return
+            
179    def gamma_method(self, **kwargs):
+180        """Estimate the error and related properties of the Obs.
+181
+182        Parameters
+183        ----------
+184        S : float
+185            specifies a custom value for the parameter S (default 2.0).
+186            If set to 0 it is assumed that the data exhibits no
+187            autocorrelation. In this case the error estimates coincides
+188            with the sample standard error.
+189        tau_exp : float
+190            positive value triggers the critical slowing down analysis
+191            (default 0.0).
+192        N_sigma : float
+193            number of standard deviations from zero until the tail is
+194            attached to the autocorrelation function (default 1).
+195        fft : bool
+196            determines whether the fft algorithm is used for the computation
+197            of the autocorrelation function (default True)
+198        """
+199
+200        e_content = self.e_content
+201        self.e_dvalue = {}
+202        self.e_ddvalue = {}
+203        self.e_tauint = {}
+204        self.e_dtauint = {}
+205        self.e_windowsize = {}
+206        self.e_n_tauint = {}
+207        self.e_n_dtauint = {}
+208        e_gamma = {}
+209        self.e_rho = {}
+210        self.e_drho = {}
+211        self._dvalue = 0
+212        self.ddvalue = 0
+213
+214        self.S = {}
+215        self.tau_exp = {}
+216        self.N_sigma = {}
+217
+218        if kwargs.get('fft') is False:
+219            fft = False
+220        else:
+221            fft = True
+222
+223        def _parse_kwarg(kwarg_name):
+224            if kwarg_name in kwargs:
+225                tmp = kwargs.get(kwarg_name)
+226                if isinstance(tmp, (int, float)):
+227                    if tmp < 0:
+228                        raise ValueError(kwarg_name + ' has to be larger or equal to 0.')
+229                    for e, e_name in enumerate(self.e_names):
+230                        getattr(self, kwarg_name)[e_name] = tmp
+231                else:
+232                    raise TypeError(kwarg_name + ' is not in proper format.')
+233            else:
+234                for e, e_name in enumerate(self.e_names):
+235                    if e_name in getattr(Obs, kwarg_name + '_dict'):
+236                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name]
+237                    else:
+238                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global')
+239
+240        _parse_kwarg('S')
+241        _parse_kwarg('tau_exp')
+242        _parse_kwarg('N_sigma')
+243
+244        for e, e_name in enumerate(self.mc_names):
+245            gapsize = _determine_gap(self, e_content, e_name)
+246
+247            r_length = []
+248            for r_name in e_content[e_name]:
+249                if isinstance(self.idl[r_name], range):
+250                    r_length.append(len(self.idl[r_name]) * self.idl[r_name].step // gapsize)
+251                else:
+252                    r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1) // gapsize)
+253
+254            e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]])
+255            w_max = max(r_length) // 2
+256            e_gamma[e_name] = np.zeros(w_max)
+257            self.e_rho[e_name] = np.zeros(w_max)
+258            self.e_drho[e_name] = np.zeros(w_max)
+259
+260            for r_name in e_content[e_name]:
+261                e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
+262
+263            gamma_div = np.zeros(w_max)
+264            for r_name in e_content[e_name]:
+265                gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft, gapsize)
+266            gamma_div[gamma_div < 1] = 1.0
+267            e_gamma[e_name] /= gamma_div[:w_max]
+268
+269            if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny:  # Prevent division by zero
+270                self.e_tauint[e_name] = 0.5
+271                self.e_dtauint[e_name] = 0.0
+272                self.e_dvalue[e_name] = 0.0
+273                self.e_ddvalue[e_name] = 0.0
+274                self.e_windowsize[e_name] = 0
+275                continue
+276
+277            self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
+278            self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:])))
+279            # Make sure no entry of tauint is smaller than 0.5
+280            self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps
+281            # hep-lat/0306017 eq. (42)
+282            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) + 0.5 - self.e_n_tauint[e_name]) / e_N)
+283            self.e_n_dtauint[e_name][0] = 0.0
+284
+285            def _compute_drho(i):
+286                tmp = (self.e_rho[e_name][i + 1:w_max]
+287                       + np.concatenate([self.e_rho[e_name][i - 1:None if i - (w_max - 1) // 2 <= 0 else (2 * i - (2 * w_max) // 2):-1],
+288                                         self.e_rho[e_name][1:max(1, w_max - 2 * i)]])
+289                       - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i])
+290                self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N)
+291
+292            if self.tau_exp[e_name] > 0:
+293                _compute_drho(1)
+294                texp = self.tau_exp[e_name]
+295                # Critical slowing down analysis
+296                if w_max // 2 <= 1:
+297                    raise ValueError("Need at least 8 samples for tau_exp error analysis")
+298                for n in range(1, w_max // 2):
+299                    _compute_drho(n + 1)
+300                    if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2:
+301                        # Bias correction hep-lat/0306017 eq. (49) included
+302                        self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1])  # The absolute makes sure, that the tail contribution is always positive
+303                        self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2)
+304                        # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2
+305                        self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+306                        self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
+307                        self.e_windowsize[e_name] = n
+308                        break
+309            else:
+310                if self.S[e_name] == 0.0:
+311                    self.e_tauint[e_name] = 0.5
+312                    self.e_dtauint[e_name] = 0.0
+313                    self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1))
+314                    self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N)
+315                    self.e_windowsize[e_name] = 0
+316                else:
+317                    # Standard automatic windowing procedure
+318                    tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][1:] + 1) / (2 * self.e_n_tauint[e_name][1:] - 1))
+319                    g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N)
+320                    for n in range(1, w_max):
+321                        if g_w[n - 1] < 0 or n >= w_max - 1:
+322                            _compute_drho(n)
+323                            self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n + 1) / e_N) / (1 + 1 / e_N)  # Bias correction hep-lat/0306017 eq. (49)
+324                            self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n]
+325                            self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+326                            self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n + 0.5) / e_N)
+327                            self.e_windowsize[e_name] = n
+328                            break
+329
+330            self._dvalue += self.e_dvalue[e_name] ** 2
+331            self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2
+332
+333        for e_name in self.cov_names:
+334            self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq())
+335            self.e_ddvalue[e_name] = 0
+336            self._dvalue += self.e_dvalue[e_name]**2
+337
+338        self._dvalue = np.sqrt(self._dvalue)
+339        if self._dvalue == 0.0:
+340            self.ddvalue = 0.0
+341        else:
+342            self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue
+343        return
 

 
 
@@ -3967,74 +3982,74 @@ of the autocorrelation function (default True)
- 
381    def details(self, ens_content=True):
-382        """Output detailed properties of the Obs.
-383
-384        Parameters
-385        ----------
-386        ens_content : bool
-387            print details about the ensembles and replica if true.
-388        """
-389        if self.tag is not None:
-390            print("Description:", self.tag)
-391        if not hasattr(self, 'e_dvalue'):
-392            print('Result\t %3.8e' % (self.value))
-393        else:
-394            if self.value == 0.0:
-395                percentage = np.nan
-396            else:
-397                percentage = np.abs(self._dvalue / self.value) * 100
-398            print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage))
-399            if len(self.e_names) > 1:
-400                print(' Ensemble errors:')
-401            e_content = self.e_content
-402            for e_name in self.mc_names:
-403                gap = _determine_gap(self, e_content, e_name)
-404
-405                if len(self.e_names) > 1:
-406                    print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name]))
-407                tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name])
-408                tau_string += f" in units of {gap} config"
-409                if gap > 1:
-410                    tau_string += "s"
-411                if self.tau_exp[e_name] > 0:
-412                    tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name])
-413                else:
-414                    tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name])
-415                print(tau_string)
-416            for e_name in self.cov_names:
-417                print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name]))
-418        if ens_content is True:
-419            if len(self.e_names) == 1:
-420                print(self.N, 'samples in', len(self.e_names), 'ensemble:')
-421            else:
-422                print(self.N, 'samples in', len(self.e_names), 'ensembles:')
-423            my_string_list = []
-424            for key, value in sorted(self.e_content.items()):
-425                if key not in self.covobs:
-426                    my_string = '  ' + "\u00B7 Ensemble '" + key + "' "
-427                    if len(value) == 1:
-428                        my_string += f': {self.shape[value[0]]} configurations'
-429                        if isinstance(self.idl[value[0]], range):
-430                            my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')'
-431                        else:
-432                            my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})'
-433                    else:
-434                        sublist = []
-435                        for v in value:
-436                            my_substring = '    ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' "
-437                            my_substring += f': {self.shape[v]} configurations'
-438                            if isinstance(self.idl[v], range):
-439                                my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')'
-440                            else:
-441                                my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})'
-442                            sublist.append(my_substring)
-443
-444                        my_string += '\n' + '\n'.join(sublist)
-445                else:
-446                    my_string = '  ' + "\u00B7 Covobs   '" + key + "' "
-447                my_string_list.append(my_string)
-448            print('\n'.join(my_string_list))
+            
383    def details(self, ens_content=True):
+384        """Output detailed properties of the Obs.
+385
+386        Parameters
+387        ----------
+388        ens_content : bool
+389            print details about the ensembles and replica if true.
+390        """
+391        if self.tag is not None:
+392            print("Description:", self.tag)
+393        if not hasattr(self, 'e_dvalue'):
+394            print('Result\t %3.8e' % (self.value))
+395        else:
+396            if self.value == 0.0:
+397                percentage = np.nan
+398            else:
+399                percentage = np.abs(self._dvalue / self.value) * 100
+400            print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage))
+401            if len(self.e_names) > 1:
+402                print(' Ensemble errors:')
+403            e_content = self.e_content
+404            for e_name in self.mc_names:
+405                gap = _determine_gap(self, e_content, e_name)
+406
+407                if len(self.e_names) > 1:
+408                    print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name]))
+409                tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name])
+410                tau_string += f" in units of {gap} config"
+411                if gap > 1:
+412                    tau_string += "s"
+413                if self.tau_exp[e_name] > 0:
+414                    tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name])
+415                else:
+416                    tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name])
+417                print(tau_string)
+418            for e_name in self.cov_names:
+419                print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name]))
+420        if ens_content is True:
+421            if len(self.e_names) == 1:
+422                print(self.N, 'samples in', len(self.e_names), 'ensemble:')
+423            else:
+424                print(self.N, 'samples in', len(self.e_names), 'ensembles:')
+425            my_string_list = []
+426            for key, value in sorted(self.e_content.items()):
+427                if key not in self.covobs:
+428                    my_string = '  ' + "\u00B7 Ensemble '" + key + "' "
+429                    if len(value) == 1:
+430                        my_string += f': {self.shape[value[0]]} configurations'
+431                        if isinstance(self.idl[value[0]], range):
+432                            my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')'
+433                        else:
+434                            my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})'
+435                    else:
+436                        sublist = []
+437                        for v in value:
+438                            my_substring = '    ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' "
+439                            my_substring += f': {self.shape[v]} configurations'
+440                            if isinstance(self.idl[v], range):
+441                                my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')'
+442                            else:
+443                                my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})'
+444                            sublist.append(my_substring)
+445
+446                        my_string += '\n' + '\n'.join(sublist)
+447                else:
+448                    my_string = '  ' + "\u00B7 Covobs   '" + key + "' "
+449                my_string_list.append(my_string)
+450            print('\n'.join(my_string_list))
 

 
 
@@ -4061,20 +4076,20 @@ print details about the ensembles and replica if true.
- 
450    def reweight(self, weight):
-451        """Reweight the obs with given rewighting factors.
-452
-453        Parameters
-454        ----------
-455        weight : Obs
-456            Reweighting factor. An Observable that has to be defined on a superset of the
-457            configurations in obs[i].idl for all i.
-458        all_configs : bool
-459            if True, the reweighted observables are normalized by the average of
-460            the reweighting factor on all configurations in weight.idl and not
-461            on the configurations in obs[i].idl. Default False.
-462        """
-463        return reweight(weight, [self])[0]
+            
452    def reweight(self, weight):
+453        """Reweight the obs with given rewighting factors.
+454
+455        Parameters
+456        ----------
+457        weight : Obs
+458            Reweighting factor. An Observable that has to be defined on a superset of the
+459            configurations in obs[i].idl for all i.
+460        all_configs : bool
+461            if True, the reweighted observables are normalized by the average of
+462            the reweighting factor on all configurations in weight.idl and not
+463            on the configurations in obs[i].idl. Default False.
+464        """
+465        return reweight(weight, [self])[0]
 

 
 
@@ -4106,17 +4121,17 @@ on the configurations in obs[i].idl. Default False.
- 
465    def is_zero_within_error(self, sigma=1):
-466        """Checks whether the observable is zero within 'sigma' standard errors.
-467
-468        Parameters
-469        ----------
-470        sigma : int
-471            Number of standard errors used for the check.
-472
-473        Works only properly when the gamma method was run.
-474        """
-475        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
+            
467    def is_zero_within_error(self, sigma=1):
+468        """Checks whether the observable is zero within 'sigma' standard errors.
+469
+470        Parameters
+471        ----------
+472        sigma : int
+473            Number of standard errors used for the check.
+474
+475        Works only properly when the gamma method was run.
+476        """
+477        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
 

 
 
@@ -4144,15 +4159,15 @@ Number of standard errors used for the check.
- 
477    def is_zero(self, atol=1e-10):
-478        """Checks whether the observable is zero within a given tolerance.
-479
-480        Parameters
-481        ----------
-482        atol : float
-483            Absolute tolerance (for details see numpy documentation).
-484        """
-485        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
+            
479    def is_zero(self, atol=1e-10):
+480        """Checks whether the observable is zero within a given tolerance.
+481
+482        Parameters
+483        ----------
+484        atol : float
+485            Absolute tolerance (for details see numpy documentation).
+486        """
+487        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
 

 
 
@@ -4179,45 +4194,45 @@ Absolute tolerance (for details see numpy documentation).
- 
487    def plot_tauint(self, save=None):
-488        """Plot integrated autocorrelation time for each ensemble.
-489
-490        Parameters
-491        ----------
-492        save : str
-493            saves the figure to a file named 'save' if.
-494        """
-495        if not hasattr(self, 'e_dvalue'):
-496            raise Exception('Run the gamma method first.')
-497
-498        for e, e_name in enumerate(self.mc_names):
-499            fig = plt.figure()
-500            plt.xlabel(r'$W$')
-501            plt.ylabel(r'$\tau_\mathrm{int}$')
-502            length = int(len(self.e_n_tauint[e_name]))
-503            if self.tau_exp[e_name] > 0:
-504                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
-505                x_help = np.arange(2 * self.tau_exp[e_name])
-506                y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base
-507                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
-508                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
-509                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
-510                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
-511                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
-512                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
-513            else:
-514                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
-515                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
-516
-517            plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label)
-518            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
-519            plt.legend()
-520            plt.xlim(-0.5, xmax)
-521            ylim = plt.ylim()
-522            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
-523            plt.draw()
-524            if save:
-525                fig.savefig(save + "_" + str(e))
+            
489    def plot_tauint(self, save=None):
+490        """Plot integrated autocorrelation time for each ensemble.
+491
+492        Parameters
+493        ----------
+494        save : str
+495            saves the figure to a file named 'save' if.
+496        """
+497        if not hasattr(self, 'e_dvalue'):
+498            raise Exception('Run the gamma method first.')
+499
+500        for e, e_name in enumerate(self.mc_names):
+501            fig = plt.figure()
+502            plt.xlabel(r'$W$')
+503            plt.ylabel(r'$\tau_\mathrm{int}$')
+504            length = int(len(self.e_n_tauint[e_name]))
+505            if self.tau_exp[e_name] > 0:
+506                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
+507                x_help = np.arange(2 * self.tau_exp[e_name])
+508                y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base
+509                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
+510                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
+511                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
+512                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
+513                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+514                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
+515            else:
+516                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
+517                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+518
+519            plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label)
+520            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
+521            plt.legend()
+522            plt.xlim(-0.5, xmax)
+523            ylim = plt.ylim()
+524            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
+525            plt.draw()
+526            if save:
+527                fig.savefig(save + "_" + str(e))
 

 
 
@@ -4244,36 +4259,36 @@ saves the figure to a file named 'save' if.
- 
527    def plot_rho(self, save=None):
-528        """Plot normalized autocorrelation function time for each ensemble.
-529
-530        Parameters
-531        ----------
-532        save : str
-533            saves the figure to a file named 'save' if.
-534        """
-535        if not hasattr(self, 'e_dvalue'):
-536            raise Exception('Run the gamma method first.')
-537        for e, e_name in enumerate(self.mc_names):
-538            fig = plt.figure()
-539            plt.xlabel('W')
-540            plt.ylabel('rho')
-541            length = int(len(self.e_drho[e_name]))
-542            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
-543            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
-544            if self.tau_exp[e_name] > 0:
-545                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
-546                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
-547                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
-548                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
-549            else:
-550                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
-551                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
-552            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
-553            plt.xlim(-0.5, xmax)
-554            plt.draw()
-555            if save:
-556                fig.savefig(save + "_" + str(e))
+            
529    def plot_rho(self, save=None):
+530        """Plot normalized autocorrelation function time for each ensemble.
+531
+532        Parameters
+533        ----------
+534        save : str
+535            saves the figure to a file named 'save' if.
+536        """
+537        if not hasattr(self, 'e_dvalue'):
+538            raise Exception('Run the gamma method first.')
+539        for e, e_name in enumerate(self.mc_names):
+540            fig = plt.figure()
+541            plt.xlabel('W')
+542            plt.ylabel('rho')
+543            length = int(len(self.e_drho[e_name]))
+544            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
+545            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
+546            if self.tau_exp[e_name] > 0:
+547                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
+548                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
+549                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+550                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
+551            else:
+552                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+553                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
+554            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
+555            plt.xlim(-0.5, xmax)
+556            plt.draw()
+557            if save:
+558                fig.savefig(save + "_" + str(e))
 

 
 
@@ -4300,27 +4315,27 @@ saves the figure to a file named 'save' if.
- 
558    def plot_rep_dist(self):
-559        """Plot replica distribution for each ensemble with more than one replicum."""
-560        if not hasattr(self, 'e_dvalue'):
-561            raise Exception('Run the gamma method first.')
-562        for e, e_name in enumerate(self.mc_names):
-563            if len(self.e_content[e_name]) == 1:
-564                print('No replica distribution for a single replicum (', e_name, ')')
-565                continue
-566            r_length = []
-567            sub_r_mean = 0
-568            for r, r_name in enumerate(self.e_content[e_name]):
-569                r_length.append(len(self.deltas[r_name]))
-570                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
-571            e_N = np.sum(r_length)
-572            sub_r_mean /= e_N
-573            arr = np.zeros(len(self.e_content[e_name]))
-574            for r, r_name in enumerate(self.e_content[e_name]):
-575                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
-576            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
-577            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
-578            plt.draw()
+            
560    def plot_rep_dist(self):
+561        """Plot replica distribution for each ensemble with more than one replicum."""
+562        if not hasattr(self, 'e_dvalue'):
+563            raise Exception('Run the gamma method first.')
+564        for e, e_name in enumerate(self.mc_names):
+565            if len(self.e_content[e_name]) == 1:
+566                print('No replica distribution for a single replicum (', e_name, ')')
+567                continue
+568            r_length = []
+569            sub_r_mean = 0
+570            for r, r_name in enumerate(self.e_content[e_name]):
+571                r_length.append(len(self.deltas[r_name]))
+572                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
+573            e_N = np.sum(r_length)
+574            sub_r_mean /= e_N
+575            arr = np.zeros(len(self.e_content[e_name]))
+576            for r, r_name in enumerate(self.e_content[e_name]):
+577                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
+578            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
+579            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
+580            plt.draw()
 

 
 
@@ -4340,37 +4355,37 @@ saves the figure to a file named 'save' if.
- 
580    def plot_history(self, expand=True):
-581        """Plot derived Monte Carlo history for each ensemble
-582
-583        Parameters
-584        ----------
-585        expand : bool
-586            show expanded history for irregular Monte Carlo chains (default: True).
-587        """
-588        for e, e_name in enumerate(self.mc_names):
-589            plt.figure()
-590            r_length = []
-591            tmp = []
-592            tmp_expanded = []
-593            for r, r_name in enumerate(self.e_content[e_name]):
-594                tmp.append(self.deltas[r_name] + self.r_values[r_name])
-595                if expand:
-596                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name], 1) + self.r_values[r_name])
-597                    r_length.append(len(tmp_expanded[-1]))
-598                else:
-599                    r_length.append(len(tmp[-1]))
-600            e_N = np.sum(r_length)
-601            x = np.arange(e_N)
-602            y_test = np.concatenate(tmp, axis=0)
-603            if expand:
-604                y = np.concatenate(tmp_expanded, axis=0)
-605            else:
-606                y = y_test
-607            plt.errorbar(x, y, fmt='.', markersize=3)
-608            plt.xlim(-0.5, e_N - 0.5)
-609            plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})')
-610            plt.draw()
+            
582    def plot_history(self, expand=True):
+583        """Plot derived Monte Carlo history for each ensemble
+584
+585        Parameters
+586        ----------
+587        expand : bool
+588            show expanded history for irregular Monte Carlo chains (default: True).
+589        """
+590        for e, e_name in enumerate(self.mc_names):
+591            plt.figure()
+592            r_length = []
+593            tmp = []
+594            tmp_expanded = []
+595            for r, r_name in enumerate(self.e_content[e_name]):
+596                tmp.append(self.deltas[r_name] + self.r_values[r_name])
+597                if expand:
+598                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name], 1) + self.r_values[r_name])
+599                    r_length.append(len(tmp_expanded[-1]))
+600                else:
+601                    r_length.append(len(tmp[-1]))
+602            e_N = np.sum(r_length)
+603            x = np.arange(e_N)
+604            y_test = np.concatenate(tmp, axis=0)
+605            if expand:
+606                y = np.concatenate(tmp_expanded, axis=0)
+607            else:
+608                y = y_test
+609            plt.errorbar(x, y, fmt='.', markersize=3)
+610            plt.xlim(-0.5, e_N - 0.5)
+611            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})')
+612            plt.draw()
 

 
 
@@ -4397,29 +4412,29 @@ show expanded history for irregular Monte Carlo chains (default: True).
- 
612    def plot_piechart(self, save=None):
-613        """Plot piechart which shows the fractional contribution of each
-614        ensemble to the error and returns a dictionary containing the fractions.
-615
-616        Parameters
-617        ----------
-618        save : str
-619            saves the figure to a file named 'save' if.
-620        """
-621        if not hasattr(self, 'e_dvalue'):
-622            raise Exception('Run the gamma method first.')
-623        if np.isclose(0.0, self._dvalue, atol=1e-15):
-624            raise ValueError('Error is 0.0')
-625        labels = self.e_names
-626        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
-627        fig1, ax1 = plt.subplots()
-628        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
-629        ax1.axis('equal')
-630        plt.draw()
-631        if save:
-632            fig1.savefig(save)
-633
-634        return dict(zip(labels, sizes))
+            
614    def plot_piechart(self, save=None):
+615        """Plot piechart which shows the fractional contribution of each
+616        ensemble to the error and returns a dictionary containing the fractions.
+617
+618        Parameters
+619        ----------
+620        save : str
+621            saves the figure to a file named 'save' if.
+622        """
+623        if not hasattr(self, 'e_dvalue'):
+624            raise Exception('Run the gamma method first.')
+625        if np.isclose(0.0, self._dvalue, atol=1e-15):
+626            raise ValueError('Error is 0.0')
+627        labels = self.e_names
+628        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
+629        fig1, ax1 = plt.subplots()
+630        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
+631        ax1.axis('equal')
+632        plt.draw()
+633        if save:
+634            fig1.savefig(save)
+635
+636        return dict(zip(labels, sizes))
 

 
 
@@ -4447,34 +4462,34 @@ saves the figure to a file named 'save' if.
- 
636    def dump(self, filename, datatype="json.gz", description="", **kwargs):
-637        """Dump the Obs to a file 'name' of chosen format.
-638
-639        Parameters
-640        ----------
-641        filename : str
-642            name of the file to be saved.
-643        datatype : str
-644            Format of the exported file. Supported formats include
-645            "json.gz" and "pickle"
-646        description : str
-647            Description for output file, only relevant for json.gz format.
-648        path : str
-649            specifies a custom path for the file (default '.')
-650        """
-651        if 'path' in kwargs:
-652            file_name = kwargs.get('path') + '/' + filename
-653        else:
-654            file_name = filename
-655
-656        if datatype == "json.gz":
-657            from .input.json import dump_to_json
-658            dump_to_json([self], file_name, description=description)
-659        elif datatype == "pickle":
-660            with open(file_name + '.p', 'wb') as fb:
-661                pickle.dump(self, fb)
-662        else:
-663            raise TypeError("Unknown datatype " + str(datatype))
+            
638    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+639        """Dump the Obs to a file 'name' of chosen format.
+640
+641        Parameters
+642        ----------
+643        filename : str
+644            name of the file to be saved.
+645        datatype : str
+646            Format of the exported file. Supported formats include
+647            "json.gz" and "pickle"
+648        description : str
+649            Description for output file, only relevant for json.gz format.
+650        path : str
+651            specifies a custom path for the file (default '.')
+652        """
+653        if 'path' in kwargs:
+654            file_name = kwargs.get('path') + '/' + filename
+655        else:
+656            file_name = filename
+657
+658        if datatype == "json.gz":
+659            from .input.json import dump_to_json
+660            dump_to_json([self], file_name, description=description)
+661        elif datatype == "pickle":
+662            with open(file_name + '.p', 'wb') as fb:
+663                pickle.dump(self, fb)
+664        else:
+665            raise TypeError("Unknown datatype " + str(datatype))
 

 
 
@@ -4508,31 +4523,31 @@ specifies a custom path for the file (default '.')
- 
665    def export_jackknife(self):
-666        """Export jackknife samples from the Obs
-667
-668        Returns
-669        -------
-670        numpy.ndarray
-671            Returns a numpy array of length N + 1 where N is the number of samples
-672            for the given ensemble and replicum. The zeroth entry of the array contains
-673            the mean value of the Obs, entries 1 to N contain the N jackknife samples
-674            derived from the Obs. The current implementation only works for observables
-675            defined on exactly one ensemble and replicum. The derived jackknife samples
-676            should agree with samples from a full jackknife analysis up to O(1/N).
-677        """
-678
-679        if len(self.names) != 1:
-680            raise ValueError("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
-681
-682        name = self.names[0]
-683        full_data = self.deltas[name] + self.r_values[name]
-684        n = full_data.size
-685        mean = self.value
-686        tmp_jacks = np.zeros(n + 1)
-687        tmp_jacks[0] = mean
-688        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
-689        return tmp_jacks
+            
667    def export_jackknife(self):
+668        """Export jackknife samples from the Obs
+669
+670        Returns
+671        -------
+672        numpy.ndarray
+673            Returns a numpy array of length N + 1 where N is the number of samples
+674            for the given ensemble and replicum. The zeroth entry of the array contains
+675            the mean value of the Obs, entries 1 to N contain the N jackknife samples
+676            derived from the Obs. The current implementation only works for observables
+677            defined on exactly one ensemble and replicum. The derived jackknife samples
+678            should agree with samples from a full jackknife analysis up to O(1/N).
+679        """
+680
+681        if len(self.names) != 1:
+682            raise ValueError("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
+683
+684        name = self.names[0]
+685        full_data = self.deltas[name] + self.r_values[name]
+686        n = full_data.size
+687        mean = self.value
+688        tmp_jacks = np.zeros(n + 1)
+689        tmp_jacks[0] = mean
+690        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
+691        return tmp_jacks
 

 
 
@@ -4563,48 +4578,48 @@ should agree with samples from a full jackknife analysis up to O(1/N).
- 
691    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
-692        """Export bootstrap samples from the Obs
-693
-694        Parameters
-695        ----------
-696        samples : int
-697            Number of bootstrap samples to generate.
-698        random_numbers : np.ndarray
-699            Array of shape (samples, length) containing the random numbers to generate the bootstrap samples.
-700            If not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
-701        save_rng : str
-702            Save the random numbers to a file if a path is specified.
-703
-704        Returns
-705        -------
-706        numpy.ndarray
-707            Returns a numpy array of length N + 1 where N is the number of samples
-708            for the given ensemble and replicum. The zeroth entry of the array contains
-709            the mean value of the Obs, entries 1 to N contain the N import_bootstrap samples
-710            derived from the Obs. The current implementation only works for observables
-711            defined on exactly one ensemble and replicum. The derived bootstrap samples
-712            should agree with samples from a full bootstrap analysis up to O(1/N).
-713        """
-714        if len(self.names) != 1:
-715            raise ValueError("'export_boostrap' is only implemented for Obs defined on one ensemble and replicum.")
-716
-717        name = self.names[0]
-718        length = self.N
-719
-720        if random_numbers is None:
-721            seed = int(hashlib.md5(name.encode()).hexdigest(), 16) & 0xFFFFFFFF
-722            rng = np.random.default_rng(seed)
-723            random_numbers = rng.integers(0, length, size=(samples, length))
-724
-725        if save_rng is not None:
-726            np.savetxt(save_rng, random_numbers, fmt='%i')
-727
-728        proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
-729        ret = np.zeros(samples + 1)
-730        ret[0] = self.value
-731        ret[1:] = proj @ (self.deltas[name] + self.r_values[name])
-732        return ret
+            
693    def export_bootstrap(self, samples=500, random_numbers=None, save_rng=None):
+694        """Export bootstrap samples from the Obs
+695
+696        Parameters
+697        ----------
+698        samples : int
+699            Number of bootstrap samples to generate.
+700        random_numbers : np.ndarray
+701            Array of shape (samples, length) containing the random numbers to generate the bootstrap samples.
+702            If not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
+703        save_rng : str
+704            Save the random numbers to a file if a path is specified.
+705
+706        Returns
+707        -------
+708        numpy.ndarray
+709            Returns a numpy array of length N + 1 where N is the number of samples
+710            for the given ensemble and replicum. The zeroth entry of the array contains
+711            the mean value of the Obs, entries 1 to N contain the N import_bootstrap samples
+712            derived from the Obs. The current implementation only works for observables
+713            defined on exactly one ensemble and replicum. The derived bootstrap samples
+714            should agree with samples from a full bootstrap analysis up to O(1/N).
+715        """
+716        if len(self.names) != 1:
+717            raise ValueError("'export_boostrap' is only implemented for Obs defined on one ensemble and replicum.")
+718
+719        name = self.names[0]
+720        length = self.N
+721
+722        if random_numbers is None:
+723            seed = int(hashlib.md5(name.encode()).hexdigest(), 16) & 0xFFFFFFFF
+724            rng = np.random.default_rng(seed)
+725            random_numbers = rng.integers(0, length, size=(samples, length))
+726
+727        if save_rng is not None:
+728            np.savetxt(save_rng, random_numbers, fmt='%i')
+729
+730        proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
+731        ret = np.zeros(samples + 1)
+732        ret[0] = self.value
+733        ret[1:] = proj @ (self.deltas[name] + self.r_values[name])
+734        return ret
 

 
 
@@ -4647,8 +4662,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
871    def sqrt(self):
-872        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
+            
873    def sqrt(self):
+874        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
 

 
 
@@ -4666,8 +4681,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
874    def log(self):
-875        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
+            
876    def log(self):
+877        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
 

 
 
@@ -4685,8 +4700,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
877    def exp(self):
-878        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
+            
879    def exp(self):
+880        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
 

 
 
@@ -4704,8 +4719,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
880    def sin(self):
-881        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
+            
882    def sin(self):
+883        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
 

 
 
@@ -4723,8 +4738,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
883    def cos(self):
-884        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
+            
885    def cos(self):
+886        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
 

 
 
@@ -4742,8 +4757,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
886    def tan(self):
-887        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
+            
888    def tan(self):
+889        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
 

 
 
@@ -4761,8 +4776,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
889    def arcsin(self):
-890        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
+            
891    def arcsin(self):
+892        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
 

 
 
@@ -4780,8 +4795,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
892    def arccos(self):
-893        return derived_observable(lambda x: anp.arccos(x[0]), [self])
+            
894    def arccos(self):
+895        return derived_observable(lambda x: anp.arccos(x[0]), [self])
 

 
 
@@ -4799,8 +4814,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
895    def arctan(self):
-896        return derived_observable(lambda x: anp.arctan(x[0]), [self])
+            
897    def arctan(self):
+898        return derived_observable(lambda x: anp.arctan(x[0]), [self])
 

 
 
@@ -4818,8 +4833,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
898    def sinh(self):
-899        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
+            
900    def sinh(self):
+901        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
 

 
 
@@ -4837,8 +4852,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
901    def cosh(self):
-902        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
+            
903    def cosh(self):
+904        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
 

 
 
@@ -4856,8 +4871,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
904    def tanh(self):
-905        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
+            
906    def tanh(self):
+907        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
 

 
 
@@ -4875,8 +4890,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
907    def arcsinh(self):
-908        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
+            
909    def arcsinh(self):
+910        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
 

 
 
@@ -4894,8 +4909,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
910    def arccosh(self):
-911        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
+            
912    def arccosh(self):
+913        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
 

 
 
@@ -4913,8 +4928,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
913    def arctanh(self):
-914        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
+            
915    def arctanh(self):
+916        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
 

 
 
@@ -5065,123 +5080,123 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
 917class CObs:
- 918    """Class for a complex valued observable."""
- 919    __slots__ = ['_real', '_imag', 'tag']
- 920
- 921    def __init__(self, real, imag=0.0):
- 922        self._real = real
- 923        self._imag = imag
- 924        self.tag = None
- 925
- 926    @property
- 927    def real(self):
- 928        return self._real
- 929
- 930    @property
- 931    def imag(self):
- 932        return self._imag
- 933
- 934    def gamma_method(self, **kwargs):
- 935        """Executes the gamma_method for the real and the imaginary part."""
- 936        if isinstance(self.real, Obs):
- 937            self.real.gamma_method(**kwargs)
- 938        if isinstance(self.imag, Obs):
- 939            self.imag.gamma_method(**kwargs)
- 940
- 941    def is_zero(self):
- 942        """Checks whether both real and imaginary part are zero within machine precision."""
- 943        return self.real == 0.0 and self.imag == 0.0
- 944
- 945    def conjugate(self):
- 946        return CObs(self.real, -self.imag)
- 947
- 948    def __add__(self, other):
- 949        if isinstance(other, np.ndarray):
- 950            return other + self
- 951        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 952            return CObs(self.real + other.real,
- 953                        self.imag + other.imag)
- 954        else:
- 955            return CObs(self.real + other, self.imag)
- 956
- 957    def __radd__(self, y):
- 958        return self + y
- 959
- 960    def __sub__(self, other):
- 961        if isinstance(other, np.ndarray):
- 962            return -1 * (other - self)
- 963        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 964            return CObs(self.real - other.real, self.imag - other.imag)
- 965        else:
- 966            return CObs(self.real - other, self.imag)
- 967
- 968    def __rsub__(self, other):
- 969        return -1 * (self - other)
- 970
- 971    def __mul__(self, other):
- 972        if isinstance(other, np.ndarray):
- 973            return other * self
- 974        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 975            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
- 976                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
- 977                                               [self.real, other.real, self.imag, other.imag],
- 978                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
- 979                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
- 980                                               [self.real, other.real, self.imag, other.imag],
- 981                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
- 982            elif getattr(other, 'imag', 0) != 0:
- 983                return CObs(self.real * other.real - self.imag * other.imag,
- 984                            self.imag * other.real + self.real * other.imag)
- 985            else:
- 986                return CObs(self.real * other.real, self.imag * other.real)
- 987        else:
- 988            return CObs(self.real * other, self.imag * other)
- 989
- 990    def __rmul__(self, other):
- 991        return self * other
- 992
- 993    def __truediv__(self, other):
- 994        if isinstance(other, np.ndarray):
- 995            return 1 / (other / self)
- 996        elif hasattr(other, 'real') and hasattr(other, 'imag'):
- 997            r = other.real ** 2 + other.imag ** 2
- 998            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
- 999        else:
-1000            return CObs(self.real / other, self.imag / other)
-1001
-1002    def __rtruediv__(self, other):
-1003        r = self.real ** 2 + self.imag ** 2
-1004        if hasattr(other, 'real') and hasattr(other, 'imag'):
-1005            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
-1006        else:
-1007            return CObs(self.real * other / r, -self.imag * other / r)
-1008
-1009    def __abs__(self):
-1010        return np.sqrt(self.real**2 + self.imag**2)
-1011
-1012    def __pos__(self):
-1013        return self
-1014
-1015    def __neg__(self):
-1016        return -1 * self
-1017
-1018    def __eq__(self, other):
-1019        return self.real == other.real and self.imag == other.imag
-1020
-1021    def __str__(self):
-1022        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
-1023
-1024    def __repr__(self):
-1025        return 'CObs[' + str(self) + ']'
-1026
-1027    def __format__(self, format_type):
-1028        if format_type == "":
-1029            significance = 2
-1030            format_type = "2"
-1031        else:
-1032            significance = int(float(format_type.replace("+", "").replace("-", "")))
-1033        return f"({self.real:{format_type}}{self.imag:+{significance}}j)"
+            
 919class CObs:
+ 920    """Class for a complex valued observable."""
+ 921    __slots__ = ['_real', '_imag', 'tag']
+ 922
+ 923    def __init__(self, real, imag=0.0):
+ 924        self._real = real
+ 925        self._imag = imag
+ 926        self.tag = None
+ 927
+ 928    @property
+ 929    def real(self):
+ 930        return self._real
+ 931
+ 932    @property
+ 933    def imag(self):
+ 934        return self._imag
+ 935
+ 936    def gamma_method(self, **kwargs):
+ 937        """Executes the gamma_method for the real and the imaginary part."""
+ 938        if isinstance(self.real, Obs):
+ 939            self.real.gamma_method(**kwargs)
+ 940        if isinstance(self.imag, Obs):
+ 941            self.imag.gamma_method(**kwargs)
+ 942
+ 943    def is_zero(self):
+ 944        """Checks whether both real and imaginary part are zero within machine precision."""
+ 945        return self.real == 0.0 and self.imag == 0.0
+ 946
+ 947    def conjugate(self):
+ 948        return CObs(self.real, -self.imag)
+ 949
+ 950    def __add__(self, other):
+ 951        if isinstance(other, np.ndarray):
+ 952            return other + self
+ 953        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 954            return CObs(self.real + other.real,
+ 955                        self.imag + other.imag)
+ 956        else:
+ 957            return CObs(self.real + other, self.imag)
+ 958
+ 959    def __radd__(self, y):
+ 960        return self + y
+ 961
+ 962    def __sub__(self, other):
+ 963        if isinstance(other, np.ndarray):
+ 964            return -1 * (other - self)
+ 965        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 966            return CObs(self.real - other.real, self.imag - other.imag)
+ 967        else:
+ 968            return CObs(self.real - other, self.imag)
+ 969
+ 970    def __rsub__(self, other):
+ 971        return -1 * (self - other)
+ 972
+ 973    def __mul__(self, other):
+ 974        if isinstance(other, np.ndarray):
+ 975            return other * self
+ 976        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 977            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
+ 978                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
+ 979                                               [self.real, other.real, self.imag, other.imag],
+ 980                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
+ 981                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
+ 982                                               [self.real, other.real, self.imag, other.imag],
+ 983                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
+ 984            elif getattr(other, 'imag', 0) != 0:
+ 985                return CObs(self.real * other.real - self.imag * other.imag,
+ 986                            self.imag * other.real + self.real * other.imag)
+ 987            else:
+ 988                return CObs(self.real * other.real, self.imag * other.real)
+ 989        else:
+ 990            return CObs(self.real * other, self.imag * other)
+ 991
+ 992    def __rmul__(self, other):
+ 993        return self * other
+ 994
+ 995    def __truediv__(self, other):
+ 996        if isinstance(other, np.ndarray):
+ 997            return 1 / (other / self)
+ 998        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+ 999            r = other.real ** 2 + other.imag ** 2
+1000            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
+1001        else:
+1002            return CObs(self.real / other, self.imag / other)
+1003
+1004    def __rtruediv__(self, other):
+1005        r = self.real ** 2 + self.imag ** 2
+1006        if hasattr(other, 'real') and hasattr(other, 'imag'):
+1007            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
+1008        else:
+1009            return CObs(self.real * other / r, -self.imag * other / r)
+1010
+1011    def __abs__(self):
+1012        return np.sqrt(self.real**2 + self.imag**2)
+1013
+1014    def __pos__(self):
+1015        return self
+1016
+1017    def __neg__(self):
+1018        return -1 * self
+1019
+1020    def __eq__(self, other):
+1021        return self.real == other.real and self.imag == other.imag
+1022
+1023    def __str__(self):
+1024        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
+1025
+1026    def __repr__(self):
+1027        return 'CObs[' + str(self) + ']'
+1028
+1029    def __format__(self, format_type):
+1030        if format_type == "":
+1031            significance = 2
+1032            format_type = "2"
+1033        else:
+1034            significance = int(float(format_type.replace("+", "").replace("-", "")))
+1035        return f"({self.real:{format_type}}{self.imag:+{significance}}j)"
 

 
 
@@ -5199,10 +5214,10 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
921    def __init__(self, real, imag=0.0):
-922        self._real = real
-923        self._imag = imag
-924        self.tag = None
+            
923    def __init__(self, real, imag=0.0):
+924        self._real = real
+925        self._imag = imag
+926        self.tag = None
 

 
 
@@ -5229,9 +5244,9 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
926    @property
-927    def real(self):
-928        return self._real
+            
928    @property
+929    def real(self):
+930        return self._real
 

 
 
@@ -5247,9 +5262,9 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
930    @property
-931    def imag(self):
-932        return self._imag
+            
932    @property
+933    def imag(self):
+934        return self._imag
 

 
 
@@ -5267,12 +5282,12 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
934    def gamma_method(self, **kwargs):
-935        """Executes the gamma_method for the real and the imaginary part."""
-936        if isinstance(self.real, Obs):
-937            self.real.gamma_method(**kwargs)
-938        if isinstance(self.imag, Obs):
-939            self.imag.gamma_method(**kwargs)
+            
936    def gamma_method(self, **kwargs):
+937        """Executes the gamma_method for the real and the imaginary part."""
+938        if isinstance(self.real, Obs):
+939            self.real.gamma_method(**kwargs)
+940        if isinstance(self.imag, Obs):
+941            self.imag.gamma_method(**kwargs)
 

 
 
@@ -5292,9 +5307,9 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
941    def is_zero(self):
-942        """Checks whether both real and imaginary part are zero within machine precision."""
-943        return self.real == 0.0 and self.imag == 0.0
+            
943    def is_zero(self):
+944        """Checks whether both real and imaginary part are zero within machine precision."""
+945        return self.real == 0.0 and self.imag == 0.0
 

 
 
@@ -5314,8 +5329,8 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
945    def conjugate(self):
-946        return CObs(self.real, -self.imag)
+            
947    def conjugate(self):
+948        return CObs(self.real, -self.imag)
 

 
 
@@ -5334,12 +5349,12 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
1036def gamma_method(x, **kwargs):
-1037    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
-1038
-1039    See docstring of pe.Obs.gamma_method for details.
-1040    """
-1041    return np.vectorize(lambda o: o.gm(**kwargs))(x)
+            
1038def gamma_method(x, **kwargs):
+1039    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
+1040
+1041    See docstring of pe.Obs.gamma_method for details.
+1042    """
+1043    return np.vectorize(lambda o: o.gm(**kwargs))(x)
 

 
 
@@ -5361,12 +5376,12 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
1036def gamma_method(x, **kwargs):
-1037    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
-1038
-1039    See docstring of pe.Obs.gamma_method for details.
-1040    """
-1041    return np.vectorize(lambda o: o.gm(**kwargs))(x)
+            
1038def gamma_method(x, **kwargs):
+1039    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
+1040
+1041    See docstring of pe.Obs.gamma_method for details.
+1042    """
+1043    return np.vectorize(lambda o: o.gm(**kwargs))(x)
 

 
 
@@ -5388,194 +5403,194 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
- 
1171def derived_observable(func, data, array_mode=False, **kwargs):
-1172    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
-1173
-1174    Parameters
-1175    ----------
-1176    func : object
-1177        arbitrary function of the form func(data, **kwargs). For the
-1178        automatic differentiation to work, all numpy functions have to have
-1179        the autograd wrapper (use 'import autograd.numpy as anp').
-1180    data : list
-1181        list of Obs, e.g. [obs1, obs2, obs3].
-1182    num_grad : bool
-1183        if True, numerical derivatives are used instead of autograd
-1184        (default False). To control the numerical differentiation the
-1185        kwargs of numdifftools.step_generators.MaxStepGenerator
-1186        can be used.
-1187    man_grad : list
-1188        manually supply a list or an array which contains the jacobian
-1189        of func. Use cautiously, supplying the wrong derivative will
-1190        not be intercepted.
-1191
-1192    Notes
-1193    -----
-1194    For simple mathematical operations it can be practical to use anonymous
-1195    functions. For the ratio of two observables one can e.g. use
-1196
-1197    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
-1198    """
-1199
-1200    data = np.asarray(data)
-1201    raveled_data = data.ravel()
-1202
-1203    # Workaround for matrix operations containing non Obs data
-1204    if not all(isinstance(x, Obs) for x in raveled_data):
-1205        for i in range(len(raveled_data)):
-1206            if isinstance(raveled_data[i], (int, float)):
-1207                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
-1208
-1209    allcov = {}
-1210    for o in raveled_data:
-1211        for name in o.cov_names:
-1212            if name in allcov:
-1213                if not np.allclose(allcov[name], o.covobs[name].cov):
-1214                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
-1215            else:
-1216                allcov[name] = o.covobs[name].cov
-1217
-1218    n_obs = len(raveled_data)
-1219    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
-1220    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
-1221    new_sample_names = sorted(set(new_names) - set(new_cov_names))
-1222
-1223    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+            
1173def derived_observable(func, data, array_mode=False, **kwargs):
+1174    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
+1175
+1176    Parameters
+1177    ----------
+1178    func : object
+1179        arbitrary function of the form func(data, **kwargs). For the
+1180        automatic differentiation to work, all numpy functions have to have
+1181        the autograd wrapper (use 'import autograd.numpy as anp').
+1182    data : list
+1183        list of Obs, e.g. [obs1, obs2, obs3].
+1184    num_grad : bool
+1185        if True, numerical derivatives are used instead of autograd
+1186        (default False). To control the numerical differentiation the
+1187        kwargs of numdifftools.step_generators.MaxStepGenerator
+1188        can be used.
+1189    man_grad : list
+1190        manually supply a list or an array which contains the jacobian
+1191        of func. Use cautiously, supplying the wrong derivative will
+1192        not be intercepted.
+1193
+1194    Notes
+1195    -----
+1196    For simple mathematical operations it can be practical to use anonymous
+1197    functions. For the ratio of two observables one can e.g. use
+1198
+1199    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
+1200    """
+1201
+1202    data = np.asarray(data)
+1203    raveled_data = data.ravel()
+1204
+1205    # Workaround for matrix operations containing non Obs data
+1206    if not all(isinstance(x, Obs) for x in raveled_data):
+1207        for i in range(len(raveled_data)):
+1208            if isinstance(raveled_data[i], (int, float)):
+1209                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
+1210
+1211    allcov = {}
+1212    for o in raveled_data:
+1213        for name in o.cov_names:
+1214            if name in allcov:
+1215                if not np.allclose(allcov[name], o.covobs[name].cov):
+1216                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
+1217            else:
+1218                allcov[name] = o.covobs[name].cov
+1219
+1220    n_obs = len(raveled_data)
+1221    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
+1222    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
+1223    new_sample_names = sorted(set(new_names) - set(new_cov_names))
 1224
-1225    if data.ndim == 1:
-1226        values = np.array([o.value for o in data])
-1227    else:
-1228        values = np.vectorize(lambda x: x.value)(data)
-1229
-1230    new_values = func(values, **kwargs)
+1225    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1226
+1227    if data.ndim == 1:
+1228        values = np.array([o.value for o in data])
+1229    else:
+1230        values = np.vectorize(lambda x: x.value)(data)
 1231
-1232    multi = int(isinstance(new_values, np.ndarray))
+1232    new_values = func(values, **kwargs)
 1233
-1234    new_r_values = {}
-1235    new_idl_d = {}
-1236    for name in new_sample_names:
-1237        idl = []
-1238        tmp_values = np.zeros(n_obs)
-1239        for i, item in enumerate(raveled_data):
-1240            tmp_values[i] = item.r_values.get(name, item.value)
-1241            tmp_idl = item.idl.get(name)
-1242            if tmp_idl is not None:
-1243                idl.append(tmp_idl)
-1244        if multi > 0:
-1245            tmp_values = np.array(tmp_values).reshape(data.shape)
-1246        new_r_values[name] = func(tmp_values, **kwargs)
-1247        new_idl_d[name] = _merge_idx(idl)
-1248
-1249    def _compute_scalefactor_missing_rep(obs):
-1250        """
-1251        Computes the scale factor that is to be multiplied with the deltas
-1252        in the case where Obs with different subsets of replica are merged.
-1253        Returns a dictionary with the scale factor for each Monte Carlo name.
-1254
-1255        Parameters
-1256        ----------
-1257        obs : Obs
-1258            The observable corresponding to the deltas that are to be scaled
-1259        """
-1260        scalef_d = {}
-1261        for mc_name in obs.mc_names:
-1262            mc_idl_d = [name for name in obs.idl if name.startswith(mc_name + '|')]
-1263            new_mc_idl_d = [name for name in new_idl_d if name.startswith(mc_name + '|')]
-1264            if len(mc_idl_d) > 0 and len(mc_idl_d) < len(new_mc_idl_d):
-1265                scalef_d[mc_name] = sum([len(new_idl_d[name]) for name in new_mc_idl_d]) / sum([len(new_idl_d[name]) for name in mc_idl_d])
-1266        return scalef_d
-1267
-1268    if 'man_grad' in kwargs:
-1269        deriv = np.asarray(kwargs.get('man_grad'))
-1270        if new_values.shape + data.shape != deriv.shape:
-1271            raise ValueError('Manual derivative does not have correct shape.')
-1272    elif kwargs.get('num_grad') is True:
-1273        if multi > 0:
-1274            raise Exception('Multi mode currently not supported for numerical derivative')
-1275        options = {
-1276            'base_step': 0.1,
-1277            'step_ratio': 2.5}
-1278        for key in options.keys():
-1279            kwarg = kwargs.get(key)
-1280            if kwarg is not None:
-1281                options[key] = kwarg
-1282        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
-1283        if tmp_df.size == 1:
-1284            deriv = np.array([tmp_df.real])
-1285        else:
-1286            deriv = tmp_df.real
-1287    else:
-1288        deriv = jacobian(func)(values, **kwargs)
-1289
-1290    final_result = np.zeros(new_values.shape, dtype=object)
+1234    multi = int(isinstance(new_values, np.ndarray))
+1235
+1236    new_r_values = {}
+1237    new_idl_d = {}
+1238    for name in new_sample_names:
+1239        idl = []
+1240        tmp_values = np.zeros(n_obs)
+1241        for i, item in enumerate(raveled_data):
+1242            tmp_values[i] = item.r_values.get(name, item.value)
+1243            tmp_idl = item.idl.get(name)
+1244            if tmp_idl is not None:
+1245                idl.append(tmp_idl)
+1246        if multi > 0:
+1247            tmp_values = np.array(tmp_values).reshape(data.shape)
+1248        new_r_values[name] = func(tmp_values, **kwargs)
+1249        new_idl_d[name] = _merge_idx(idl)
+1250
+1251    def _compute_scalefactor_missing_rep(obs):
+1252        """
+1253        Computes the scale factor that is to be multiplied with the deltas
+1254        in the case where Obs with different subsets of replica are merged.
+1255        Returns a dictionary with the scale factor for each Monte Carlo name.
+1256
+1257        Parameters
+1258        ----------
+1259        obs : Obs
+1260            The observable corresponding to the deltas that are to be scaled
+1261        """
+1262        scalef_d = {}
+1263        for mc_name in obs.mc_names:
+1264            mc_idl_d = [name for name in obs.idl if name.startswith(mc_name + '|')]
+1265            new_mc_idl_d = [name for name in new_idl_d if name.startswith(mc_name + '|')]
+1266            if len(mc_idl_d) > 0 and len(mc_idl_d) < len(new_mc_idl_d):
+1267                scalef_d[mc_name] = sum([len(new_idl_d[name]) for name in new_mc_idl_d]) / sum([len(new_idl_d[name]) for name in mc_idl_d])
+1268        return scalef_d
+1269
+1270    if 'man_grad' in kwargs:
+1271        deriv = np.asarray(kwargs.get('man_grad'))
+1272        if new_values.shape + data.shape != deriv.shape:
+1273            raise ValueError('Manual derivative does not have correct shape.')
+1274    elif kwargs.get('num_grad') is True:
+1275        if multi > 0:
+1276            raise Exception('Multi mode currently not supported for numerical derivative')
+1277        options = {
+1278            'base_step': 0.1,
+1279            'step_ratio': 2.5}
+1280        for key in options.keys():
+1281            kwarg = kwargs.get(key)
+1282            if kwarg is not None:
+1283                options[key] = kwarg
+1284        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
+1285        if tmp_df.size == 1:
+1286            deriv = np.array([tmp_df.real])
+1287        else:
+1288            deriv = tmp_df.real
+1289    else:
+1290        deriv = jacobian(func)(values, **kwargs)
 1291
-1292    if array_mode is True:
+1292    final_result = np.zeros(new_values.shape, dtype=object)
 1293
-1294        class _Zero_grad():
-1295            def __init__(self, N):
-1296                self.grad = np.zeros((N, 1))
-1297
-1298        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
-1299        d_extracted = {}
-1300        g_extracted = {}
-1301        for name in new_sample_names:
-1302            d_extracted[name] = []
-1303            ens_length = len(new_idl_d[name])
-1304            for i_dat, dat in enumerate(data):
-1305                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], _compute_scalefactor_missing_rep(o).get(name.split('|')[0], 1)) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
-1306        for name in new_cov_names:
-1307            g_extracted[name] = []
-1308            zero_grad = _Zero_grad(new_covobs_lengths[name])
-1309            for i_dat, dat in enumerate(data):
-1310                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)))
-1311
-1312    for i_val, new_val in np.ndenumerate(new_values):
-1313        new_deltas = {}
-1314        new_grad = {}
-1315        if array_mode is True:
-1316            for name in new_sample_names:
-1317                ens_length = d_extracted[name][0].shape[-1]
-1318                new_deltas[name] = np.zeros(ens_length)
-1319                for i_dat, dat in enumerate(d_extracted[name]):
-1320                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1321            for name in new_cov_names:
-1322                new_grad[name] = 0
-1323                for i_dat, dat in enumerate(g_extracted[name]):
-1324                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1325        else:
-1326            for j_obs, obs in np.ndenumerate(data):
-1327                scalef_d = _compute_scalefactor_missing_rep(obs)
-1328                for name in obs.names:
-1329                    if name in obs.cov_names:
-1330                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
-1331                    else:
-1332                        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], scalef_d.get(name.split('|')[0], 1))
-1333
-1334        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1294    if array_mode is True:
+1295
+1296        class _Zero_grad():
+1297            def __init__(self, N):
+1298                self.grad = np.zeros((N, 1))
+1299
+1300        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]))
+1301        d_extracted = {}
+1302        g_extracted = {}
+1303        for name in new_sample_names:
+1304            d_extracted[name] = []
+1305            ens_length = len(new_idl_d[name])
+1306            for i_dat, dat in enumerate(data):
+1307                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], _compute_scalefactor_missing_rep(o).get(name.split('|')[0], 1)) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
+1308        for name in new_cov_names:
+1309            g_extracted[name] = []
+1310            zero_grad = _Zero_grad(new_covobs_lengths[name])
+1311            for i_dat, dat in enumerate(data):
+1312                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)))
+1313
+1314    for i_val, new_val in np.ndenumerate(new_values):
+1315        new_deltas = {}
+1316        new_grad = {}
+1317        if array_mode is True:
+1318            for name in new_sample_names:
+1319                ens_length = d_extracted[name][0].shape[-1]
+1320                new_deltas[name] = np.zeros(ens_length)
+1321                for i_dat, dat in enumerate(d_extracted[name]):
+1322                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1323            for name in new_cov_names:
+1324                new_grad[name] = 0
+1325                for i_dat, dat in enumerate(g_extracted[name]):
+1326                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1327        else:
+1328            for j_obs, obs in np.ndenumerate(data):
+1329                scalef_d = _compute_scalefactor_missing_rep(obs)
+1330                for name in obs.names:
+1331                    if name in obs.cov_names:
+1332                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
+1333                    else:
+1334                        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], scalef_d.get(name.split('|')[0], 1))
 1335
-1336        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
-1337            raise ValueError('The same name has been used for deltas and covobs!')
-1338        new_samples = []
-1339        new_means = []
-1340        new_idl = []
-1341        new_names_obs = []
-1342        for name in new_names:
-1343            if name not in new_covobs:
-1344                new_samples.append(new_deltas[name])
-1345                new_idl.append(new_idl_d[name])
-1346                new_means.append(new_r_values[name][i_val])
-1347                new_names_obs.append(name)
-1348        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
-1349        for name in new_covobs:
-1350            final_result[i_val].names.append(name)
-1351        final_result[i_val]._covobs = new_covobs
-1352        final_result[i_val]._value = new_val
-1353        final_result[i_val].reweighted = reweighted
-1354
-1355    if multi == 0:
-1356        final_result = final_result.item()
-1357
-1358    return final_result
+1336        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1337
+1338        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
+1339            raise ValueError('The same name has been used for deltas and covobs!')
+1340        new_samples = []
+1341        new_means = []
+1342        new_idl = []
+1343        new_names_obs = []
+1344        for name in new_names:
+1345            if name not in new_covobs:
+1346                new_samples.append(new_deltas[name])
+1347                new_idl.append(new_idl_d[name])
+1348                new_means.append(new_r_values[name][i_val])
+1349                new_names_obs.append(name)
+1350        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
+1351        for name in new_covobs:
+1352            final_result[i_val].names.append(name)
+1353        final_result[i_val]._covobs = new_covobs
+1354        final_result[i_val]._value = new_val
+1355        final_result[i_val].reweighted = reweighted
+1356
+1357    if multi == 0:
+1358        final_result = final_result.item()
+1359
+1360    return final_result
 

 
 
@@ -5622,46 +5637,48 @@ functions. For the ratio of two observables one can e.g. use
- 
1390def reweight(weight, obs, **kwargs):
-1391    """Reweight a list of observables.
-1392
-1393    Parameters
-1394    ----------
-1395    weight : Obs
-1396        Reweighting factor. An Observable that has to be defined on a superset of the
-1397        configurations in obs[i].idl for all i.
-1398    obs : list
-1399        list of Obs, e.g. [obs1, obs2, obs3].
-1400    all_configs : bool
-1401        if True, the reweighted observables are normalized by the average of
-1402        the reweighting factor on all configurations in weight.idl and not
-1403        on the configurations in obs[i].idl. Default False.
-1404    """
-1405    result = []
-1406    for i in range(len(obs)):
-1407        if len(obs[i].cov_names):
-1408            raise ValueError('Error: Not possible to reweight an Obs that contains covobs!')
-1409        if not set(obs[i].names).issubset(weight.names):
-1410            raise ValueError('Error: Ensembles do not fit')
-1411        for name in obs[i].names:
-1412            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
-1413                raise ValueError('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
-1414        new_samples = []
-1415        w_deltas = {}
-1416        for name in sorted(obs[i].names):
-1417            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
-1418            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
-1419        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1420
-1421        if kwargs.get('all_configs'):
-1422            new_weight = weight
-1423        else:
-1424            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)])
-1425
-1426        result.append(tmp_obs / new_weight)
-1427        result[-1].reweighted = True
-1428
-1429    return result
+            
1392def reweight(weight, obs, **kwargs):
+1393    """Reweight a list of observables.
+1394
+1395    Parameters
+1396    ----------
+1397    weight : Obs
+1398        Reweighting factor. An Observable that has to be defined on a superset of the
+1399        configurations in obs[i].idl for all i.
+1400    obs : list
+1401        list of Obs, e.g. [obs1, obs2, obs3].
+1402    all_configs : bool
+1403        if True, the reweighted observables are normalized by the average of
+1404        the reweighting factor on all configurations in weight.idl and not
+1405        on the configurations in obs[i].idl. Default False.
+1406    """
+1407    result = []
+1408    for i in range(len(obs)):
+1409        if len(obs[i].cov_names):
+1410            raise ValueError('Error: Not possible to reweight an Obs that contains covobs!')
+1411        if not set(obs[i].names).issubset(weight.names):
+1412            raise ValueError('Error: Ensembles do not fit')
+1413        if len(obs[i].mc_names) > 1 or len(weight.mc_names) > 1:
+1414            raise ValueError('Error: Cannot reweight an Obs that contains multiple ensembles.')
+1415        for name in obs[i].names:
+1416            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
+1417                raise ValueError('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
+1418        new_samples = []
+1419        w_deltas = {}
+1420        for name in sorted(obs[i].names):
+1421            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
+1422            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
+1423        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1424
+1425        if kwargs.get('all_configs'):
+1426            new_weight = weight
+1427        else:
+1428            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)])
+1429
+1430        result.append(tmp_obs / new_weight)
+1431        result[-1].reweighted = True
+1432
+1433    return result
 

 
 
@@ -5695,47 +5712,50 @@ on the configurations in obs[i].idl. Default False.
- 
1432def correlate(obs_a, obs_b):
-1433    """Correlate two observables.
-1434
-1435    Parameters
-1436    ----------
-1437    obs_a : Obs
-1438        First observable
-1439    obs_b : Obs
-1440        Second observable
-1441
-1442    Notes
-1443    -----
-1444    Keep in mind to only correlate primary observables which have not been reweighted
-1445    yet. The reweighting has to be applied after correlating the observables.
-1446    Currently only works if ensembles are identical (this is not strictly necessary).
-1447    """
-1448
-1449    if sorted(obs_a.names) != sorted(obs_b.names):
-1450        raise ValueError(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
-1451    if len(obs_a.cov_names) or len(obs_b.cov_names):
-1452        raise ValueError('Error: Not possible to correlate Obs that contain covobs!')
-1453    for name in obs_a.names:
-1454        if obs_a.shape[name] != obs_b.shape[name]:
-1455            raise ValueError('Shapes of ensemble', name, 'do not fit')
-1456        if obs_a.idl[name] != obs_b.idl[name]:
-1457            raise ValueError('idl of ensemble', name, 'do not fit')
-1458
-1459    if obs_a.reweighted is True:
-1460        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
-1461    if obs_b.reweighted is True:
-1462        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
-1463
-1464    new_samples = []
-1465    new_idl = []
-1466    for name in sorted(obs_a.names):
-1467        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
-1468        new_idl.append(obs_a.idl[name])
-1469
-1470    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
-1471    o.reweighted = obs_a.reweighted or obs_b.reweighted
-1472    return o
+            
1436def correlate(obs_a, obs_b):
+1437    """Correlate two observables.
+1438
+1439    Parameters
+1440    ----------
+1441    obs_a : Obs
+1442        First observable
+1443    obs_b : Obs
+1444        Second observable
+1445
+1446    Notes
+1447    -----
+1448    Keep in mind to only correlate primary observables which have not been reweighted
+1449    yet. The reweighting has to be applied after correlating the observables.
+1450    Only works if a single ensemble is present in the Obs.
+1451    Currently only works if ensemble content is identical (this is not strictly necessary).
+1452    """
+1453
+1454    if len(obs_a.mc_names) > 1 or len(obs_b.mc_names) > 1:
+1455        raise ValueError('Error: Cannot correlate Obs that contain multiple ensembles.')
+1456    if sorted(obs_a.names) != sorted(obs_b.names):
+1457        raise ValueError(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
+1458    if len(obs_a.cov_names) or len(obs_b.cov_names):
+1459        raise ValueError('Error: Not possible to correlate Obs that contain covobs!')
+1460    for name in obs_a.names:
+1461        if obs_a.shape[name] != obs_b.shape[name]:
+1462            raise ValueError('Shapes of ensemble', name, 'do not fit')
+1463        if obs_a.idl[name] != obs_b.idl[name]:
+1464            raise ValueError('idl of ensemble', name, 'do not fit')
+1465
+1466    if obs_a.reweighted is True:
+1467        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
+1468    if obs_b.reweighted is True:
+1469        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
+1470
+1471    new_samples = []
+1472    new_idl = []
+1473    for name in sorted(obs_a.names):
+1474        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
+1475        new_idl.append(obs_a.idl[name])
+1476
+1477    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
+1478    o.reweighted = obs_a.reweighted or obs_b.reweighted
+1479    return o
 

 
 
@@ -5754,7 +5774,8 @@ Second observable
 
 
Keep in mind to only correlate primary observables which have not been reweighted
 yet. The reweighting has to be applied after correlating the observables.
-Currently only works if ensembles are identical (this is not strictly necessary).

+Only works if a single ensemble is present in the Obs.
+Currently only works if ensemble content is identical (this is not strictly necessary).
@@ -5770,74 +5791,74 @@ Currently only works if ensembles are identical (this is not strictly necessary) - 
1475def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
-1476    r'''Calculates the error covariance matrix of a set of observables.
-1477
-1478    WARNING: This function should be used with care, especially for observables with support on multiple
-1479             ensembles with differing autocorrelations. See the notes below for details.
-1480
-1481    The gamma method has to be applied first to all observables.
-1482
-1483    Parameters
-1484    ----------
-1485    obs : list or numpy.ndarray
-1486        List or one dimensional array of Obs
-1487    visualize : bool
-1488        If True plots the corresponding normalized correlation matrix (default False).
-1489    correlation : bool
-1490        If True the correlation matrix instead of the error covariance matrix is returned (default False).
-1491    smooth : None or int
-1492        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
-1493        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
-1494        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
-1495        small ones.
-1496
-1497    Notes
-1498    -----
-1499    The error covariance is defined such that it agrees with the squared standard error for two identical observables
-1500    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
-1501    in the absence of autocorrelation.
-1502    The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite
-1503    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
-1504    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.
-1505    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
-1506    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
-1507    '''
-1508
-1509    length = len(obs)
-1510
-1511    max_samples = np.max([o.N for o in obs])
-1512    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
-1513        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)
-1514
-1515    cov = np.zeros((length, length))
-1516    for i in range(length):
-1517        for j in range(i, length):
-1518            cov[i, j] = _covariance_element(obs[i], obs[j])
-1519    cov = cov + cov.T - np.diag(np.diag(cov))
-1520
-1521    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
-1522
-1523    if isinstance(smooth, int):
-1524        corr = _smooth_eigenvalues(corr, smooth)
-1525
-1526    if visualize:
-1527        plt.matshow(corr, vmin=-1, vmax=1)
-1528        plt.set_cmap('RdBu')
-1529        plt.colorbar()
-1530        plt.draw()
-1531
-1532    if correlation is True:
-1533        return corr
-1534
-1535    errors = [o.dvalue for o in obs]
-1536    cov = np.diag(errors) @ corr @ np.diag(errors)
-1537
-1538    eigenvalues = np.linalg.eigh(cov)[0]
-1539    if not np.all(eigenvalues >= 0):
-1540        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
+            
1482def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+1483    r'''Calculates the error covariance matrix of a set of observables.
+1484
+1485    WARNING: This function should be used with care, especially for observables with support on multiple
+1486             ensembles with differing autocorrelations. See the notes below for details.
+1487
+1488    The gamma method has to be applied first to all observables.
+1489
+1490    Parameters
+1491    ----------
+1492    obs : list or numpy.ndarray
+1493        List or one dimensional array of Obs
+1494    visualize : bool
+1495        If True plots the corresponding normalized correlation matrix (default False).
+1496    correlation : bool
+1497        If True the correlation matrix instead of the error covariance matrix is returned (default False).
+1498    smooth : None or int
+1499        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
+1500        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
+1501        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
+1502        small ones.
+1503
+1504    Notes
+1505    -----
+1506    The error covariance is defined such that it agrees with the squared standard error for two identical observables
+1507    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
+1508    in the absence of autocorrelation.
+1509    The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite
+1510    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
+1511    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.
+1512    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
+1513    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
+1514    '''
+1515
+1516    length = len(obs)
+1517
+1518    max_samples = np.max([o.N for o in obs])
+1519    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
+1520        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)
+1521
+1522    cov = np.zeros((length, length))
+1523    for i in range(length):
+1524        for j in range(i, length):
+1525            cov[i, j] = _covariance_element(obs[i], obs[j])
+1526    cov = cov + cov.T - np.diag(np.diag(cov))
+1527
+1528    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
+1529
+1530    if isinstance(smooth, int):
+1531        corr = _smooth_eigenvalues(corr, smooth)
+1532
+1533    if visualize:
+1534        plt.matshow(corr, vmin=-1, vmax=1)
+1535        plt.set_cmap('RdBu')
+1536        plt.colorbar()
+1537        plt.draw()
+1538
+1539    if correlation is True:
+1540        return corr
 1541
-1542    return cov
+1542    errors = [o.dvalue for o in obs]
+1543    cov = np.diag(errors) @ corr @ np.diag(errors)
+1544
+1545    eigenvalues = np.linalg.eigh(cov)[0]
+1546    if not np.all(eigenvalues >= 0):
+1547        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
+1548
+1549    return cov
 

 
 
@@ -5889,27 +5910,27 @@ This construction ensures that the estimated covariance matrix is positive semi-
- 
1545def invert_corr_cov_cholesky(corr, inverrdiag):
-1546    """Constructs a lower triangular matrix `chol` via the Cholesky decomposition of the correlation matrix `corr`
-1547       and then returns the inverse covariance matrix `chol_inv` as a lower triangular matrix by solving `chol * x = inverrdiag`.
-1548
-1549    Parameters
-1550    ----------
-1551    corr : np.ndarray
-1552           correlation matrix
-1553    inverrdiag : np.ndarray
-1554              diagonal matrix, the entries are the inverse errors of the data points considered
-1555    """
-1556
-1557    condn = np.linalg.cond(corr)
-1558    if condn > 0.1 / np.finfo(float).eps:
-1559        raise ValueError(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
-1560    if condn > 1e13:
-1561        warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
-1562    chol = np.linalg.cholesky(corr)
-1563    chol_inv = scipy.linalg.solve_triangular(chol, inverrdiag, lower=True)
-1564
-1565    return chol_inv
+            
1552def invert_corr_cov_cholesky(corr, inverrdiag):
+1553    """Constructs a lower triangular matrix `chol` via the Cholesky decomposition of the correlation matrix `corr`
+1554       and then returns the inverse covariance matrix `chol_inv` as a lower triangular matrix by solving `chol * x = inverrdiag`.
+1555
+1556    Parameters
+1557    ----------
+1558    corr : np.ndarray
+1559           correlation matrix
+1560    inverrdiag : np.ndarray
+1561              diagonal matrix, the entries are the inverse errors of the data points considered
+1562    """
+1563
+1564    condn = np.linalg.cond(corr)
+1565    if condn > 0.1 / np.finfo(float).eps:
+1566        raise ValueError(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
+1567    if condn > 1e13:
+1568        warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
+1569    chol = np.linalg.cholesky(corr)
+1570    chol_inv = scipy.linalg.solve_triangular(chol, inverrdiag, lower=True)
+1571
+1572    return chol_inv
 

 
 
@@ -5939,67 +5960,67 @@ diagonal matrix, the entries are the inverse errors of the data points considere
- 
1568def sort_corr(corr, kl, yd):
-1569    """ Reorders a correlation matrix to match the alphabetical order of its underlying y data.
-1570
-1571    The ordering of the input correlation matrix `corr` is given by the list of keys `kl`.
-1572    The input dictionary `yd` (with the same keys `kl`) must contain the corresponding y data
-1573    that the correlation matrix is based on.
-1574    This function sorts the list of keys `kl` alphabetically and sorts the matrix `corr`
-1575    according to this alphabetical order such that the sorted matrix `corr_sorted` corresponds
-1576    to the y data `yd` when arranged in an alphabetical order by its keys.
+            
1575def sort_corr(corr, kl, yd):
+1576    """ Reorders a correlation matrix to match the alphabetical order of its underlying y data.
 1577
-1578    Parameters
-1579    ----------
-1580    corr : np.ndarray
-1581        A square correlation matrix constructed using the order of the y data specified by `kl`.
-1582        The dimensions of `corr` should match the total number of y data points in `yd` combined.
-1583    kl : list of str
-1584        A list of keys that denotes the order in which the y data from `yd` was used to build the
-1585        input correlation matrix `corr`.
-1586    yd : dict of list
-1587        A dictionary where each key corresponds to a unique identifier, and its value is a list of
-1588        y data points. The total number of y data points across all keys must match the dimensions
-1589        of `corr`. The lists in the dictionary can be lists of Obs.
-1590
-1591    Returns
-1592    -------
-1593    np.ndarray
-1594        A new, sorted correlation matrix that corresponds to the y data from `yd` when arranged alphabetically by its keys.
-1595
-1596    Example
-1597    -------
-1598    >>> import numpy as np
-1599    >>> import pyerrors as pe
-1600    >>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])
-1601    >>> kl = ['b', 'a']
-1602    >>> yd = {'a': [1, 2], 'b': [3]}
-1603    >>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)
-1604    >>> print(sorted_corr)
-1605    array([[1. , 0.3, 0.4],
-1606           [0.3, 1. , 0.2],
-1607           [0.4, 0.2, 1. ]])
-1608
-1609    """
-1610    kl_sorted = sorted(kl)
-1611
-1612    posd = {}
-1613    ofs = 0
-1614    for ki, k in enumerate(kl):
-1615        posd[k] = [i + ofs for i in range(len(yd[k]))]
-1616        ofs += len(posd[k])
-1617
-1618    mapping = []
-1619    for k in kl_sorted:
-1620        for i in range(len(yd[k])):
-1621            mapping.append(posd[k][i])
-1622
-1623    corr_sorted = np.zeros_like(corr)
-1624    for i in range(corr.shape[0]):
-1625        for j in range(corr.shape[0]):
-1626            corr_sorted[i][j] = corr[mapping[i]][mapping[j]]
-1627
-1628    return corr_sorted
+1578    The ordering of the input correlation matrix `corr` is given by the list of keys `kl`.
+1579    The input dictionary `yd` (with the same keys `kl`) must contain the corresponding y data
+1580    that the correlation matrix is based on.
+1581    This function sorts the list of keys `kl` alphabetically and sorts the matrix `corr`
+1582    according to this alphabetical order such that the sorted matrix `corr_sorted` corresponds
+1583    to the y data `yd` when arranged in an alphabetical order by its keys.
+1584
+1585    Parameters
+1586    ----------
+1587    corr : np.ndarray
+1588        A square correlation matrix constructed using the order of the y data specified by `kl`.
+1589        The dimensions of `corr` should match the total number of y data points in `yd` combined.
+1590    kl : list of str
+1591        A list of keys that denotes the order in which the y data from `yd` was used to build the
+1592        input correlation matrix `corr`.
+1593    yd : dict of list
+1594        A dictionary where each key corresponds to a unique identifier, and its value is a list of
+1595        y data points. The total number of y data points across all keys must match the dimensions
+1596        of `corr`. The lists in the dictionary can be lists of Obs.
+1597
+1598    Returns
+1599    -------
+1600    np.ndarray
+1601        A new, sorted correlation matrix that corresponds to the y data from `yd` when arranged alphabetically by its keys.
+1602
+1603    Example
+1604    -------
+1605    >>> import numpy as np
+1606    >>> import pyerrors as pe
+1607    >>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])
+1608    >>> kl = ['b', 'a']
+1609    >>> yd = {'a': [1, 2], 'b': [3]}
+1610    >>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)
+1611    >>> print(sorted_corr)
+1612    array([[1. , 0.3, 0.4],
+1613           [0.3, 1. , 0.2],
+1614           [0.4, 0.2, 1. ]])
+1615
+1616    """
+1617    kl_sorted = sorted(kl)
+1618
+1619    posd = {}
+1620    ofs = 0
+1621    for ki, k in enumerate(kl):
+1622        posd[k] = [i + ofs for i in range(len(yd[k]))]
+1623        ofs += len(posd[k])
+1624
+1625    mapping = []
+1626    for k in kl_sorted:
+1627        for i in range(len(yd[k])):
+1628            mapping.append(posd[k][i])
+1629
+1630    corr_sorted = np.zeros_like(corr)
+1631    for i in range(corr.shape[0]):
+1632        for j in range(corr.shape[0]):
+1633            corr_sorted[i][j] = corr[mapping[i]][mapping[j]]
+1634
+1635    return corr_sorted
 

 
 
@@ -6063,24 +6084,24 @@ of corr. The lists in the dictionary can be lists of Obs.
- 
1708def import_jackknife(jacks, name, idl=None):
-1709    """Imports jackknife samples and returns an Obs
-1710
-1711    Parameters
-1712    ----------
-1713    jacks : numpy.ndarray
-1714        numpy array containing the mean value as zeroth entry and
-1715        the N jackknife samples as first to Nth entry.
-1716    name : str
-1717        name of the ensemble the samples are defined on.
-1718    """
-1719    length = len(jacks) - 1
-1720    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
-1721    samples = jacks[1:] @ prj
-1722    mean = np.mean(samples)
-1723    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
-1724    new_obs._value = jacks[0]
-1725    return new_obs
+            
1715def import_jackknife(jacks, name, idl=None):
+1716    """Imports jackknife samples and returns an Obs
+1717
+1718    Parameters
+1719    ----------
+1720    jacks : numpy.ndarray
+1721        numpy array containing the mean value as zeroth entry and
+1722        the N jackknife samples as first to Nth entry.
+1723    name : str
+1724        name of the ensemble the samples are defined on.
+1725    """
+1726    length = len(jacks) - 1
+1727    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
+1728    samples = jacks[1:] @ prj
+1729    mean = np.mean(samples)
+1730    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
+1731    new_obs._value = jacks[0]
+1732    return new_obs
 

 
 
@@ -6110,34 +6131,34 @@ name of the ensemble the samples are defined on.
- 
1728def import_bootstrap(boots, name, random_numbers):
-1729    """Imports bootstrap samples and returns an Obs
-1730
-1731    Parameters
-1732    ----------
-1733    boots : numpy.ndarray
-1734        numpy array containing the mean value as zeroth entry and
-1735        the N bootstrap samples as first to Nth entry.
-1736    name : str
-1737        name of the ensemble the samples are defined on.
-1738    random_numbers : np.ndarray
-1739        Array of shape (samples, length) containing the random numbers to generate the bootstrap samples,
-1740        where samples is the number of bootstrap samples and length is the length of the original Monte Carlo
-1741        chain to be reconstructed.
-1742    """
-1743    samples, length = random_numbers.shape
-1744    if samples != len(boots) - 1:
-1745        raise ValueError("Random numbers do not have the correct shape.")
-1746
-1747    if samples < length:
-1748        raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.")
-1749
-1750    proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
-1751
-1752    samples = scipy.linalg.lstsq(proj, boots[1:])[0]
-1753    ret = Obs([samples], [name])
-1754    ret._value = boots[0]
-1755    return ret
+            
1735def import_bootstrap(boots, name, random_numbers):
+1736    """Imports bootstrap samples and returns an Obs
+1737
+1738    Parameters
+1739    ----------
+1740    boots : numpy.ndarray
+1741        numpy array containing the mean value as zeroth entry and
+1742        the N bootstrap samples as first to Nth entry.
+1743    name : str
+1744        name of the ensemble the samples are defined on.
+1745    random_numbers : np.ndarray
+1746        Array of shape (samples, length) containing the random numbers to generate the bootstrap samples,
+1747        where samples is the number of bootstrap samples and length is the length of the original Monte Carlo
+1748        chain to be reconstructed.
+1749    """
+1750    samples, length = random_numbers.shape
+1751    if samples != len(boots) - 1:
+1752        raise ValueError("Random numbers do not have the correct shape.")
+1753
+1754    if samples < length:
+1755        raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.")
+1756
+1757    proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
+1758
+1759    samples = scipy.linalg.lstsq(proj, boots[1:])[0]
+1760    ret = Obs([samples], [name])
+1761    ret._value = boots[0]
+1762    return ret
 

 
 
@@ -6171,38 +6192,46 @@ chain to be reconstructed.
- 
1758def merge_obs(list_of_obs):
-1759    """Combine all observables in list_of_obs into one new observable
-1760
-1761    Parameters
-1762    ----------
-1763    list_of_obs : list
-1764        list of the Obs object to be combined
-1765
-1766    Notes
-1767    -----
-1768    It is not possible to combine obs which are based on the same replicum
-1769    """
-1770    replist = [item for obs in list_of_obs for item in obs.names]
-1771    if (len(replist) == len(set(replist))) is False:
-1772        raise ValueError('list_of_obs contains duplicate replica: %s' % (str(replist)))
-1773    if any([len(o.cov_names) for o in list_of_obs]):
-1774        raise ValueError('Not possible to merge data that contains covobs!')
-1775    new_dict = {}
-1776    idl_dict = {}
-1777    for o in list_of_obs:
-1778        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
-1779                        for key in set(o.deltas) | set(o.r_values)})
-1780        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
-1781
-1782    names = sorted(new_dict.keys())
-1783    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
-1784    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
-1785    return o
+            
1765def merge_obs(list_of_obs):
+1766    """Combine all observables in list_of_obs into one new observable.
+1767    This allows to merge Obs that have been computed on multiple replica
+1768    of the same ensemble.
+1769    If you like to merge Obs that are based on several ensembles, please
+1770    average them yourself.
+1771
+1772    Parameters
+1773    ----------
+1774    list_of_obs : list
+1775        list of the Obs object to be combined
+1776
+1777    Notes
+1778    -----
+1779    It is not possible to combine obs which are based on the same replicum
+1780    """
+1781    replist = [item for obs in list_of_obs for item in obs.names]
+1782    if (len(replist) == len(set(replist))) is False:
+1783        raise ValueError('list_of_obs contains duplicate replica: %s' % (str(replist)))
+1784    if any([len(o.cov_names) for o in list_of_obs]):
+1785        raise ValueError('Not possible to merge data that contains covobs!')
+1786    new_dict = {}
+1787    idl_dict = {}
+1788    for o in list_of_obs:
+1789        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
+1790                        for key in set(o.deltas) | set(o.r_values)})
+1791        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
+1792
+1793    names = sorted(new_dict.keys())
+1794    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
+1795    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
+1796    return o
 

 
 
-            
Combine all observables in list_of_obs into one new observable

+            
Combine all observables in list_of_obs into one new observable.
+This allows to merge Obs that have been computed on multiple replica
+of the same ensemble.
+If you like to merge Obs that are based on several ensembles, please
+average them yourself.

 
 
Parameters

 
@@ -6229,47 +6258,47 @@ list of the Obs object to be combined
 
     

     
-            
1788def cov_Obs(means, cov, name, grad=None):
-1789    """Create an Obs based on mean(s) and a covariance matrix
-1790
-1791    Parameters
-1792    ----------
-1793    mean : list of floats or float
-1794        N mean value(s) of the new Obs
-1795    cov : list or array
-1796        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
-1797    name : str
-1798        identifier for the covariance matrix
-1799    grad : list or array
-1800        Gradient of the Covobs wrt. the means belonging to cov.
-1801    """
-1802
-1803    def covobs_to_obs(co):
-1804        """Make an Obs out of a Covobs
-1805
-1806        Parameters
-1807        ----------
-1808        co : Covobs
-1809            Covobs to be embedded into the Obs
-1810        """
-1811        o = Obs([], [], means=[])
-1812        o._value = co.value
-1813        o.names.append(co.name)
-1814        o._covobs[co.name] = co
-1815        o._dvalue = np.sqrt(co.errsq())
-1816        return o
-1817
-1818    ol = []
-1819    if isinstance(means, (float, int)):
-1820        means = [means]
-1821
-1822    for i in range(len(means)):
-1823        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
-1824    if ol[0].covobs[name].N != len(means):
-1825        raise ValueError('You have to provide %d mean values!' % (ol[0].N))
-1826    if len(ol) == 1:
-1827        return ol[0]
-1828    return ol
+            
1799def cov_Obs(means, cov, name, grad=None):
+1800    """Create an Obs based on mean(s) and a covariance matrix
+1801
+1802    Parameters
+1803    ----------
+1804    mean : list of floats or float
+1805        N mean value(s) of the new Obs
+1806    cov : list or array
+1807        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
+1808    name : str
+1809        identifier for the covariance matrix
+1810    grad : list or array
+1811        Gradient of the Covobs wrt. the means belonging to cov.
+1812    """
+1813
+1814    def covobs_to_obs(co):
+1815        """Make an Obs out of a Covobs
+1816
+1817        Parameters
+1818        ----------
+1819        co : Covobs
+1820            Covobs to be embedded into the Obs
+1821        """
+1822        o = Obs([], [], means=[])
+1823        o._value = co.value
+1824        o.names.append(co.name)
+1825        o._covobs[co.name] = co
+1826        o._dvalue = np.sqrt(co.errsq())
+1827        return o
+1828
+1829    ol = []
+1830    if isinstance(means, (float, int)):
+1831        means = [means]
+1832
+1833    for i in range(len(means)):
+1834        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
+1835    if ol[0].covobs[name].N != len(means):
+1836        raise ValueError('You have to provide %d mean values!' % (ol[0].N))
+1837    if len(ol) == 1:
+1838        return ol[0]
+1839    return ol
 

 
 
diff --git a/docs/search.js b/docs/search.js
index 34f59c0f..7a26d026 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
\n\n
    \n
  • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
    • \n
  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
    • \n
  • coherent error propagation for data from different Markov chains.
    • \n
  • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
    • \n
  • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
    • \n
\n\n
More detailed examples can found in the GitHub repository \"badge\".
\n\n
If you use pyerrors for research that leads to a publication please consider citing:
\n\n
    \n
  • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
    • \n
  • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
    • \n
  • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
    • \n
\n\n
and
\n\n
    \n
  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
    • \n
\n\n
where applicable.
\n\n
There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
\n\n
Installation
\n\n
Install the most recent release using pip and pypi:
\n\n
\n
python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
\n
\n\n
Install the most recent release using conda and conda-forge:
\n\n
\n
conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
\n
\n\n
Install the current develop version:
\n\n
\n
python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
\n
\n\n
(Also works for any feature branch).
\n\n
Basic example
\n\n
\n
import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
\n
\n\n
The Obs class
\n\n
pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
\n\n
\n
import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
\n
\n\n
Error propagation
\n\n
When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
\n\n
The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
\n\n
\n
import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
\n
\n\n
Error estimation
\n\n
The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
\n\n
\n
my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
\n
\n\n
The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
\n\n
We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
\n\n
\n
my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
\n
\n\n
The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
\n\n
If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
\n\n
Exponential tails
\n\n
Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
\n\n
\n
my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
\n
\n\n
For the full API see pyerrors.obs.Obs.gamma_method.
\n\n
Multiple ensembles/replica
\n\n
Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
\n\n
\n
obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
\n
\n\n
Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
\n\n
pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
\n\n
\n
obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
\n
\n\n
Error estimation for multiple ensembles
\n\n
In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
\n\n
\n
pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
\n
\n\n
In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
\n\n
Irregular Monte Carlo chains
\n\n
Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
\n\n
\n
# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
\n
\n\n
Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
\n\n
Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
\n\n
For the full API see pyerrors.obs.Obs.
\n\n
Correlators
\n\n
When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
\n\n
\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
\n
\n\n
In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
\n\n
\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
\n
\n\n
The individual entries of a correlator can be accessed via slicing
\n\n
\n
print(my_corr[3])\n> 0.3227(33)\n
\n
\n\n
Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
\n\n
\n
my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
\n
\n\n
pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
\n\n
    \n
  • Corr.gamma_method applies the gamma method to all entries of the correlator.
    • \n
  • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
    • \n
  • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
    • \n
  • Corr.plateau extracts a plateau value from the correlator in a given range.
    • \n
  • Corr.roll periodically shifts the correlator.
    • \n
  • Corr.reverse reverses the time ordering of the correlator.
    • \n
  • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
    • \n
  • Corr.reweight reweights the correlator.
    • \n
\n\n
pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
\n\n
For the full API see pyerrors.correlators.Corr.
\n\n
Complex valued observables
\n\n
pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
\n\n
\n
my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
\n
\n\n
Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
\n\n
\n
my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
\n
\n\n
The Covobs class
\n\n
In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
\n\n
This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
\n\n
\n
import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
\n
\n\n
The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
\n\n
Correlated auxiliary data is defined similarly to above, e.g., via
\n\n
\n
RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
\n
\n\n
where RAP now is a list of two Obs that contains the two correlated parameters.
\n\n
Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
\n\n
\n
o.covobs[k].grad\n
\n
\n\n
Error propagation in iterative algorithms
\n\n
pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
\n\n
Least squares fits
\n\n
Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
\n\n
Fit functions have to be of the following form
\n\n
\n
import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
\n
\n\n
It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
\n\n
Fits can then be performed via
\n\n
\n
fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
\n
\n\n
where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
\n\n
Data stored in Corr objects can be fitted directly using the Corr.fit method.
\n\n
\n
my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
\n
\n\n
this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
\n\n
For fit functions with multiple independent variables the fit function can be of the form
\n\n
\n
def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
\n
\n\n
pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
\n\n
For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
\n\n
Total least squares fits
\n\n
pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
\n\n
For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
\n\n
Matrix operations
\n\n
pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
\n\n
    \n
  • inv for the matrix inverse.
    • \n
  • cholseky for the Cholesky decomposition.
    • \n
  • det for the matrix determinant.
    • \n
  • eigh for eigenvalues and eigenvectors of hermitean matrices.
    • \n
  • eig for eigenvalues of general matrices.
    • \n
  • pinv for the Moore-Penrose pseudoinverse.
    • \n
  • svd for the singular-value-decomposition.
    • \n
\n\n
For the full API see pyerrors.linalg.
\n\n
Export data
\n\n
\n\n
The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
\n\n
    \n
  • What observables are stored? Possibly: How exactly are they defined.
    • \n
  • How does each single ensemble or external quantity contribute to the error of the observable?
    • \n
  • Who did write the file when and on which machine?
    • \n
\n\n
This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
\n\n
\n
my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
\n
\n\n
The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
\n\n
json.gz format specification
\n\n
The first entries of the file provide optional auxiliary information:
\n\n
    \n
  • program is a string that indicates which program was used to write the file.
    • \n
  • version is a string that specifies the version of the format.
    • \n
  • who is a string that specifies the user name of the creator of the file.
    • \n
  • date is a string and contains the creation date of the file.
    • \n
  • host is a string and contains the hostname of the machine where the file has been written.
    • \n
  • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
    • \n
\n\n
The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
\n\n
Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
\n\n
    \n
  • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
    • \n
  • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
    • \n
  • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
    • \n
  • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
    • \n
  • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
    • \n
  • data is an array that contains the data from MC chains. We will define it below.
    • \n
  • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
    • \n
\n\n
The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
\n\n
    \n
  • id, a string that contains the name of the ensemble
    • \n
  • replica, an array that contains an entry per replica of the ensemble.
    • \n
\n\n
Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
\n\n
Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
\n\n
The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
\n\n
    \n
  • id, a string that identifies the covariance matrix
    • \n
  • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
    • \n
  • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
    • \n
  • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
    • \n
\n\n
A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
\n\n
Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
The class for a correlator (time dependent sequence of pe.Obs).
\n\n
Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
\n\n
The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.
\n\n
The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.
\n\n
Initialization
\n\n
A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs
\n\n
\n
corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
\n
\n\n
A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects
\n\n
\n
matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
\n
\n\n
or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.
\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
Initialize a Corr object.
\n\n
Parameters
\n\n
    \n
  • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
    • \n
  • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
    • \n
  • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.
    • \n
\n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
Apply the gamma method to the content of the Corr.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
Apply the gamma method to the content of the Corr.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
We need to project the Correlator with a Vector to get a single value at each timeslice.
\n\n
The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
\n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
\n\n
Parameters
\n\n
    \n
  • i (int):\nFirst index to be picked.
    • \n
  • j (int):\nSecond index to be picked.
    • \n
\n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
Outputs the correlator in a plotable format.
\n\n
Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
Symmetrize the correlator around x0=0.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
Anti-symmetrize the correlator around x0=0.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
Checks whether a correlator matrices is symmetric on every timeslice.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "
Calculates the per-timeslice trace of a correlator matrix.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
Symmetrizes the correlator matrices on every timeslice.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
\n\n
The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
\n\n
\n
C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
\n
\n\n
Parameters
\n\n
    \n
  • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
    • \n
  • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
    • \n
  • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
      \n
    • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
      • \n
    • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
      • \n
    • None: The GEVP is solved only at ts, no sorting is necessary
      • \n
    • \n
  • vector_obs (bool):\nIf True, uncertainties are propagated in the eigenvector computation (default False).
    • \n
\n\n
Other Parameters
\n\n
    \n
  • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
    • \n
  • method (str):\nMethod used to solve the GEVP.\n
      \n
    • \"eigh\": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
      • \n
    • \"cholesky\": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
      • \n
    • \n
\n", "signature": "(self, t0, ts=None, sort='Eigenvalue', vector_obs=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
Determines the eigenvalue of the GEVP by solving and projecting the correlator
\n\n
Parameters
\n\n
    \n
  • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
    • \n
  • All other parameters are identical to the ones of Corr.GEVP.
    • \n
\n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
Constructs an NxN Hankel matrix
\n\n
C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
\n\n
Parameters
\n\n
    \n
  • N (int):\nDimension of the Hankel matrix
    • \n
  • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
    • \n
\n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
Periodically shift the correlator by dt timeslices
\n\n
Parameters
\n\n
    \n
  • dt (int):\nnumber of timeslices
    • \n
\n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
Reverse the time ordering of the Corr
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
Thin out a correlator to suppress correlations
\n\n
Parameters
\n\n
    \n
  • spacing (int):\nKeep only every 'spacing'th entry of the correlator
    • \n
  • offset (int):\nOffset the equal spacing
    • \n
\n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
Correlate the correlator with another correlator or Obs
\n\n
Parameters
\n\n
    \n
  • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
    • \n
\n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
Reweight the correlator.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
Return the time symmetry average of the correlator and its partner
\n\n
Parameters
\n\n
    \n
  • partner (Corr):\nTime symmetry partner of the Corr
    • \n
  • parity (int):\nParity quantum number of the correlator, can be +1 or -1
    • \n
\n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
Return the first derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
Return the second derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
Returns the effective mass of the correlator as correlator object
\n\n
Parameters
\n\n
    \n
  • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
    • \n
  • guess (float):\nguess for the root finder, only relevant for the root variant
    • \n
\n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
Fits function to the data
\n\n
Parameters
\n\n
    \n
  • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
    • \n
  • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
    • \n
  • silent (bool):\nDecides whether output is printed to the standard output.
    • \n
\n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
Extract a plateau value from a Corr object
\n\n
Parameters
\n\n
    \n
  • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
    • \n
  • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
    • \n
  • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
    • \n
\n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
Sets the attribute prange of the Corr object.
\n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
Plots the correlator using the tag of the correlator as label if available.
\n\n
Parameters
\n\n
    \n
  • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
    • \n
  • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
    • \n
  • logscale (bool):\nSets y-axis to logscale.
    • \n
  • plateau (Obs):\nPlateau value to be visualized in the figure.
    • \n
  • fit_res (Fit_result):\nFit_result object to be visualized.
    • \n
  • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
    • \n
  • ylabel (str):\nLabel for the y-axis.
    • \n
  • save (str):\npath to file in which the figure should be saved.
    • \n
  • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
    • \n
  • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
    • \n
  • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
    • \n
  • title (string):\nOptional title of the figure.
    • \n
\n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\n
Parameters
\n\n
    \n
  • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
    • \n
\n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
Dumps the Corr into a file of chosen type
\n\n
Parameters
\n\n
    \n
  • filename (str):\nName of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
\n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
Project large correlation matrix to lowest states
\n\n
This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
\n\n
Parameters
\n\n
    \n
  • Ntrunc (int):\nRank of the target matrix.
    • \n
  • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
    • \n
  • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
    • \n
  • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
    • \n
\n\n
Notes
\n\n
We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
Initialize Covobs object.
\n\n
Parameters
\n\n
    \n
  • mean (float):\nMean value of the new Obs
    • \n
  • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
Return the variance (= square of the error) of the Covobs
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
\n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
\n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
\n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
\n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
\n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
Rank-3 epsilon tensor
\n\n
Based on https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
    • \n
\n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
Rank-4 epsilon tensor
\n\n
Extension of https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
    • \n
\n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
Represents fit results.
\n\n
Attributes
\n\n
    \n
  • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
    • \n
  • chisquare_by_dof (float):\nreduced chisquare.
    • \n
  • p_value (float):\np-value of the fit
    • \n
  • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
    • \n
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
\n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x).\n    ```
\n\n
Parameters
\n\n
    \n
  • For an uncombined fit:
    • \n
  • x (list):\nlist of floats.
    • \n
  • y (list):\nlist of Obs.
    • \n
  • func (object):\nfit function, has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • OR For a combined fit:
    • \n
  • x (dict):\ndict of lists.
    • \n
  • y (dict):\ndict of lists of Obs.
    • \n
  • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n        \"b\": func_b}
    \n\n
    def func_a(a, x):\n    return a[1] * anp.exp(-a[0] * x)
    \n\n
    def func_b(a, x):\n    return a[2] * anp.exp(-a[0] * x)
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
    • \n
  • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
    • \n
  • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
    • \n
  • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
    • \n
  • inv_chol_cov_matrix [array,list], optional: array: shape = (no of y values) X (no of y values)\nlist:   for an uncombined fit: [\"\"]\nfor a combined fit: list of keys belonging to the corr_matrix saved in the array, must be the same as the keys of the y dict in alphabetical order\nIf correlated_fit=True is set as well, can provide an inverse covariance matrix (y errors, dy_f included!) of your own choosing for a correlated fit.\nThe matrix must be a lower triangular matrix constructed from a Cholesky decomposition: The function invert_corr_cov_cholesky(corr, inverrdiag) can be\nused to construct it from a correlation matrix (corr) and the errors dy_f of the data points (inverrdiag = np.diag(1 / np.asarray(dy_f))). For the correct\nordering the correlation matrix (corr) can be sorted via the function sort_corr(corr, kl, yd) where kl is the list of keys and yd the y dict.
    • \n
  • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
    • \n
  • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
    • \n
  • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n\n
Examples
\n\n
\n
>>> # Example of a correlated (correlated_fit = True, inv_chol_cov_matrix handed over) combined fit, based on a randomly generated data set\n>>> import numpy as np\n>>> from scipy.stats import norm\n>>> from scipy.linalg import cholesky\n>>> import pyerrors as pe\n>>> # generating the random data set\n>>> num_samples = 400\n>>> N = 3\n>>> x = np.arange(N)\n>>> x1 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> x2 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> r = r1 = r2 = np.zeros((N, N))\n>>> y = {}\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] = np.exp(-0.8 * np.fabs(i - j)) # element in correlation matrix\n>>> errl = np.sqrt([3.4, 2.5, 3.6]) # set y errors\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] *= errl[i] * errl[j] # element in covariance matrix\n>>> c = cholesky(r, lower=True)\n>>> y = {'a': np.dot(c, x1), 'b': np.dot(c, x2)} # generate y data with the covariance matrix defined\n>>> # random data set has been generated, now the dictionaries and the inverse covariance matrix to be handed over are built\n>>> x_dict = {}\n>>> y_dict = {}\n>>> chol_inv_dict = {}\n>>> data = []\n>>> for key in y.keys():\n>>>    x_dict[key] = x\n>>>    for i in range(N):\n>>>        data.append(pe.Obs([[i + 1 + o for o in y[key][i]]], ['ens'])) # generate y Obs from the y data\n>>>    [o.gamma_method() for o in data]\n>>>    corr = pe.covariance(data, correlation=True)\n>>>    inverrdiag = np.diag(1 / np.asarray([o.dvalue for o in data]))\n>>>    chol_inv = pe.obs.invert_corr_cov_cholesky(corr, inverrdiag) # gives form of the inverse covariance matrix needed for the combined correlated fit below\n>>> y_dict = {'a': data[:3], 'b': data[3:]}\n>>> # common fit parameter p[0] in combined fit\n>>> def fit1(p, x):\n>>>    return p[0] + p[1] * x\n>>> def fit2(p, x):\n>>>    return p[0] + p[2] * x\n>>> fitf_dict = {'a': fit1, 'b':fit2}\n>>> fitp_inv_cov_combined_fit = pe.least_squares(x_dict,y_dict, fitf_dict, correlated_fit = True, inv_chol_cov_matrix = [chol_inv,['a','b']])\nFit with 3 parameters\nMethod: Levenberg-Marquardt\n`ftol` termination condition is satisfied.\nchisquare/d.o.f.: 0.5388013574561786 # random\nfit parameters [1.11897846 0.96361162 0.92325319] # random\n
\n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of Obs, or a tuple of lists of Obs
    • \n
  • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
    • \n
  • func (object):\nfunc has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
    • \n
  • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy.
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n\n
Returns
\n\n
    \n
  • fit_parameters (list[Obs]):\nLIist of fitted observables.
    • \n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n\n
For uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\n
Returns
\n\n
    \n
  • err (np.array(Obs)):\nError band for an array of sample values x
    • \n
\n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\n
Jackknife samples
\n\n
For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
Extract generic MCMC data from a bdio file
\n\n
read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • data (List[Obs]):\nExtracted data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
Write Obs to a bdio file according to ADerrors conventions
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • success (int):\nreturns 0 is successful
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
Extract mesons data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n\n
Returns
\n\n
    \n
  • data (dict):\nExtracted meson data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
Extract dSdm data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, kappa)
\n\n
read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML formatted string of the input data
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
Import a list of Obs from a string in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator |is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML string generated from the data
    • \n
\n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
Read hadrons hdf5 file and extract entry based on attributes.
\n\n
Parameters
\n\n
    \n
  • filestem (str):\nFull namestem of the files to read, including the full path.
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • group (str):\nlabel of the group to be extracted.
    • \n
  • attrs (dict or int):\nDictionary containing the attributes. For example
    \n\n
    \n
    attrs = {"gamma_snk": "Gamma5",\n         "gamma_src": "Gamma5"}\n
    \n
    \n\n
    Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
Read hadrons FlowObservables hdf5 file and extract t0
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
Read hadrons DistillationContraction hdf5 files in given directory structure
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
    • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
\n\n
An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\n
Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\n
For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n
array:  Construct an array.
\nzeros:  Create an array, each element of which is zero.
\nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype:  Create a data-type.
\nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
\n\n
Notes
\n\n
There are two modes of creating an array using __new__:
\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n
No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\n
Examples
\n\n
These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\n
First mode, buffer is None:
\n\n
\n
>>> import numpy as np\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n
\n\n
Second mode:
\n\n
\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
Gamma_5 hermitean conjugate
\n\n
Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
Read hadrons ExternalLeg hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Npr_matrix):\nread Cobs-matrix
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
Read hadrons Bilinear hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict[Npr_matrix]):\nextracted Bilinears
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • vertices (list):\nVertex functions to be extracted.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict):\nextracted fourquark matrizes
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
\n\n
Returns
\n\n
    \n
  • json_string (str):\nString for export to .json(.gz) file
    • \n
\n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • Null
    • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
Reconstruct a list of Obs or structures containing Obs from a json string.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
Import a list of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
Export a dict of Obs or structures containing Obs to a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
Import a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
    • \n
\n\n
Returns
\n\n
    \n
  • data (Obs / list / Corr):\nRead data
    • \n
  • or
    • \n
  • data (dict):\nRead data and meta-data
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
\n\n
It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
\n\n
A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
\n\n
Parameters
\n\n
    \n
  • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
    • \n
  • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
    • \n
\n\n
Returns
\n\n
    \n
  • root (Obs):\nThe root of the data series.
    • \n
\n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
Read pbp format from given folder structure.
\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of observables read
    • \n
\n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
Read rwms format from given folder structure. Returns a list of length nrw
\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
    • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
    • \n
  • version (str):\nversion of openQCD, default 2.0
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
    • \n
\n\n
Returns
\n\n
    \n
  • rwms (Obs):\nReweighting factors read
    • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • t0 (Obs):\nExtracted t0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
Extract w0/a from given .ms.dat files. Returns w0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • w0 (Obs):\nExtracted w0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
Read the topologial charge based on openQCD gradient flow measurements.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Obs):\nRead topological charge
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
\n\n
Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
Returns the projection to the topological charge sector defined by target.
\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
Constructs reweighting factors to a specified topological sector.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
    • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
\n\n
Parameters
\n\n
    \n
  • path (str):\nThe directory to search for the files in.
    • \n
  • prefix (str):\nThe prefix to match the files against.
    • \n
  • qc (str):\nThe quark combination extension to match the files against.
    • \n
  • corr (str):\nThe correlator to extract data for.
    • \n
  • sep (str, optional):\nThe separator to use when parsing the replika names.
    • \n
  • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
    \n\n
      \n
    • names (List[str]): A list of names to use for the replicas.
      • \n
    • files (List[str]): A list of files to read data from.
      • \n
    • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
      • \n
    • \n
\n\n
Returns
\n\n
    \n
  • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
    • \n
  • or
    • \n
  • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
    • \n
\n\n
Raises
\n\n
    \n
  • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
    • \n
  • IOError: If there is an error reading a file.
    • \n
  • struct.error: If there is an error unpacking binary data.
    • \n
\n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
Write DataFrame including Obs or Corr valued columns to sqlite database.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be written to the database.
    • \n
  • table_name (str):\nName of the table in the database.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
    • \n
  • gz (bool):\nIf True the json strings are gzipped.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
\n\n
Parameters
\n\n
    \n
  • sql (str):\nSQL query to be executed.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
\n\n
Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be dumped to a file.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
\n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
\n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
    • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks_list (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type_list (list[str]):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset_list (list[int]):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf_list (int):\nID of wave function
    • \n
  • wf2_list (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list[list[int]]):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
  • rep_string (str):\nSeparator of ensemble name and replicum. Example: In \"ensAr0\", \"r\" would be the separator string.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]
    • \n
\n", "signature": "(\tpath,\tprefix,\tname_list,\tquarks_list=['.*'],\tcorr_type_list=['bi'],\tnoffset_list=[0],\twf_list=[0],\twf2_list=[0],\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\tkeyed_out=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
Utilities for the input
\n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
\n\n
Parameters
\n\n
    \n
  • ll (list):\nlist to sort
    • \n
\n\n
Returns
\n\n
    \n
  • ll (list):\nsorted list
    • \n
\n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
Checks if list of configurations is contained in an idl
\n\n
Parameters
\n\n
    \n
  • idl (range or list):\nidl of the current replicum
    • \n
  • che (list):\nlist of configurations to be checked against
    • \n
\n\n
Returns
\n\n
    \n
  • miss_str (str):\nstring with integers of which idls are missing
    • \n
\n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "
Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
\n\n
Parameters
\n\n
    \n
  • path (str):\nmeasurement path, same as for sfcf read method
    • \n
  • param_hash (str):\nexpected parameter hash
    • \n
  • prefix (str):\ndata prefix to find the appropriate replicum folders in path
    • \n
  • param_prefix (str):\nprefix of the parameter file. Defaults to 'parameters_'
    • \n
\n\n
Returns
\n\n
    \n
  • nums (dict):\ndictionary of faulty parameter files sorted by the replica paths
    • \n
\n", "signature": "(path, param_hash, prefix, param_prefix='parameters_'):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
\n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
\n\n
The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
\n\n
Parameters
\n\n
    \n
  • func (object):\nfunction to integrate, has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(p, x):\n    return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
    \n
    \n\n
    where x is the integration variable.
    • \n
  • p (list of floats or Obs):\nparameters of the function func.
    • \n
  • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
    • \n
  • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
    • \n
  • All parameters of scipy.integrate.quad
    • \n
\n\n
Returns
\n\n
    \n
  • y (Obs):\nThe integral of func from a to b.
    • \n
  • abserr (float):\nAn estimate of the absolute error in the result.
    • \n
  • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
    • \n
  • message: A convergence message.
    • \n
  • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
    • \n
\n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
Matrix multiply all operands.
\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • This implementation is faster compared to standard multiplication via the @ operator.
    • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
Matrix multiply both operands making use of the jackknife approximation.
\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • For large matrices this is considerably faster compared to matmul.
    • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
Wrapper for numpy.einsum
\n\n
Parameters
\n\n
    \n
  • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
    • \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
\n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
Inverse of Obs or CObs valued matrices.
\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
Cholesky decomposition of Obs valued matrices.
\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
Determinant of Obs valued matrices.
\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eigv": {"fullname": "pyerrors.linalg.eigv", "modulename": "pyerrors.linalg", "qualname": "eigv", "kind": "function", "doc": "
Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
Computes the singular value decomposition of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
Print information about version of python, pyerrors and dependencies.
\n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
pyerrors wrapper for the errorbars method of matplotlib
\n\n
Parameters
\n\n
    \n
  • x (list):\nA list of x-values which can be Obs.
    • \n
  • y (list):\nA list of y-values which can be Obs.
    • \n
  • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
    • \n
\n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.16/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
Dump object into pickle file.
\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
    • \n
  • name (str):\nname of the file
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
Load object from pickle file.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n\n
Returns
\n\n
    \n
  • object (Obs):\nLoaded Object
    • \n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
Generate an Obs object with given value, dvalue and name for test purposes
\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
    • \n
  • dvalue (float):\nerror of the Obs to be generated.
    • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
    • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nGenerated Observable
    • \n
\n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
Generate observables with given covariance and autocorrelation times.
\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
    • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
    • \n
  • name (str):\nensemble name for the data to be geneated.
    • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
    • \n
  • samples (int):\nnumber of samples to be generated for each observable.
    • \n
\n\n
Returns
\n\n
    \n
  • corr_obs (list[Obs]):\nGenerated observable list
    • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
Matrix pencil method to extract k energy levels from data
\n\n
Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
    • \n
  • k (int):\nNumber of states to extract (default 1).
    • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
    • \n
\n\n
Returns
\n\n
    \n
  • energy_levels (list[Obs]):\nExtracted energy levels
    • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
Class for a general observable.
\n\n
Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
    • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
    • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
    • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
    • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
Initialize Obs object.
\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
    • \n
  • names (list):\nlist of strings labeling the individual samples
    • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
    • \n
\n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
Output detailed properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
    • \n
\n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
Reweight the obs with given rewighting factors.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
Checks whether the observable is zero within 'sigma' standard errors.
\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
    • \n
  • Works only properly when the gamma method was run.
    • \n
\n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
Checks whether the observable is zero within a given tolerance.
\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
    • \n
\n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
Plot integrated autocorrelation time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
Plot normalized autocorrelation function time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
Plot replica distribution for each ensemble with more than one replicum.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
Plot derived Monte Carlo history for each ensemble
\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
    • \n
\n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
Dump the Obs to a file 'name' of chosen format.
\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
Export jackknife samples from the Obs
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
    • \n
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
Export bootstrap samples from the Obs
\n\n
Parameters
\n\n
    \n
  • samples (int):\nNumber of bootstrap samples to generate.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
    • \n
  • save_rng (str):\nSave the random numbers to a file if a path is specified.
    • \n
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
    • \n
\n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
\n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
Executes the gamma_method for the real and the imaginary part.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
Checks whether both real and imaginary part are zero within machine precision.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
Vectorized version of the gamma_method applicable to lists or arrays of Obs.
\n\n
See docstring of pe.Obs.gamma_method for details.
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
Vectorized version of the gamma_method applicable to lists or arrays of Obs.
\n\n
See docstring of pe.Obs.gamma_method for details.
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
\n\n
Parameters
\n\n
    \n
  • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
    • \n
  • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
    • \n
  • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
    • \n
\n\n
Notes
\n\n
For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\n
new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
\n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
Reweight a list of observables.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
Correlate two observables.
\n\n
Parameters
\n\n
    \n
  • obs_a (Obs):\nFirst observable
    • \n
  • obs_b (Obs):\nSecond observable
    • \n
\n\n
Notes
\n\n
Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
\n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
Calculates the error covariance matrix of a set of observables.
\n\n
WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
\n\n
The gamma method has to be applied first to all observables.
\n\n
Parameters
\n\n
    \n
  • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
    • \n
  • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
    • \n
  • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
    • \n
  • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
    • \n
\n\n
Notes
\n\n
The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.invert_corr_cov_cholesky": {"fullname": "pyerrors.obs.invert_corr_cov_cholesky", "modulename": "pyerrors.obs", "qualname": "invert_corr_cov_cholesky", "kind": "function", "doc": "
Constructs a lower triangular matrix chol via the Cholesky decomposition of the correlation matrix corr\n   and then returns the inverse covariance matrix chol_inv as a lower triangular matrix by solving chol * x = inverrdiag.
\n\n
Parameters
\n\n
    \n
  • corr (np.ndarray):\ncorrelation matrix
    • \n
  • inverrdiag (np.ndarray):\ndiagonal matrix, the entries are the inverse errors of the data points considered
    • \n
\n", "signature": "(corr, inverrdiag):", "funcdef": "def"}, "pyerrors.obs.sort_corr": {"fullname": "pyerrors.obs.sort_corr", "modulename": "pyerrors.obs", "qualname": "sort_corr", "kind": "function", "doc": "
Reorders a correlation matrix to match the alphabetical order of its underlying y data.
\n\n
The ordering of the input correlation matrix corr is given by the list of keys kl.\nThe input dictionary yd (with the same keys kl) must contain the corresponding y data\nthat the correlation matrix is based on.\nThis function sorts the list of keys kl alphabetically and sorts the matrix corr\naccording to this alphabetical order such that the sorted matrix corr_sorted corresponds\nto the y data yd when arranged in an alphabetical order by its keys.
\n\n
Parameters
\n\n
    \n
  • corr (np.ndarray):\nA square correlation matrix constructed using the order of the y data specified by kl.\nThe dimensions of corr should match the total number of y data points in yd combined.
    • \n
  • kl (list of str):\nA list of keys that denotes the order in which the y data from yd was used to build the\ninput correlation matrix corr.
    • \n
  • yd (dict of list):\nA dictionary where each key corresponds to a unique identifier, and its value is a list of\ny data points. The total number of y data points across all keys must match the dimensions\nof corr. The lists in the dictionary can be lists of Obs.
    • \n
\n\n
Returns
\n\n
    \n
  • np.ndarray: A new, sorted correlation matrix that corresponds to the y data from yd when arranged alphabetically by its keys.
    • \n
\n\n
Example
\n\n
\n
>>> import numpy as np\n>>> import pyerrors as pe\n>>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])\n>>> kl = ['b', 'a']\n>>> yd = {'a': [1, 2], 'b': [3]}\n>>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)\n>>> print(sorted_corr)\narray([[1. , 0.3, 0.4],\n       [0.3, 1. , 0.2],\n       [0.4, 0.2, 1. ]])\n
\n
\n", "signature": "(corr, kl, yd):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
Imports jackknife samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
\n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
Imports bootstrap samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
    • \n
\n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
Combine all observables in list_of_obs into one new observable
\n\n
Parameters
\n\n
    \n
  • list_of_obs (list):\nlist of the Obs object to be combined
    • \n
\n\n
Notes
\n\n
It is not possible to combine obs which are based on the same replicum
\n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
Create an Obs based on mean(s) and a covariance matrix
\n\n
Parameters
\n\n
    \n
  • mean (list of floats or float):\nN mean value(s) of the new Obs
    • \n
  • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
Finds the root of the function func(x, d) where d is an Obs.
\n\n
Parameters
\n\n
    \n
  • d (Obs):\nObs passed to the function.
    • \n
  • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
    \n\n
    \n
    import autograd.numpy as anp\ndef root_func(x, d):\n    return anp.exp(-x ** 2) - d\n
    \n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nObs valued root of the function.
    • \n
\n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.special": {"fullname": "pyerrors.special", "modulename": "pyerrors.special", "kind": "module", "doc": "
\n"}, "pyerrors.special.beta": {"fullname": "pyerrors.special.beta", "modulename": "pyerrors.special", "qualname": "beta", "kind": "function", "doc": "
beta(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
beta(a, b, out=None)
\n\n
Beta function.
\n\n
This function is defined in 1 as
\n\n
$$B(a, b) = \\int_0^1 t^{a-1}(1-t)^{b-1}dt\n        = \\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a+b)},$$
\n\n
where \\( \\Gamma \\) is the gamma function.
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nReal-valued arguments
    • \n
  • out (ndarray, optional):\nOptional output array for the function result
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the beta function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\nbetainc:   the regularized incomplete beta function
\nbetaln:  the natural logarithm of the absolute\nvalue of the beta function  
\n\n
References
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
The beta function relates to the gamma function by the\ndefinition given above:
\n\n
\n
>>> sc.beta(2, 3)\n0.08333333333333333\n>>> sc.gamma(2)*sc.gamma(3)/sc.gamma(2 + 3)\n0.08333333333333333\n
\n
\n\n
As this relationship demonstrates, the beta function\nis symmetric:
\n\n
\n
>>> sc.beta(1.7, 2.4)\n0.16567527689031739\n>>> sc.beta(2.4, 1.7)\n0.16567527689031739\n
\n
\n\n
This function satisfies \\( B(1, b) = 1/b \\):
\n\n
\n
>>> sc.beta(1, 4)\n0.25\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions,\nEq. 5.12.1. https://dlmf.nist.gov/5.12 ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betainc": {"fullname": "pyerrors.special.betainc", "modulename": "pyerrors.special", "qualname": "betainc", "kind": "function", "doc": "
betainc(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
betainc(a, b, x, out=None)
\n\n
Regularized incomplete beta function.
\n\n
Computes the regularized incomplete beta function, defined as 1:
\n\n
$$I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\nt^{a-1}(1-t)^{b-1}dt,$$
\n\n
for \\( 0 \\leq x \\leq 1 \\).
\n\n
This function is the cumulative distribution function for the beta\ndistribution; its range is [0, 1].
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nPositive, real-valued parameters
    • \n
  • x (array_like):\nReal-valued such that \\( 0 \\leq x \\leq 1 \\),\nthe upper limit of integration
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the regularized incomplete beta function
    • \n
\n\n
See Also
\n\n
beta:  beta function
\nbetaincinv:  inverse of the regularized incomplete beta function
\nbetaincc:  complement of the regularized incomplete beta function
\nscipy.stats.beta:  beta distribution  
\n\n
Notes
\n\n
The term regularized in the name of this function refers to the\nscaling of the function by the gamma function terms shown in the\nformula.  When not qualified as regularized, the name incomplete\nbeta function often refers to just the integral expression,\nwithout the gamma terms.  One can use the function beta from\nscipy.special to get this \"nonregularized\" incomplete beta\nfunction by multiplying the result of betainc(a, b, x) by\nbeta(a, b).
\n\n
This function wraps the ibeta routine from the\nBoost Math C++ library 2.
\n\n
References
\n\n
Examples
\n\n
Let \\( B(a, b) \\) be the beta function.
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
The coefficient in terms of gamma is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).
\n\n
\n
>>> sc.betainc(0.2, 3.5, 1.0)\n1.0\n
\n
\n\n
It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function hyp2f1:
\n\n
\n
>>> a, b, x = 1.4, 3.1, 0.5\n>>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n0.8148904036225295\n>>> sc.betainc(a, b, x)\n0.8148904036225296\n
\n
\n\n
This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):
\n\n
\n
>>> sc.betainc(2.2, 3.1, 0.4)\n0.49339638807619446\n>>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n0.49339638807619446\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/8.17 ↩
    \n
    2. \n\n
  2. \n
    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "
betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
betaln(a, b, out=None)
\n\n
Natural logarithm of absolute value of beta function.
\n\n
Computes ln(abs(beta(a, b))).
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nPositive, real-valued parameters
    • \n
  • out (ndarray, optional):\nOptional output array for function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the betaln function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\nbetainc:   the regularized incomplete beta function
\nbeta:  the beta function  
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import betaln, beta\n
\n
\n\n
Verify that, for moderate values of a and b, betaln(a, b)\nis the same as log(beta(a, b)):
\n\n
\n
>>> betaln(3, 4)\n-4.0943445622221\n
\n
\n\n
\n
>>> np.log(beta(3, 4))\n-4.0943445622221\n
\n
\n\n
In the following beta(a, b) underflows to 0, so we can't compute\nthe logarithm of the actual value.
\n\n
\n
>>> a = 400\n>>> b = 900\n>>> beta(a, b)\n0.0\n
\n
\n\n
We can compute the logarithm of beta(a, b) by using betaln:
\n\n
\n
>>> betaln(a, b)\n-804.3069951764146\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "
Polygamma functions.
\n\n
Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\ndigamma function. See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • n (array_like):\nThe order of the derivative of the digamma function; must be\nintegral
    • \n
  • x (array_like):\nReal valued input
    • \n
\n\n
Returns
\n\n
    \n
  • ndarray: Function results
    • \n
\n\n
See Also
\n\n
digamma  
\n\n
References
\n\n
.. [dlmf] NIST, Digital Library of Mathematical Functions,\n    https://dlmf.nist.gov/5.15
\n\n
Examples
\n\n
\n
>>> from scipy import special\n>>> x = [2, 3, 25.5]\n>>> special.polygamma(1, x)\narray([ 0.64493407,  0.39493407,  0.03999467])\n>>> special.polygamma(0, x) == special.psi(x)\narray([ True,  True,  True], dtype=bool)\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "
gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gamma(z, out=None)
\n\n
gamma function.
\n\n
The gamma function is defined as
\n\n
$$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$
\n\n
for \\( \\Re(z) > 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex valued argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the gamma function
    • \n
\n\n
Notes
\n\n
The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).
\n\n
The gamma function has poles at non-negative integers and the sign\nof infinity as z approaches each pole depends upon the direction in\nwhich the pole is approached. For this reason, the consistent thing\nis for gamma(z) to return NaN at negative integers, and to return\n-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero\nto signify the direction in which the origin is being approached. This\nis for instance what is recommended for the gamma function in annex F\nentry 9.5.4 of the Iso C 99 standard [isoc99]_.
\n\n
Prior to SciPy version 1.15, scipy.special.gamma(z) returned +inf\nat each pole. This was fixed in version 1.15, but with the following\nconsequence. Expressions where gamma appears in the denominator\nsuch as
\n\n
gamma(u) * gamma(v) / (gamma(w) * gamma(x))
\n\n
no longer evaluate to 0 if the numerator is well defined but there is a\npole in the denominator. Instead such expressions evaluate to NaN. We\nrecommend instead using the function rgamma for the reciprocal gamma\nfunction in such cases. The above expression could for instance be written\nas
\n\n
gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1\n.. [isoc99] https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import gamma, factorial\n
\n
\n\n
\n
>>> gamma([0, 0.5, 1, 5])\narray([         inf,   1.77245385,   1.        ,  24.        ])\n
\n
\n\n
\n
>>> z = 2.5 + 1j\n>>> gamma(z)\n(0.77476210455108352+0.70763120437959293j)\n>>> gamma(z+1), z*gamma(z)  # Recurrence property\n((1.2292740569981171+2.5438401155000685j),\n (1.2292740569981158+2.5438401155000658j))\n
\n
\n\n
\n
>>> gamma(0.5)**2  # gamma(0.5) = sqrt(pi)\n3.1415926535897927\n
\n
\n\n
Plot gamma(x) for real x
\n\n
\n
>>> x = np.linspace(-3.5, 5.5, 2251)\n>>> y = gamma(x)\n
\n
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)')\n>>> k = np.arange(1, 7)\n>>> plt.plot(k, factorial(k-1), 'k*', alpha=0.6,\n...          label='(x-1)!, x = 1, 2, ...')\n>>> plt.xlim(-3.5, 5.5)\n>>> plt.ylim(-10, 25)\n>>> plt.grid()\n>>> plt.xlabel('x')\n>>> plt.legend(loc='lower right')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "
gammaln(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammaln(x, out=None)
\n\n
Logarithm of the absolute value of the gamma function.
\n\n
Defined as
\n\n
$$\\ln(\\lvert\\Gamma(x)\\rvert)$$
\n\n
where \\( \\Gamma \\) is the gamma function. For more details on\nthe gamma function, see [dlmf]_.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nReal argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the log of the absolute value of gamma
    • \n
\n\n
See Also
\n\n
gammasgn:  sign of the gamma function
\nloggamma:  principal branch of the logarithm of the gamma function  
\n\n
Notes
\n\n
It is the same function as the Python standard library function\nmath.lgamma().
\n\n
When used in conjunction with gammasgn, this function is useful\nfor working in logspace on the real axis without having to deal\nwith complex numbers via the relation exp(gammaln(x)) =\ngammasgn(x) * gamma(x).
\n\n
For complex-valued log-gamma, use loggamma instead of gammaln.
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import scipy.special as sc\n
\n
\n\n
It has two positive zeros.
\n\n
\n
>>> sc.gammaln([1, 2])\narray([0., 0.])\n
\n
\n\n
It has poles at nonpositive integers.
\n\n
\n
>>> sc.gammaln([0, -1, -2, -3, -4])\narray([inf, inf, inf, inf, inf])\n
\n
\n\n
It asymptotically approaches x * log(x) (Stirling's formula).
\n\n
\n
>>> x = np.array([1e10, 1e20, 1e40, 1e80])\n>>> sc.gammaln(x)\narray([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82])\n>>> x * np.log(x)\narray([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammainc": {"fullname": "pyerrors.special.gammainc", "modulename": "pyerrors.special", "qualname": "gammainc", "kind": "function", "doc": "
gammainc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammainc(a, x, out=None)
\n\n
Regularized lower incomplete gamma function.
\n\n
It is defined as
\n\n
$$P(a, x) = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a - 1}e^{-t} dt$$
\n\n
for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • a (array_like):\nPositive parameter
    • \n
  • x (array_like):\nNonnegative argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the lower incomplete gamma function
    • \n
\n\n
See Also
\n\n
gammaincc:  regularized upper incomplete gamma function
\ngammaincinv:  inverse of the regularized lower incomplete gamma function
\ngammainccinv:  inverse of the regularized upper incomplete gamma function  
\n\n
Notes
\n\n
The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammaincc is the regularized upper\nincomplete gamma function.
\n\n
The implementation largely follows that of [boost]_.
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
It is the CDF of the gamma distribution, so it starts at 0 and\nmonotonically increases to 1.
\n\n
\n
>>> sc.gammainc(0.5, [0, 1, 10, 100])\narray([0.        , 0.84270079, 0.99999226, 1.        ])\n
\n
\n\n
It is equal to one minus the upper incomplete gamma function.
\n\n
\n
>>> a, x = 0.5, 0.4\n>>> sc.gammainc(a, x)\n0.6289066304773024\n>>> 1 - sc.gammaincc(a, x)\n0.6289066304773024\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaincc": {"fullname": "pyerrors.special.gammaincc", "modulename": "pyerrors.special", "qualname": "gammaincc", "kind": "function", "doc": "
gammaincc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammaincc(a, x, out=None)
\n\n
Regularized upper incomplete gamma function.
\n\n
It is defined as
\n\n
$$Q(a, x) = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a - 1}e^{-t} dt$$
\n\n
for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • a (array_like):\nPositive parameter
    • \n
  • x (array_like):\nNonnegative argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the upper incomplete gamma function
    • \n
\n\n
See Also
\n\n
gammainc:  regularized lower incomplete gamma function
\ngammaincinv:  inverse of the regularized lower incomplete gamma function
\ngammainccinv:  inverse of the regularized upper incomplete gamma function  
\n\n
Notes
\n\n
The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammainc is the regularized lower\nincomplete gamma function.
\n\n
The implementation largely follows that of [boost]_.
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
It is the survival function of the gamma distribution, so it\nstarts at 1 and monotonically decreases to 0.
\n\n
\n
>>> sc.gammaincc(0.5, [0, 1, 10, 100, 1000])\narray([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45,\n       0.00000000e+00])\n
\n
\n\n
It is equal to one minus the lower incomplete gamma function.
\n\n
\n
>>> a, x = 0.5, 0.4\n>>> sc.gammaincc(a, x)\n0.37109336952269756\n>>> 1 - sc.gammainc(a, x)\n0.37109336952269756\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammasgn": {"fullname": "pyerrors.special.gammasgn", "modulename": "pyerrors.special", "qualname": "gammasgn", "kind": "function", "doc": "
gammasgn(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammasgn(x, out=None)
\n\n
Sign of the gamma function.
\n\n
It is defined as
\n\n
$$\\text{gammasgn}(x) =\n\\begin{cases}\n  +1 & \\Gamma(x) > 0 \\\n  -1 & \\Gamma(x) < 0\n\\end{cases}$$
\n\n
where \\( \\Gamma \\) is the gamma function; see gamma. This\ndefinition is complete since the gamma function is never zero;\nsee the discussion after [dlmf]_.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nReal argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Sign of the gamma function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\ngammaln:  log of the absolute value of the gamma function
\nloggamma:  analytic continuation of the log of the gamma function  
\n\n
Notes
\n\n
The gamma function can be computed as gammasgn(x) *\nnp.exp(gammaln(x)).
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import scipy.special as sc\n
\n
\n\n
It is 1 for x > 0.
\n\n
\n
>>> sc.gammasgn([1, 2, 3, 4])\narray([1., 1., 1., 1.])\n
\n
\n\n
It alternates between -1 and 1 for negative integers.
\n\n
\n
>>> sc.gammasgn([-0.5, -1.5, -2.5, -3.5])\narray([-1.,  1., -1.,  1.])\n
\n
\n\n
It can be used to compute the gamma function.
\n\n
\n
>>> x = [1.5, 0.5, -0.5, -1.5]\n>>> sc.gammasgn(x) * np.exp(sc.gammaln(x))\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n>>> sc.gamma(x)\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.rgamma": {"fullname": "pyerrors.special.rgamma", "modulename": "pyerrors.special", "qualname": "rgamma", "kind": "function", "doc": "
rgamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
rgamma(z, out=None)
\n\n
Reciprocal of the gamma function.
\n\n
Defined as \\( 1 / \\Gamma(z) \\), where \\( \\Gamma \\) is the\ngamma function. For more on the gamma function see gamma.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex valued input
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Function results
    • \n
\n\n
See Also
\n\n
gamma,, gammaln,, loggamma  
\n\n
Notes
\n\n
The gamma function has no zeros and has simple poles at\nnonpositive integers, so rgamma is an entire function with zeros\nat the nonpositive integers. See the discussion in [dlmf]_ for\nmore details.
\n\n
References
\n\n
.. [dlmf] Nist, Digital Library of Mathematical functions,\n    https://dlmf.nist.gov/5.2#i
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
It is the reciprocal of the gamma function.
\n\n
\n
>>> sc.rgamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n>>> 1 / sc.gamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n
\n
\n\n
It is zero at nonpositive integers.
\n\n
\n
>>> sc.rgamma([0, -1, -2, -3])\narray([0., 0., 0., 0.])\n
\n
\n\n
It rapidly underflows to zero along the positive real axis.
\n\n
\n
>>> sc.rgamma([10, 100, 179])\narray([2.75573192e-006, 1.07151029e-156, 0.00000000e+000])\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.multigammaln": {"fullname": "pyerrors.special.multigammaln", "modulename": "pyerrors.special", "qualname": "multigammaln", "kind": "function", "doc": "
Returns the log of multivariate gamma, also sometimes called the\ngeneralized gamma.
\n\n
Parameters
\n\n
    \n
  • a (ndarray):\nThe multivariate gamma is computed for each item of a.
    • \n
  • d (int):\nThe dimension of the space of integration.
    • \n
\n\n
Returns
\n\n
    \n
  • res (ndarray):\nThe values of the log multivariate gamma at the given points a.
    • \n
\n\n
Notes
\n\n
The formal definition of the multivariate gamma of dimension d for a real\na is
\n\n
$$\\Gamma_d(a) = \\int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA$$
\n\n
with the condition \\( a > (d-1)/2 \\), and \\( A > 0 \\) being the set of\nall the positive definite matrices of dimension d.  Note that a is a\nscalar: the integrand only is multivariate, the argument is not (the\nfunction is defined over a subset of the real set).
\n\n
This can be proven to be equal to the much friendlier equation
\n\n
$$\\Gamma_d(a) = \\pi^{d(d-1)/4} \\prod_{i=1}^{d} \\Gamma(a - (i-1)/2).$$
\n\n
References
\n\n
R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in\nprobability and mathematical statistics).
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import multigammaln, gammaln\n>>> a = 23.5\n>>> d = 10\n>>> multigammaln(a, d)\n454.1488605074416\n
\n
\n\n
Verify that the result agrees with the logarithm of the equation\nshown above:
\n\n
\n
>>> d*(d-1)/4*np.log(np.pi) + gammaln(a - 0.5*np.arange(0, d)).sum()\n454.1488605074416\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.kn": {"fullname": "pyerrors.special.kn", "modulename": "pyerrors.special", "qualname": "kn", "kind": "function", "doc": "
Modified Bessel function of the second kind of integer order n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j0": {"fullname": "pyerrors.special.j0", "modulename": "pyerrors.special", "qualname": "j0", "kind": "function", "doc": "
j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
j0(x, out=None)
\n\n
Bessel function of the first kind of order 0.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 0 at x.
    • \n
\n\n
See Also
\n\n
jv:  Bessel function of real order and complex argument.
\nspherical_jn:  spherical Bessel functions.  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval the following rational approximation is used:
\n\n
$$J_0(x) \\approx (w - r_1^2)(w - r_2^2) \\frac{P_3(w)}{Q_8(w)},$$
\n\n
where \\( w = x^2 \\) and \\( r_1 \\), \\( r_2 \\) are the zeros of\n\\( J_0 \\), and \\( P_3 \\) and \\( Q_8 \\) are polynomials of degrees 3\nand 8, respectively.
\n\n
In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
\n\n
This function is a wrapper for the Cephes 1 routine j0.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import j0\n>>> j0(1.)\n0.7651976865579665\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> j0(np.array([-2., 0., 4.]))\narray([ 0.22389078,  1.        , -0.39714981])\n
\n
\n\n
Plot the function from -20 to 20.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y0": {"fullname": "pyerrors.special.y0", "modulename": "pyerrors.special", "qualname": "y0", "kind": "function", "doc": "
y0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
y0(x, out=None)
\n\n
Bessel function of the second kind of order 0.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 0 at x.
    • \n
\n\n
See Also
\n\n
j0:  Bessel function of the first kind of order 0
\nyv:  Bessel function of the first kind  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval a rational approximation \\( R(x) \\) is employed to\ncompute,
\n\n
$$Y_0(x) = R(x) + \\frac{2 \\log(x) J_0(x)}{\\pi},$$
\n\n
where \\( J_0 \\) is the Bessel function of the first kind of order 0.
\n\n
In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
\n\n
This function is a wrapper for the Cephes 1 routine y0.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import y0\n>>> y0(1.)\n0.08825696421567697\n
\n
\n\n
Calculate at several points:
\n\n
\n
>>> import numpy as np\n>>> y0(np.array([0.5, 2., 3.]))\narray([-0.44451873,  0.51037567,  0.37685001])\n
\n
\n\n
Plot the function from 0 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j1": {"fullname": "pyerrors.special.j1", "modulename": "pyerrors.special", "qualname": "j1", "kind": "function", "doc": "
j1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
j1(x, out=None)
\n\n
Bessel function of the first kind of order 1.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 1 at x.
    • \n
\n\n
See Also
\n\n
jv:  Bessel function of the first kind
\nspherical_jn:  spherical Bessel functions.  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 24 term Chebyshev expansion is used. In the second, the\nasymptotic trigonometric representation is employed using two rational\nfunctions of degree 5/5.
\n\n
This function is a wrapper for the Cephes 1 routine j1.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import j1\n>>> j1(1.)\n0.44005058574493355\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> j1(np.array([-2., 0., 4.]))\narray([-0.57672481,  0.        , -0.06604333])\n
\n
\n\n
Plot the function from -20 to 20.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y1": {"fullname": "pyerrors.special.y1", "modulename": "pyerrors.special", "qualname": "y1", "kind": "function", "doc": "
y1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
y1(x, out=None)
\n\n
Bessel function of the second kind of order 1.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 1 at x.
    • \n
\n\n
See Also
\n\n
j1:  Bessel function of the first kind of order 1
\nyn:  Bessel function of the second kind
\nyv:  Bessel function of the second kind  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 25 term Chebyshev expansion is used, and computing\n\\( J_1 \\) (the Bessel function of the first kind) is required. In the\nsecond, the asymptotic trigonometric representation is employed using two\nrational functions of degree 5/5.
\n\n
This function is a wrapper for the Cephes 1 routine y1.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import y1\n>>> y1(1.)\n-0.7812128213002888\n
\n
\n\n
Calculate at several points:
\n\n
\n
>>> import numpy as np\n>>> y1(np.array([0.5, 2., 3.]))\narray([-1.47147239, -0.10703243,  0.32467442])\n
\n
\n\n
Plot the function from 0 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.jn": {"fullname": "pyerrors.special.jn", "modulename": "pyerrors.special", "qualname": "jn", "kind": "function", "doc": "
jv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
jv(v, z, out=None)
\n\n
Bessel function of the first kind of real order and complex argument.
\n\n
Parameters
\n\n
    \n
  • v (array_like):\nOrder (float).
    • \n
  • z (array_like):\nArgument (float or complex).
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • J (scalar or ndarray):\nValue of the Bessel function, \\( J_v(z) \\).
    • \n
\n\n
See Also
\n\n
jve:  \\( J_v \\) with leading exponential behavior stripped off.
\nspherical_jn:  spherical Bessel functions.
\nj0:  faster version of this function for order 0.
\nj1:  faster version of this function for order 1.  
\n\n
Notes
\n\n
For positive v values, the computation is carried out using the AMOS\n1 zbesj routine, which exploits the connection to the modified\nBessel function \\( I_v \\),
\n\n
$$J_v(z) = \\exp(v\\pi\\imath/2) I_v(-\\imath z)\\qquad (\\Im z > 0)
\n\n
J_v(z) = \\exp(-v\\pi\\imath/2) I_v(\\imath z)\\qquad (\\Im z < 0)$$
\n\n
For negative v values the formula,
\n\n
$$J_{-v}(z) = J_v(z) \\cos(\\pi v) - Y_v(z) \\sin(\\pi v)$$
\n\n
is used, where \\( Y_v(z) \\) is the Bessel function of the second\nkind, computed using the AMOS routine zbesy.  Note that the second\nterm is exactly zero for integer v; to improve accuracy the second\nterm is explicitly omitted for v values such that v = floor(v).
\n\n
Not to be confused with the spherical Bessel functions (see spherical_jn).
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import jv\n>>> jv(0, 1.)\n0.7651976865579666\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> jv(0, 1.), jv(1, 1.), jv(1.5, 1.)\n(0.7651976865579666, 0.44005058574493355, 0.24029783912342725)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> jv([0, 1, 1.5], 1.)\narray([0.76519769, 0.44005059, 0.24029784])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> jv(0, points)\narray([ 0.22389078,  1.        , -0.26005195])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> jv(orders, points)\narray([[ 0.22389078,  1.        , -0.26005195],\n       [-0.57672481,  0.        ,  0.33905896]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -10 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, jv(i, x), label=f'$J_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.yn": {"fullname": "pyerrors.special.yn", "modulename": "pyerrors.special", "qualname": "yn", "kind": "function", "doc": "
yn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
yn(n, x, out=None)
\n\n
Bessel function of the second kind of integer order and real argument.
\n\n
Parameters
\n\n
    \n
  • n (array_like):\nOrder (integer).
    • \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • Y (scalar or ndarray):\nValue of the Bessel function, \\( Y_n(x) \\).
    • \n
\n\n
See Also
\n\n
yv:  For real order and real or complex argument.
\ny0:  faster implementation of this function for order 0
\ny1:  faster implementation of this function for order 1  
\n\n
Notes
\n\n
Wrapper for the Cephes 1 routine yn.
\n\n
The function is evaluated by forward recurrence on n, starting with\nvalues computed by the Cephes routines y0 and y1. If n = 0 or 1,\nthe routine for y0 or y1 is called directly.
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import yn\n>>> yn(0, 1.)\n0.08825696421567697\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> yn(0, 1.), yn(1, 1.), yn(2, 1.)\n(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> yn([0, 1, 2], 1.)\narray([ 0.08825696, -0.78121282, -1.65068261])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([0.5, 3., 8.])\n>>> yn(0, points)\narray([-0.44451873,  0.37685001,  0.22352149])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> yn(orders, points)\narray([[-0.44451873,  0.37685001,  0.22352149],\n       [-1.47147239,  0.32467442, -0.15806046]])\n
\n
\n\n
Plot the functions of order 0 to 3 from 0 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')\n>>> ax.set_ylim(-3, 1)\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i0": {"fullname": "pyerrors.special.i0", "modulename": "pyerrors.special", "qualname": "i0", "kind": "function", "doc": "
i0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
i0(x, out=None)
\n\n
Modified Bessel function of order 0.
\n\n
Defined as,
\n\n
$$I_0(x) = \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{(k!)^2} = J_0(\\imath x),$$
\n\n
where \\( J_0 \\) is the Bessel function of the first kind of order 0.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float)
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • I (scalar or ndarray):\nValue of the modified Bessel function of order 0 at x.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of any order
\ni0e:  Exponentially scaled modified Bessel function of order 0  
\n\n
Notes
\n\n
The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
\n\n
This function is a wrapper for the Cephes 1 routine i0.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import i0\n>>> i0(1.)\n1.2660658777520082\n
\n
\n\n
Calculate at several points:
\n\n
\n
>>> import numpy as np\n>>> i0(np.array([-2., 0., 3.5]))\narray([2.2795853 , 1.        , 7.37820343])\n
\n
\n\n
Plot the function from -10 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i1": {"fullname": "pyerrors.special.i1", "modulename": "pyerrors.special", "qualname": "i1", "kind": "function", "doc": "
i1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
i1(x, out=None)
\n\n
Modified Bessel function of order 1.
\n\n
Defined as,
\n\n
$$I_1(x) = \\frac{1}{2}x \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{k! (k + 1)!}\n       = -\\imath J_1(\\imath x),$$
\n\n
where \\( J_1 \\) is the Bessel function of the first kind of order 1.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float)
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • I (scalar or ndarray):\nValue of the modified Bessel function of order 1 at x.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of the first kind
\ni1e:  Exponentially scaled modified Bessel function of order 1  
\n\n
Notes
\n\n
The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
\n\n
This function is a wrapper for the Cephes 1 routine i1.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import i1\n>>> i1(1.)\n0.5651591039924851\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> i1(np.array([-2., 0., 6.]))\narray([-1.59063685,  0.        , 61.34193678])\n
\n
\n\n
Plot the function between -10 and 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "
iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
iv(v, z, out=None)
\n\n
Modified Bessel function of the first kind of real order.
\n\n
Parameters
\n\n
    \n
  • v (array_like):\nOrder. If z is of real type and negative, v must be integer\nvalued.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the modified Bessel function.
    • \n
\n\n
See Also
\n\n
ive:  This function with leading exponential behavior stripped off.
\ni0:  Faster version of this function for order 0.
\ni1:  Faster version of this function for order 1.  
\n\n
Notes
\n\n
For real z and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method 1.  For larger orders, uniform asymptotic\nexpansions are applied.
\n\n
For complex z and positive v, the AMOS 2 zbesi routine is\ncalled. It uses a power series for small z, the asymptotic expansion\nfor large abs(z), the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import iv\n>>> iv(0, 1.)\n1.2660658777520084\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> iv(0, 1.), iv(1, 1.), iv(1.5, 1.)\n(1.2660658777520084, 0.565159103992485, 0.2935253263474798)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> iv([0, 1, 1.5], 1.)\narray([1.26606588, 0.5651591 , 0.29352533])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> iv(0, points)\narray([2.2795853 , 1.        , 4.88079259])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> iv(orders, points)\narray([[ 2.2795853 ,  1.        ,  4.88079259],\n       [-1.59063685,  0.        ,  3.95337022]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, iv(i, x), label=f'$I_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Temme, Journal of Computational Physics, vol 21, 343 (1976) ↩
    \n
    2. \n\n
  2. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "
ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
ive(v, z, out=None)
\n\n
Exponentially scaled modified Bessel function of the first kind.
\n\n
Defined as::
\n\n
ive(v, z) = iv(v, z) * exp(-abs(z.real))\n
\n\n
For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind iv.
\n\n
Parameters
\n\n
    \n
  • v (array_like of float):\nOrder.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the exponentially scaled modified Bessel function.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of the first kind
\ni0e:  Faster implementation of this function for order 0
\ni1e:  Faster implementation of this function for order 1  
\n\n
Notes
\n\n
For positive v, the AMOS 1 zbesi routine is called. It uses a\npower series for small z, the asymptotic expansion for large\nabs(z), the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
ive is useful for large arguments z: for these, iv easily overflows,\nwhile ive does not due to the exponential scaling.
\n\n
References
\n\n
Examples
\n\n
In the following example iv returns infinity whereas ive still returns\na finite number.
\n\n
\n
>>> from scipy.special import iv, ive\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> iv(3, 1000.), ive(3, 1000.)\n(inf, 0.01256056218254712)\n
\n
\n\n
Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> ive([0, 1, 1.5], 1.)\narray([0.46575961, 0.20791042, 0.10798193])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> points = np.array([-2., 0., 3.])\n>>> ive(0, points)\narray([0.30850832, 1.        , 0.24300035])\n
\n
\n\n
Evaluate the function at several points for different orders by\nproviding arrays for both v for z. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:
\n\n
\n
>>> ive([[0], [1], [2]], points)\narray([[ 0.30850832,  1.        ,  0.24300035],\n       [-0.21526929,  0.        ,  0.19682671],\n       [ 0.09323903,  0.        ,  0.11178255]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, ive(i, x), label=fr'$I_{i!r}(z)\\cdot e^{{-|z|}}$')\n>>> ax.legend()\n>>> ax.set_xlabel(r"$z$")\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "
erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erf(z, out=None)
\n\n
Returns the error function of complex argument.
\n\n
It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).
\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nInput array.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • res (scalar or ndarray):\nThe values of the error function at the given points x.
    • \n
\n\n
See Also
\n\n
erfc,, erfinv,, erfcinv,, wofz,, erfcx,, erfi  
\n\n
Notes
\n\n
The cumulative of the unit normal distribution is given by\nPhi(z) = 1/2[1 + erf(z/sqrt(2))].
\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erf(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erf(x)$')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfc": {"fullname": "pyerrors.special.erfc", "modulename": "pyerrors.special", "qualname": "erfc", "kind": "function", "doc": "
erfc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erfc(x, out=None)
\n\n
Complementary error function, 1 - erf(x).
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nReal or complex valued argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the complementary error function
    • \n
\n\n
See Also
\n\n
erf,, erfi,, erfcx,, dawsn,, wofz  
\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erfc(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erfc(x)$')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfinv": {"fullname": "pyerrors.special.erfinv", "modulename": "pyerrors.special", "qualname": "erfinv", "kind": "function", "doc": "
erfinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erfinv(y, out=None)
\n\n
Inverse of the error function.
\n\n
Computes the inverse of the error function.
\n\n
In the complex domain, there is no unique complex number w satisfying\nerf(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, -1 < x < 1, there is a unique real\nnumber satisfying erf(erfinv(x)) = x.
\n\n
Parameters
\n\n
    \n
  • y (ndarray):\nArgument at which to evaluate. Domain: [-1, 1]
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • erfinv (scalar or ndarray):\nThe inverse of erf of y, element-wise
    • \n
\n\n
See Also
\n\n
erf:  Error function of a complex argument
\nerfc:  Complementary error function, 1 - erf(x)
\nerfcinv:  Inverse of the complementary error function  
\n\n
Notes
\n\n
This function wraps the erf_inv routine from the\nBoost Math C++ library 1.
\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfinv, erf\n
\n
\n\n
\n
>>> erfinv(0.5)\n0.4769362762044699\n
\n
\n\n
\n
>>> y = np.linspace(-1.0, 1.0, num=9)\n>>> x = erfinv(y)\n>>> x\narray([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,\n        0.22531206,  0.47693628,  0.81341985,         inf])\n
\n
\n\n
Verify that erf(erfinv(y)) is y.
\n\n
\n
>>> erf(x)\narray([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])\n
\n
\n\n
Plot the function:
\n\n
\n
>>> y = np.linspace(-1, 1, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfinv(y)')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfcinv": {"fullname": "pyerrors.special.erfcinv", "modulename": "pyerrors.special", "qualname": "erfcinv", "kind": "function", "doc": "
erfcinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erfcinv(y, out=None)
\n\n
Inverse of the complementary error function.
\n\n
Computes the inverse of the complementary error function.
\n\n
In the complex domain, there is no unique complex number w satisfying\nerfc(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, 0 < x < 2, there is a unique real\nnumber satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).
\n\n
It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)
\n\n
Parameters
\n\n
    \n
  • y (ndarray):\nArgument at which to evaluate. Domain: [0, 2]
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • erfcinv (scalar or ndarray):\nThe inverse of erfc of y, element-wise
    • \n
\n\n
See Also
\n\n
erf:  Error function of a complex argument
\nerfc:  Complementary error function, 1 - erf(x)
\nerfinv:  Inverse of the error function  
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfcinv\n
\n
\n\n
\n
>>> erfcinv(0.5)\n0.4769362762044699\n
\n
\n\n
\n
>>> y = np.linspace(0.0, 2.0, num=11)\n>>> erfcinv(y)\narray([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,\n       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,\n              -inf])\n
\n
\n\n
Plot the function:
\n\n
\n
>>> y = np.linspace(0, 2, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfcinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfcinv(y)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logit": {"fullname": "pyerrors.special.logit", "modulename": "pyerrors.special", "qualname": "logit", "kind": "function", "doc": "
logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
logit(x, out=None)
\n\n
Logit ufunc for ndarrays.
\n\n
The logit function is defined as logit(p) = log(p/(1-p)).\nNote that logit(0) = -inf, logit(1) = inf, and logit(p)\nfor p<0 or p>1 yields nan.
\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nThe ndarray to apply logit to element-wise.
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare logit of the corresponding entry of x.
    • \n
\n\n
See Also
\n\n
expit  
\n\n
Notes
\n\n
As a ufunc logit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
\n\n
New in version 0.10.0.
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import logit, expit\n
\n
\n\n
\n
>>> logit([0, 0.25, 0.5, 0.75, 1])\narray([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])\n
\n
\n\n
expit is the inverse of logit:
\n\n
\n
>>> expit(logit([0.1, 0.75, 0.999]))\narray([ 0.1  ,  0.75 ,  0.999])\n
\n
\n\n
Plot logit(x) for x in [0, 1]:
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(0, 1, 501)\n>>> y = logit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.ylim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('logit(x)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.expit": {"fullname": "pyerrors.special.expit", "modulename": "pyerrors.special", "qualname": "expit", "kind": "function", "doc": "
expit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
expit(x, out=None)
\n\n
Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.
\n\n
The expit function, also known as the logistic sigmoid function, is\ndefined as expit(x) = 1/(1+exp(-x)).  It is the inverse of the\nlogit function.
\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nThe ndarray to apply expit to element-wise.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare expit of the corresponding entry of x.
    • \n
\n\n
See Also
\n\n
logit  
\n\n
Notes
\n\n
As a ufunc expit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
\n\n
New in version 0.10.0.
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import expit, logit\n
\n
\n\n
\n
>>> expit([-np.inf, -1.5, 0, 1.5, np.inf])\narray([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])\n
\n
\n\n
logit is the inverse of expit:
\n\n
\n
>>> logit(expit([-2.5, 0, 3.1, 5.0]))\narray([-2.5,  0. ,  3.1,  5. ])\n
\n
\n\n
Plot expit(x) for x in [-6, 6]:
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-6, 6, 121)\n>>> y = expit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.xlim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('expit(x)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logsumexp": {"fullname": "pyerrors.special.logsumexp", "modulename": "pyerrors.special", "qualname": "logsumexp", "kind": "function", "doc": "
Compute the log of the sum of exponentials of input elements.
\n\n
Parameters
\n\n
    \n
  • a (array_like):\nInput array.
    • \n
  • axis (None or int or tuple of ints, optional):\nAxis or axes over which the sum is taken. By default axis is None,\nand all elements are summed.
    \n\n
    New in version 0.11.0.
    • \n
  • b (array-like, optional):\nScaling factor for exp(a) must be of the same shape as a or\nbroadcastable to a. These values may be negative in order to\nimplement subtraction.
    \n\n
    New in version 0.12.0.
    • \n
  • keepdims (bool, optional):\nIf this is set to True, the axes which are reduced are left in the\nresult as dimensions with size one. With this option, the result\nwill broadcast correctly against the original array.
    \n\n
    New in version 0.15.0.
    • \n
  • return_sign (bool, optional):\nIf this is set to True, the result will be a pair containing sign\ninformation; if False, results that are negative will be returned\nas NaN. Default is False (no sign information).
    \n\n
    New in version 0.16.0.
    • \n
\n\n
Returns
\n\n
    \n
  • res (ndarray):\nThe result, np.log(np.sum(np.exp(a))) calculated in a numerically\nmore stable way. If b is given then np.log(np.sum(b*np.exp(a)))\nis returned. If return_sign is True, res contains the log of\nthe absolute value of the argument.
    • \n
  • sgn (ndarray):\nIf return_sign is True, this will be an array of floating-point\nnumbers matching res containing +1, 0, -1 (for real-valued inputs)\nor a complex phase (for complex inputs). This gives the sign of the\nargument of the logarithm in res.\nIf return_sign is False, only one result is returned.
    • \n
\n\n
See Also
\n\n
numpy.logaddexp,, numpy.logaddexp2  
\n\n
Notes
\n\n
NumPy has a logaddexp function which is very similar to logsumexp, but\nonly handles two arguments. logaddexp.reduce is similar to this\nfunction, but may be less stable.
\n\n
The logarithm is a multivalued function: for each \\( x \\) there is an\ninfinite number of \\( z \\) such that \\( exp(z) = x \\). The convention\nis to return the \\( z \\) whose imaginary part lies in \\( (-pi, pi] \\).
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import logsumexp\n>>> a = np.arange(10)\n>>> logsumexp(a)\n9.4586297444267107\n>>> np.log(np.sum(np.exp(a)))\n9.4586297444267107\n
\n
\n\n
With weights
\n\n
\n
>>> a = np.arange(10)\n>>> b = np.arange(10, 0, -1)\n>>> logsumexp(a, b=b)\n9.9170178533034665\n>>> np.log(np.sum(b*np.exp(a)))\n9.9170178533034647\n
\n
\n\n
Returning a sign flag
\n\n
\n
>>> logsumexp([1,2],b=[1,-1],return_sign=True)\n(1.5413248546129181, -1.0)\n
\n
\n\n
Notice that logsumexp does not directly support masked arrays. To use it\non a masked array, convert the mask into zero weights:
\n\n
\n
>>> a = np.ma.array([np.log(2), 2, np.log(3)],\n...                  mask=[False, True, False])\n>>> b = (~a.mask).astype(int)\n>>> logsumexp(a.data, b=b), np.log(5)\n1.6094379124341005, 1.6094379124341005\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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What is pyerrors?
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pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
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  • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
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  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
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  • coherent error propagation for data from different Markov chains.
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  • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
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  • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
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More detailed examples can found in the GitHub repository \"badge\".
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If you use pyerrors for research that leads to a publication please consider citing:
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  • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
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  • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
    • \n
  • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
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and
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  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
    • \n
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where applicable.
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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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Installation
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Install the most recent release using pip and pypi:
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python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
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Install the most recent release using conda and conda-forge:
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conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
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Install the current develop version:
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python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
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(Also works for any feature branch).
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Basic example
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import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
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The Obs class
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pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
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import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
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Error propagation
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When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
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The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
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import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
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Error estimation
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The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
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my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
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We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
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my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
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If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
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Exponential tails
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Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
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my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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For the full API see pyerrors.obs.Obs.gamma_method.
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Multiple ensembles/replica
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Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
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obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
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Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
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pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
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obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
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Error estimation for multiple ensembles
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In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
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pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
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In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
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Irregular Monte Carlo chains
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Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
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# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
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Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
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Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
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For the full API see pyerrors.obs.Obs.
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Correlators
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When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
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my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
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In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
\n\n
\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
\n
\n\n
The individual entries of a correlator can be accessed via slicing
\n\n
\n
print(my_corr[3])\n> 0.3227(33)\n
\n
\n\n
Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
\n\n
\n
my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
\n
\n\n
pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
\n\n
    \n
  • Corr.gamma_method applies the gamma method to all entries of the correlator.
    • \n
  • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
    • \n
  • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
    • \n
  • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
    • \n
  • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
    • \n
  • Corr.plateau extracts a plateau value from the correlator in a given range.
    • \n
  • Corr.roll periodically shifts the correlator.
    • \n
  • Corr.reverse reverses the time ordering of the correlator.
    • \n
  • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
    • \n
  • Corr.reweight reweights the correlator.
    • \n
\n\n
pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
\n\n
For the full API see pyerrors.correlators.Corr.
\n\n
Complex valued observables
\n\n
pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
\n\n
\n
my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
\n
\n\n
Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
\n\n
\n
my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
\n
\n\n
The Covobs class
\n\n
In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
\n\n
This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
\n\n
\n
import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
\n
\n\n
The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
\n\n
Correlated auxiliary data is defined similarly to above, e.g., via
\n\n
\n
RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
\n
\n\n
where RAP now is a list of two Obs that contains the two correlated parameters.
\n\n
Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
\n\n
\n
o.covobs[k].grad\n
\n
\n\n
Error propagation in iterative algorithms
\n\n
pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
\n\n
Least squares fits
\n\n
Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
\n\n
Fit functions have to be of the following form
\n\n
\n
import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
\n
\n\n
It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
\n\n
Fits can then be performed via
\n\n
\n
fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
\n
\n\n
where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
\n\n
Data stored in Corr objects can be fitted directly using the Corr.fit method.
\n\n
\n
my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
\n
\n\n
this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
\n\n
For fit functions with multiple independent variables the fit function can be of the form
\n\n
\n
def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
\n
\n\n
pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
\n\n
For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
\n\n
Total least squares fits
\n\n
pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
\n\n
For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
\n\n
Matrix operations
\n\n
pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
\n\n
    \n
  • inv for the matrix inverse.
    • \n
  • cholseky for the Cholesky decomposition.
    • \n
  • det for the matrix determinant.
    • \n
  • eigh for eigenvalues and eigenvectors of hermitean matrices.
    • \n
  • eig for eigenvalues of general matrices.
    • \n
  • pinv for the Moore-Penrose pseudoinverse.
    • \n
  • svd for the singular-value-decomposition.
    • \n
\n\n
For the full API see pyerrors.linalg.
\n\n
Export data
\n\n
\n\n
The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
\n\n
    \n
  • What observables are stored? Possibly: How exactly are they defined.
    • \n
  • How does each single ensemble or external quantity contribute to the error of the observable?
    • \n
  • Who did write the file when and on which machine?
    • \n
\n\n
This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
\n\n
\n
my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
\n
\n\n
The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
\n\n
json.gz format specification
\n\n
The first entries of the file provide optional auxiliary information:
\n\n
    \n
  • program is a string that indicates which program was used to write the file.
    • \n
  • version is a string that specifies the version of the format.
    • \n
  • who is a string that specifies the user name of the creator of the file.
    • \n
  • date is a string and contains the creation date of the file.
    • \n
  • host is a string and contains the hostname of the machine where the file has been written.
    • \n
  • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
    • \n
\n\n
The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
\n\n
Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
\n\n
    \n
  • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
    • \n
  • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
    • \n
  • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
    • \n
  • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
    • \n
  • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
    • \n
  • data is an array that contains the data from MC chains. We will define it below.
    • \n
  • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
    • \n
\n\n
The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
\n\n
    \n
  • id, a string that contains the name of the ensemble
    • \n
  • replica, an array that contains an entry per replica of the ensemble.
    • \n
\n\n
Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
\n\n
Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
\n\n
The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
\n\n
    \n
  • id, a string that identifies the covariance matrix
    • \n
  • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
    • \n
  • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
    • \n
  • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
    • \n
\n\n
A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
\n\n
Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
The class for a correlator (time dependent sequence of pe.Obs).
\n\n
Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
\n\n
The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.
\n\n
The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.
\n\n
Initialization
\n\n
A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs
\n\n
\n
corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
\n
\n\n
A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects
\n\n
\n
matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
\n
\n\n
or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.
\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
Initialize a Corr object.
\n\n
Parameters
\n\n
    \n
  • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
    • \n
  • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
    • \n
  • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.
    • \n
\n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
Apply the gamma method to the content of the Corr.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
Apply the gamma method to the content of the Corr.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
We need to project the Correlator with a Vector to get a single value at each timeslice.
\n\n
The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
\n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
\n\n
Parameters
\n\n
    \n
  • i (int):\nFirst index to be picked.
    • \n
  • j (int):\nSecond index to be picked.
    • \n
\n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
Outputs the correlator in a plotable format.
\n\n
Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
Symmetrize the correlator around x0=0.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
Anti-symmetrize the correlator around x0=0.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
Checks whether a correlator matrices is symmetric on every timeslice.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "
Calculates the per-timeslice trace of a correlator matrix.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
Symmetrizes the correlator matrices on every timeslice.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
\n\n
The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
\n\n
\n
C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
\n
\n\n
Parameters
\n\n
    \n
  • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
    • \n
  • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
    • \n
  • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
      \n
    • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
      • \n
    • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
      • \n
    • None: The GEVP is solved only at ts, no sorting is necessary
      • \n
    • \n
  • vector_obs (bool):\nIf True, uncertainties are propagated in the eigenvector computation (default False).
    • \n
\n\n
Other Parameters
\n\n
    \n
  • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
    • \n
  • method (str):\nMethod used to solve the GEVP.\n
      \n
    • \"eigh\": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
      • \n
    • \"cholesky\": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
      • \n
    • \n
\n", "signature": "(self, t0, ts=None, sort='Eigenvalue', vector_obs=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
Determines the eigenvalue of the GEVP by solving and projecting the correlator
\n\n
Parameters
\n\n
    \n
  • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
    • \n
  • All other parameters are identical to the ones of Corr.GEVP.
    • \n
\n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
Constructs an NxN Hankel matrix
\n\n
C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
\n\n
Parameters
\n\n
    \n
  • N (int):\nDimension of the Hankel matrix
    • \n
  • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
    • \n
\n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
Periodically shift the correlator by dt timeslices
\n\n
Parameters
\n\n
    \n
  • dt (int):\nnumber of timeslices
    • \n
\n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
Reverse the time ordering of the Corr
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
Thin out a correlator to suppress correlations
\n\n
Parameters
\n\n
    \n
  • spacing (int):\nKeep only every 'spacing'th entry of the correlator
    • \n
  • offset (int):\nOffset the equal spacing
    • \n
\n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
Correlate the correlator with another correlator or Obs
\n\n
Parameters
\n\n
    \n
  • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
    • \n
\n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
Reweight the correlator.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
Return the time symmetry average of the correlator and its partner
\n\n
Parameters
\n\n
    \n
  • partner (Corr):\nTime symmetry partner of the Corr
    • \n
  • parity (int):\nParity quantum number of the correlator, can be +1 or -1
    • \n
\n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
Return the first derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
Return the second derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
Returns the effective mass of the correlator as correlator object
\n\n
Parameters
\n\n
    \n
  • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
    • \n
  • guess (float):\nguess for the root finder, only relevant for the root variant
    • \n
\n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
Fits function to the data
\n\n
Parameters
\n\n
    \n
  • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
    • \n
  • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
    • \n
  • silent (bool):\nDecides whether output is printed to the standard output.
    • \n
\n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
Extract a plateau value from a Corr object
\n\n
Parameters
\n\n
    \n
  • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
    • \n
  • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
    • \n
  • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
    • \n
\n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
Sets the attribute prange of the Corr object.
\n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
Plots the correlator using the tag of the correlator as label if available.
\n\n
Parameters
\n\n
    \n
  • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
    • \n
  • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
    • \n
  • logscale (bool):\nSets y-axis to logscale.
    • \n
  • plateau (Obs):\nPlateau value to be visualized in the figure.
    • \n
  • fit_res (Fit_result):\nFit_result object to be visualized.
    • \n
  • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
    • \n
  • ylabel (str):\nLabel for the y-axis.
    • \n
  • save (str):\npath to file in which the figure should be saved.
    • \n
  • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
    • \n
  • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
    • \n
  • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
    • \n
  • title (string):\nOptional title of the figure.
    • \n
\n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\n
Parameters
\n\n
    \n
  • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
    • \n
\n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
Dumps the Corr into a file of chosen type
\n\n
Parameters
\n\n
    \n
  • filename (str):\nName of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
\n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
Project large correlation matrix to lowest states
\n\n
This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
\n\n
Parameters
\n\n
    \n
  • Ntrunc (int):\nRank of the target matrix.
    • \n
  • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
    • \n
  • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
    • \n
  • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
    • \n
\n\n
Notes
\n\n
We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
Initialize Covobs object.
\n\n
Parameters
\n\n
    \n
  • mean (float):\nMean value of the new Obs
    • \n
  • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
Return the variance (= square of the error) of the Covobs
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
\n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
\n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
\n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
\n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
\n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
Rank-3 epsilon tensor
\n\n
Based on https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
    • \n
\n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
Rank-4 epsilon tensor
\n\n
Extension of https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
    • \n
\n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
Represents fit results.
\n\n
Attributes
\n\n
    \n
  • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
    • \n
  • chisquare_by_dof (float):\nreduced chisquare.
    • \n
  • p_value (float):\np-value of the fit
    • \n
  • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
    • \n
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
\n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x).\n    ```
\n\n
Parameters
\n\n
    \n
  • For an uncombined fit:
    • \n
  • x (list):\nlist of floats.
    • \n
  • y (list):\nlist of Obs.
    • \n
  • func (object):\nfit function, has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • OR For a combined fit:
    • \n
  • x (dict):\ndict of lists.
    • \n
  • y (dict):\ndict of lists of Obs.
    • \n
  • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n        \"b\": func_b}
    \n\n
    def func_a(a, x):\n    return a[1] * anp.exp(-a[0] * x)
    \n\n
    def func_b(a, x):\n    return a[2] * anp.exp(-a[0] * x)
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
    • \n
  • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
    • \n
  • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
    • \n
  • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
    • \n
  • inv_chol_cov_matrix [array,list], optional: array: shape = (no of y values) X (no of y values)\nlist:   for an uncombined fit: [\"\"]\nfor a combined fit: list of keys belonging to the corr_matrix saved in the array, must be the same as the keys of the y dict in alphabetical order\nIf correlated_fit=True is set as well, can provide an inverse covariance matrix (y errors, dy_f included!) of your own choosing for a correlated fit.\nThe matrix must be a lower triangular matrix constructed from a Cholesky decomposition: The function invert_corr_cov_cholesky(corr, inverrdiag) can be\nused to construct it from a correlation matrix (corr) and the errors dy_f of the data points (inverrdiag = np.diag(1 / np.asarray(dy_f))). For the correct\nordering the correlation matrix (corr) can be sorted via the function sort_corr(corr, kl, yd) where kl is the list of keys and yd the y dict.
    • \n
  • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
    • \n
  • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
    • \n
  • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n\n
Examples
\n\n
\n
>>> # Example of a correlated (correlated_fit = True, inv_chol_cov_matrix handed over) combined fit, based on a randomly generated data set\n>>> import numpy as np\n>>> from scipy.stats import norm\n>>> from scipy.linalg import cholesky\n>>> import pyerrors as pe\n>>> # generating the random data set\n>>> num_samples = 400\n>>> N = 3\n>>> x = np.arange(N)\n>>> x1 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> x2 = norm.rvs(size=(N, num_samples)) # generate random numbers\n>>> r = r1 = r2 = np.zeros((N, N))\n>>> y = {}\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] = np.exp(-0.8 * np.fabs(i - j)) # element in correlation matrix\n>>> errl = np.sqrt([3.4, 2.5, 3.6]) # set y errors\n>>> for i in range(N):\n>>>    for j in range(N):\n>>>        r[i, j] *= errl[i] * errl[j] # element in covariance matrix\n>>> c = cholesky(r, lower=True)\n>>> y = {'a': np.dot(c, x1), 'b': np.dot(c, x2)} # generate y data with the covariance matrix defined\n>>> # random data set has been generated, now the dictionaries and the inverse covariance matrix to be handed over are built\n>>> x_dict = {}\n>>> y_dict = {}\n>>> chol_inv_dict = {}\n>>> data = []\n>>> for key in y.keys():\n>>>    x_dict[key] = x\n>>>    for i in range(N):\n>>>        data.append(pe.Obs([[i + 1 + o for o in y[key][i]]], ['ens'])) # generate y Obs from the y data\n>>>    [o.gamma_method() for o in data]\n>>>    corr = pe.covariance(data, correlation=True)\n>>>    inverrdiag = np.diag(1 / np.asarray([o.dvalue for o in data]))\n>>>    chol_inv = pe.obs.invert_corr_cov_cholesky(corr, inverrdiag) # gives form of the inverse covariance matrix needed for the combined correlated fit below\n>>> y_dict = {'a': data[:3], 'b': data[3:]}\n>>> # common fit parameter p[0] in combined fit\n>>> def fit1(p, x):\n>>>    return p[0] + p[1] * x\n>>> def fit2(p, x):\n>>>    return p[0] + p[2] * x\n>>> fitf_dict = {'a': fit1, 'b':fit2}\n>>> fitp_inv_cov_combined_fit = pe.least_squares(x_dict,y_dict, fitf_dict, correlated_fit = True, inv_chol_cov_matrix = [chol_inv,['a','b']])\nFit with 3 parameters\nMethod: Levenberg-Marquardt\n`ftol` termination condition is satisfied.\nchisquare/d.o.f.: 0.5388013574561786 # random\nfit parameters [1.11897846 0.96361162 0.92325319] # random\n
\n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of Obs, or a tuple of lists of Obs
    • \n
  • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
    • \n
  • func (object):\nfunc has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
    • \n
  • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy.
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n\n
Returns
\n\n
    \n
  • fit_parameters (list[Obs]):\nLIist of fitted observables.
    • \n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n\n
For uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\n
Returns
\n\n
    \n
  • err (np.array(Obs)):\nError band for an array of sample values x
    • \n
\n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\n
Jackknife samples
\n\n
For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
Extract generic MCMC data from a bdio file
\n\n
read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • data (List[Obs]):\nExtracted data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
Write Obs to a bdio file according to ADerrors conventions
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • success (int):\nreturns 0 is successful
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
Extract mesons data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n\n
Returns
\n\n
    \n
  • data (dict):\nExtracted meson data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
Extract dSdm data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, kappa)
\n\n
read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML formatted string of the input data
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
Import a list of Obs from a string in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator |is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML string generated from the data
    • \n
\n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
Read hadrons hdf5 file and extract entry based on attributes.
\n\n
Parameters
\n\n
    \n
  • filestem (str):\nFull namestem of the files to read, including the full path.
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • group (str):\nlabel of the group to be extracted.
    • \n
  • attrs (dict or int):\nDictionary containing the attributes. For example
    \n\n
    \n
    attrs = {"gamma_snk": "Gamma5",\n         "gamma_src": "Gamma5"}\n
    \n
    \n\n
    Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
Read hadrons FlowObservables hdf5 file and extract t0
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
Read hadrons DistillationContraction hdf5 files in given directory structure
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
    • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
\n\n
An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\n
Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\n
For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n
array:  Construct an array.
\nzeros:  Create an array, each element of which is zero.
\nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype:  Create a data-type.
\nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
\n\n
Notes
\n\n
There are two modes of creating an array using __new__:
\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n
No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\n
Examples
\n\n
These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\n
First mode, buffer is None:
\n\n
\n
>>> import numpy as np\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n
\n\n
Second mode:
\n\n
\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
Gamma_5 hermitean conjugate
\n\n
Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
Read hadrons ExternalLeg hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Npr_matrix):\nread Cobs-matrix
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
Read hadrons Bilinear hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict[Npr_matrix]):\nextracted Bilinears
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • vertices (list):\nVertex functions to be extracted.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict):\nextracted fourquark matrizes
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
\n\n
Returns
\n\n
    \n
  • json_string (str):\nString for export to .json(.gz) file
    • \n
\n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • Null
    • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
Reconstruct a list of Obs or structures containing Obs from a json string.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
Import a list of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
Export a dict of Obs or structures containing Obs to a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
Import a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
    • \n
\n\n
Returns
\n\n
    \n
  • data (Obs / list / Corr):\nRead data
    • \n
  • or
    • \n
  • data (dict):\nRead data and meta-data
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
\n\n
It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
\n\n
A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
\n\n
Parameters
\n\n
    \n
  • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
    • \n
  • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
    • \n
\n\n
Returns
\n\n
    \n
  • root (Obs):\nThe root of the data series.
    • \n
\n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
Read pbp format from given folder structure.
\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of observables read
    • \n
\n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
Read rwms format from given folder structure. Returns a list of length nrw
\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
    • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
    • \n
  • version (str):\nversion of openQCD, default 2.0
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
    • \n
\n\n
Returns
\n\n
    \n
  • rwms (Obs):\nReweighting factors read
    • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • t0 (Obs):\nExtracted t0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
Extract w0/a from given .ms.dat files. Returns w0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • w0 (Obs):\nExtracted w0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
Read the topologial charge based on openQCD gradient flow measurements.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Obs):\nRead topological charge
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
\n\n
Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
Returns the projection to the topological charge sector defined by target.
\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
Constructs reweighting factors to a specified topological sector.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
    • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
\n\n
Parameters
\n\n
    \n
  • path (str):\nThe directory to search for the files in.
    • \n
  • prefix (str):\nThe prefix to match the files against.
    • \n
  • qc (str):\nThe quark combination extension to match the files against.
    • \n
  • corr (str):\nThe correlator to extract data for.
    • \n
  • sep (str, optional):\nThe separator to use when parsing the replika names.
    • \n
  • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
    \n\n
      \n
    • names (List[str]): A list of names to use for the replicas.
      • \n
    • files (List[str]): A list of files to read data from.
      • \n
    • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
      • \n
    • \n
\n\n
Returns
\n\n
    \n
  • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
    • \n
  • or
    • \n
  • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
    • \n
\n\n
Raises
\n\n
    \n
  • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
    • \n
  • IOError: If there is an error reading a file.
    • \n
  • struct.error: If there is an error unpacking binary data.
    • \n
\n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
Write DataFrame including Obs or Corr valued columns to sqlite database.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be written to the database.
    • \n
  • table_name (str):\nName of the table in the database.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
    • \n
  • gz (bool):\nIf True the json strings are gzipped.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
\n\n
Parameters
\n\n
    \n
  • sql (str):\nSQL query to be executed.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
\n\n
Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be dumped to a file.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
\n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
\n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
    • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks_list (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type_list (list[str]):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset_list (list[int]):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf_list (int):\nID of wave function
    • \n
  • wf2_list (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list[list[int]]):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
  • rep_string (str):\nSeparator of ensemble name and replicum. Example: In \"ensAr0\", \"r\" would be the separator string.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]
    • \n
\n", "signature": "(\tpath,\tprefix,\tname_list,\tquarks_list=['.*'],\tcorr_type_list=['bi'],\tnoffset_list=[0],\twf_list=[0],\twf2_list=[0],\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\tkeyed_out=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
Utilities for the input
\n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
\n\n
Parameters
\n\n
    \n
  • ll (list):\nlist to sort
    • \n
\n\n
Returns
\n\n
    \n
  • ll (list):\nsorted list
    • \n
\n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
Checks if list of configurations is contained in an idl
\n\n
Parameters
\n\n
    \n
  • idl (range or list):\nidl of the current replicum
    • \n
  • che (list):\nlist of configurations to be checked against
    • \n
\n\n
Returns
\n\n
    \n
  • miss_str (str):\nstring with integers of which idls are missing
    • \n
\n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "
Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
\n\n
Parameters
\n\n
    \n
  • path (str):\nmeasurement path, same as for sfcf read method
    • \n
  • param_hash (str):\nexpected parameter hash
    • \n
  • prefix (str):\ndata prefix to find the appropriate replicum folders in path
    • \n
  • param_prefix (str):\nprefix of the parameter file. Defaults to 'parameters_'
    • \n
\n\n
Returns
\n\n
    \n
  • nums (dict):\ndictionary of faulty parameter files sorted by the replica paths
    • \n
\n", "signature": "(path, param_hash, prefix, param_prefix='parameters_'):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
\n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
\n\n
The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
\n\n
Parameters
\n\n
    \n
  • func (object):\nfunction to integrate, has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(p, x):\n    return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
    \n
    \n\n
    where x is the integration variable.
    • \n
  • p (list of floats or Obs):\nparameters of the function func.
    • \n
  • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
    • \n
  • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
    • \n
  • All parameters of scipy.integrate.quad
    • \n
\n\n
Returns
\n\n
    \n
  • y (Obs):\nThe integral of func from a to b.
    • \n
  • abserr (float):\nAn estimate of the absolute error in the result.
    • \n
  • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
    • \n
  • message: A convergence message.
    • \n
  • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
    • \n
\n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
Matrix multiply all operands.
\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • This implementation is faster compared to standard multiplication via the @ operator.
    • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
Matrix multiply both operands making use of the jackknife approximation.
\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
  • For large matrices this is considerably faster compared to matmul.
    • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
Wrapper for numpy.einsum
\n\n
Parameters
\n\n
    \n
  • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
    • \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
    • \n
\n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
Inverse of Obs or CObs valued matrices.
\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
Cholesky decomposition of Obs valued matrices.
\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
Determinant of Obs valued matrices.
\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eigv": {"fullname": "pyerrors.linalg.eigv", "modulename": "pyerrors.linalg", "qualname": "eigv", "kind": "function", "doc": "
Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
Computes the singular value decomposition of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
Print information about version of python, pyerrors and dependencies.
\n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
pyerrors wrapper for the errorbars method of matplotlib
\n\n
Parameters
\n\n
    \n
  • x (list):\nA list of x-values which can be Obs.
    • \n
  • y (list):\nA list of y-values which can be Obs.
    • \n
  • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
    • \n
\n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.16/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
Dump object into pickle file.
\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
    • \n
  • name (str):\nname of the file
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
Load object from pickle file.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n\n
Returns
\n\n
    \n
  • object (Obs):\nLoaded Object
    • \n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
Generate an Obs object with given value, dvalue and name for test purposes
\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
    • \n
  • dvalue (float):\nerror of the Obs to be generated.
    • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
    • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nGenerated Observable
    • \n
\n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
Generate observables with given covariance and autocorrelation times.
\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
    • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
    • \n
  • name (str):\nensemble name for the data to be geneated.
    • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
    • \n
  • samples (int):\nnumber of samples to be generated for each observable.
    • \n
\n\n
Returns
\n\n
    \n
  • corr_obs (list[Obs]):\nGenerated observable list
    • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
Matrix pencil method to extract k energy levels from data
\n\n
Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
    • \n
  • k (int):\nNumber of states to extract (default 1).
    • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
    • \n
\n\n
Returns
\n\n
    \n
  • energy_levels (list[Obs]):\nExtracted energy levels
    • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
Class for a general observable.
\n\n
Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
    • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
    • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
    • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
    • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
Initialize Obs object.
\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
    • \n
  • names (list):\nlist of strings labeling the individual samples
    • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
    • \n
\n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
Output detailed properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
    • \n
\n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
Reweight the obs with given rewighting factors.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
Checks whether the observable is zero within 'sigma' standard errors.
\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
    • \n
  • Works only properly when the gamma method was run.
    • \n
\n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
Checks whether the observable is zero within a given tolerance.
\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
    • \n
\n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
Plot integrated autocorrelation time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
Plot normalized autocorrelation function time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
Plot replica distribution for each ensemble with more than one replicum.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
Plot derived Monte Carlo history for each ensemble
\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
    • \n
\n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
Dump the Obs to a file 'name' of chosen format.
\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
Export jackknife samples from the Obs
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
    • \n
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
Export bootstrap samples from the Obs
\n\n
Parameters
\n\n
    \n
  • samples (int):\nNumber of bootstrap samples to generate.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
    • \n
  • save_rng (str):\nSave the random numbers to a file if a path is specified.
    • \n
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
    • \n
\n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
\n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
Executes the gamma_method for the real and the imaginary part.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
Checks whether both real and imaginary part are zero within machine precision.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
Vectorized version of the gamma_method applicable to lists or arrays of Obs.
\n\n
See docstring of pe.Obs.gamma_method for details.
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
Vectorized version of the gamma_method applicable to lists or arrays of Obs.
\n\n
See docstring of pe.Obs.gamma_method for details.
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
\n\n
Parameters
\n\n
    \n
  • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
    • \n
  • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
    • \n
  • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
    • \n
\n\n
Notes
\n\n
For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\n
new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
\n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
Reweight a list of observables.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
Correlate two observables.
\n\n
Parameters
\n\n
    \n
  • obs_a (Obs):\nFirst observable
    • \n
  • obs_b (Obs):\nSecond observable
    • \n
\n\n
Notes
\n\n
Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nOnly works if a single ensemble is present in the Obs.\nCurrently only works if ensemble content is identical (this is not strictly necessary).
\n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
Calculates the error covariance matrix of a set of observables.
\n\n
WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
\n\n
The gamma method has to be applied first to all observables.
\n\n
Parameters
\n\n
    \n
  • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
    • \n
  • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
    • \n
  • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
    • \n
  • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
    • \n
\n\n
Notes
\n\n
The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.invert_corr_cov_cholesky": {"fullname": "pyerrors.obs.invert_corr_cov_cholesky", "modulename": "pyerrors.obs", "qualname": "invert_corr_cov_cholesky", "kind": "function", "doc": "
Constructs a lower triangular matrix chol via the Cholesky decomposition of the correlation matrix corr\n   and then returns the inverse covariance matrix chol_inv as a lower triangular matrix by solving chol * x = inverrdiag.
\n\n
Parameters
\n\n
    \n
  • corr (np.ndarray):\ncorrelation matrix
    • \n
  • inverrdiag (np.ndarray):\ndiagonal matrix, the entries are the inverse errors of the data points considered
    • \n
\n", "signature": "(corr, inverrdiag):", "funcdef": "def"}, "pyerrors.obs.sort_corr": {"fullname": "pyerrors.obs.sort_corr", "modulename": "pyerrors.obs", "qualname": "sort_corr", "kind": "function", "doc": "
Reorders a correlation matrix to match the alphabetical order of its underlying y data.
\n\n
The ordering of the input correlation matrix corr is given by the list of keys kl.\nThe input dictionary yd (with the same keys kl) must contain the corresponding y data\nthat the correlation matrix is based on.\nThis function sorts the list of keys kl alphabetically and sorts the matrix corr\naccording to this alphabetical order such that the sorted matrix corr_sorted corresponds\nto the y data yd when arranged in an alphabetical order by its keys.
\n\n
Parameters
\n\n
    \n
  • corr (np.ndarray):\nA square correlation matrix constructed using the order of the y data specified by kl.\nThe dimensions of corr should match the total number of y data points in yd combined.
    • \n
  • kl (list of str):\nA list of keys that denotes the order in which the y data from yd was used to build the\ninput correlation matrix corr.
    • \n
  • yd (dict of list):\nA dictionary where each key corresponds to a unique identifier, and its value is a list of\ny data points. The total number of y data points across all keys must match the dimensions\nof corr. The lists in the dictionary can be lists of Obs.
    • \n
\n\n
Returns
\n\n
    \n
  • np.ndarray: A new, sorted correlation matrix that corresponds to the y data from yd when arranged alphabetically by its keys.
    • \n
\n\n
Example
\n\n
\n
>>> import numpy as np\n>>> import pyerrors as pe\n>>> corr = np.array([[1, 0.2, 0.3], [0.2, 1, 0.4], [0.3, 0.4, 1]])\n>>> kl = ['b', 'a']\n>>> yd = {'a': [1, 2], 'b': [3]}\n>>> sorted_corr = pe.obs.sort_corr(corr, kl, yd)\n>>> print(sorted_corr)\narray([[1. , 0.3, 0.4],\n       [0.3, 1. , 0.2],\n       [0.4, 0.2, 1. ]])\n
\n
\n", "signature": "(corr, kl, yd):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
Imports jackknife samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
\n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
Imports bootstrap samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
    • \n
\n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
Combine all observables in list_of_obs into one new observable.\nThis allows to merge Obs that have been computed on multiple replica\nof the same ensemble.\nIf you like to merge Obs that are based on several ensembles, please\naverage them yourself.
\n\n
Parameters
\n\n
    \n
  • list_of_obs (list):\nlist of the Obs object to be combined
    • \n
\n\n
Notes
\n\n
It is not possible to combine obs which are based on the same replicum
\n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
Create an Obs based on mean(s) and a covariance matrix
\n\n
Parameters
\n\n
    \n
  • mean (list of floats or float):\nN mean value(s) of the new Obs
    • \n
  • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
Finds the root of the function func(x, d) where d is an Obs.
\n\n
Parameters
\n\n
    \n
  • d (Obs):\nObs passed to the function.
    • \n
  • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
    \n\n
    \n
    import autograd.numpy as anp\ndef root_func(x, d):\n    return anp.exp(-x ** 2) - d\n
    \n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nObs valued root of the function.
    • \n
\n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.special": {"fullname": "pyerrors.special", "modulename": "pyerrors.special", "kind": "module", "doc": "
\n"}, "pyerrors.special.beta": {"fullname": "pyerrors.special.beta", "modulename": "pyerrors.special", "qualname": "beta", "kind": "function", "doc": "
beta(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
beta(a, b, out=None)
\n\n
Beta function.
\n\n
This function is defined in 1 as
\n\n
$$B(a, b) = \\int_0^1 t^{a-1}(1-t)^{b-1}dt\n        = \\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a+b)},$$
\n\n
where \\( \\Gamma \\) is the gamma function.
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nReal-valued arguments
    • \n
  • out (ndarray, optional):\nOptional output array for the function result
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the beta function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\nbetainc:   the regularized incomplete beta function
\nbetaln:  the natural logarithm of the absolute\nvalue of the beta function  
\n\n
References
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
The beta function relates to the gamma function by the\ndefinition given above:
\n\n
\n
>>> sc.beta(2, 3)\n0.08333333333333333\n>>> sc.gamma(2)*sc.gamma(3)/sc.gamma(2 + 3)\n0.08333333333333333\n
\n
\n\n
As this relationship demonstrates, the beta function\nis symmetric:
\n\n
\n
>>> sc.beta(1.7, 2.4)\n0.16567527689031739\n>>> sc.beta(2.4, 1.7)\n0.16567527689031739\n
\n
\n\n
This function satisfies \\( B(1, b) = 1/b \\):
\n\n
\n
>>> sc.beta(1, 4)\n0.25\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions,\nEq. 5.12.1. https://dlmf.nist.gov/5.12 ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betainc": {"fullname": "pyerrors.special.betainc", "modulename": "pyerrors.special", "qualname": "betainc", "kind": "function", "doc": "
betainc(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
betainc(a, b, x, out=None)
\n\n
Regularized incomplete beta function.
\n\n
Computes the regularized incomplete beta function, defined as 1:
\n\n
$$I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\nt^{a-1}(1-t)^{b-1}dt,$$
\n\n
for \\( 0 \\leq x \\leq 1 \\).
\n\n
This function is the cumulative distribution function for the beta\ndistribution; its range is [0, 1].
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nPositive, real-valued parameters
    • \n
  • x (array_like):\nReal-valued such that \\( 0 \\leq x \\leq 1 \\),\nthe upper limit of integration
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the regularized incomplete beta function
    • \n
\n\n
See Also
\n\n
beta:  beta function
\nbetaincinv:  inverse of the regularized incomplete beta function
\nbetaincc:  complement of the regularized incomplete beta function
\nscipy.stats.beta:  beta distribution  
\n\n
Notes
\n\n
The term regularized in the name of this function refers to the\nscaling of the function by the gamma function terms shown in the\nformula.  When not qualified as regularized, the name incomplete\nbeta function often refers to just the integral expression,\nwithout the gamma terms.  One can use the function beta from\nscipy.special to get this \"nonregularized\" incomplete beta\nfunction by multiplying the result of betainc(a, b, x) by\nbeta(a, b).
\n\n
This function wraps the ibeta routine from the\nBoost Math C++ library 2.
\n\n
References
\n\n
Examples
\n\n
Let \\( B(a, b) \\) be the beta function.
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
The coefficient in terms of gamma is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).
\n\n
\n
>>> sc.betainc(0.2, 3.5, 1.0)\n1.0\n
\n
\n\n
It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function hyp2f1:
\n\n
\n
>>> a, b, x = 1.4, 3.1, 0.5\n>>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n0.8148904036225295\n>>> sc.betainc(a, b, x)\n0.8148904036225296\n
\n
\n\n
This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):
\n\n
\n
>>> sc.betainc(2.2, 3.1, 0.4)\n0.49339638807619446\n>>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n0.49339638807619446\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/8.17 ↩
    \n
    2. \n\n
  2. \n
    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "
betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
betaln(a, b, out=None)
\n\n
Natural logarithm of absolute value of beta function.
\n\n
Computes ln(abs(beta(a, b))).
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nPositive, real-valued parameters
    • \n
  • out (ndarray, optional):\nOptional output array for function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the betaln function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\nbetainc:   the regularized incomplete beta function
\nbeta:  the beta function  
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import betaln, beta\n
\n
\n\n
Verify that, for moderate values of a and b, betaln(a, b)\nis the same as log(beta(a, b)):
\n\n
\n
>>> betaln(3, 4)\n-4.0943445622221\n
\n
\n\n
\n
>>> np.log(beta(3, 4))\n-4.0943445622221\n
\n
\n\n
In the following beta(a, b) underflows to 0, so we can't compute\nthe logarithm of the actual value.
\n\n
\n
>>> a = 400\n>>> b = 900\n>>> beta(a, b)\n0.0\n
\n
\n\n
We can compute the logarithm of beta(a, b) by using betaln:
\n\n
\n
>>> betaln(a, b)\n-804.3069951764146\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "
Polygamma functions.
\n\n
Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\ndigamma function. See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • n (array_like):\nThe order of the derivative of the digamma function; must be\nintegral
    • \n
  • x (array_like):\nReal valued input
    • \n
\n\n
Returns
\n\n
    \n
  • ndarray: Function results
    • \n
\n\n
See Also
\n\n
digamma  
\n\n
References
\n\n
.. [dlmf] NIST, Digital Library of Mathematical Functions,\n    https://dlmf.nist.gov/5.15
\n\n
Examples
\n\n
\n
>>> from scipy import special\n>>> x = [2, 3, 25.5]\n>>> special.polygamma(1, x)\narray([ 0.64493407,  0.39493407,  0.03999467])\n>>> special.polygamma(0, x) == special.psi(x)\narray([ True,  True,  True], dtype=bool)\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "
gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gamma(z, out=None)
\n\n
gamma function.
\n\n
The gamma function is defined as
\n\n
$$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$
\n\n
for \\( \\Re(z) > 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex valued argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the gamma function
    • \n
\n\n
Notes
\n\n
The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).
\n\n
The gamma function has poles at non-negative integers and the sign\nof infinity as z approaches each pole depends upon the direction in\nwhich the pole is approached. For this reason, the consistent thing\nis for gamma(z) to return NaN at negative integers, and to return\n-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero\nto signify the direction in which the origin is being approached. This\nis for instance what is recommended for the gamma function in annex F\nentry 9.5.4 of the Iso C 99 standard [isoc99]_.
\n\n
Prior to SciPy version 1.15, scipy.special.gamma(z) returned +inf\nat each pole. This was fixed in version 1.15, but with the following\nconsequence. Expressions where gamma appears in the denominator\nsuch as
\n\n
gamma(u) * gamma(v) / (gamma(w) * gamma(x))
\n\n
no longer evaluate to 0 if the numerator is well defined but there is a\npole in the denominator. Instead such expressions evaluate to NaN. We\nrecommend instead using the function rgamma for the reciprocal gamma\nfunction in such cases. The above expression could for instance be written\nas
\n\n
gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1\n.. [isoc99] https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import gamma, factorial\n
\n
\n\n
\n
>>> gamma([0, 0.5, 1, 5])\narray([         inf,   1.77245385,   1.        ,  24.        ])\n
\n
\n\n
\n
>>> z = 2.5 + 1j\n>>> gamma(z)\n(0.77476210455108352+0.70763120437959293j)\n>>> gamma(z+1), z*gamma(z)  # Recurrence property\n((1.2292740569981171+2.5438401155000685j),\n (1.2292740569981158+2.5438401155000658j))\n
\n
\n\n
\n
>>> gamma(0.5)**2  # gamma(0.5) = sqrt(pi)\n3.1415926535897927\n
\n
\n\n
Plot gamma(x) for real x
\n\n
\n
>>> x = np.linspace(-3.5, 5.5, 2251)\n>>> y = gamma(x)\n
\n
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)')\n>>> k = np.arange(1, 7)\n>>> plt.plot(k, factorial(k-1), 'k*', alpha=0.6,\n...          label='(x-1)!, x = 1, 2, ...')\n>>> plt.xlim(-3.5, 5.5)\n>>> plt.ylim(-10, 25)\n>>> plt.grid()\n>>> plt.xlabel('x')\n>>> plt.legend(loc='lower right')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "
gammaln(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammaln(x, out=None)
\n\n
Logarithm of the absolute value of the gamma function.
\n\n
Defined as
\n\n
$$\\ln(\\lvert\\Gamma(x)\\rvert)$$
\n\n
where \\( \\Gamma \\) is the gamma function. For more details on\nthe gamma function, see [dlmf]_.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nReal argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the log of the absolute value of gamma
    • \n
\n\n
See Also
\n\n
gammasgn:  sign of the gamma function
\nloggamma:  principal branch of the logarithm of the gamma function  
\n\n
Notes
\n\n
It is the same function as the Python standard library function\nmath.lgamma().
\n\n
When used in conjunction with gammasgn, this function is useful\nfor working in logspace on the real axis without having to deal\nwith complex numbers via the relation exp(gammaln(x)) =\ngammasgn(x) * gamma(x).
\n\n
For complex-valued log-gamma, use loggamma instead of gammaln.
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import scipy.special as sc\n
\n
\n\n
It has two positive zeros.
\n\n
\n
>>> sc.gammaln([1, 2])\narray([0., 0.])\n
\n
\n\n
It has poles at nonpositive integers.
\n\n
\n
>>> sc.gammaln([0, -1, -2, -3, -4])\narray([inf, inf, inf, inf, inf])\n
\n
\n\n
It asymptotically approaches x * log(x) (Stirling's formula).
\n\n
\n
>>> x = np.array([1e10, 1e20, 1e40, 1e80])\n>>> sc.gammaln(x)\narray([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82])\n>>> x * np.log(x)\narray([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammainc": {"fullname": "pyerrors.special.gammainc", "modulename": "pyerrors.special", "qualname": "gammainc", "kind": "function", "doc": "
gammainc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammainc(a, x, out=None)
\n\n
Regularized lower incomplete gamma function.
\n\n
It is defined as
\n\n
$$P(a, x) = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a - 1}e^{-t} dt$$
\n\n
for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • a (array_like):\nPositive parameter
    • \n
  • x (array_like):\nNonnegative argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the lower incomplete gamma function
    • \n
\n\n
See Also
\n\n
gammaincc:  regularized upper incomplete gamma function
\ngammaincinv:  inverse of the regularized lower incomplete gamma function
\ngammainccinv:  inverse of the regularized upper incomplete gamma function  
\n\n
Notes
\n\n
The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammaincc is the regularized upper\nincomplete gamma function.
\n\n
The implementation largely follows that of [boost]_.
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
It is the CDF of the gamma distribution, so it starts at 0 and\nmonotonically increases to 1.
\n\n
\n
>>> sc.gammainc(0.5, [0, 1, 10, 100])\narray([0.        , 0.84270079, 0.99999226, 1.        ])\n
\n
\n\n
It is equal to one minus the upper incomplete gamma function.
\n\n
\n
>>> a, x = 0.5, 0.4\n>>> sc.gammainc(a, x)\n0.6289066304773024\n>>> 1 - sc.gammaincc(a, x)\n0.6289066304773024\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaincc": {"fullname": "pyerrors.special.gammaincc", "modulename": "pyerrors.special", "qualname": "gammaincc", "kind": "function", "doc": "
gammaincc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammaincc(a, x, out=None)
\n\n
Regularized upper incomplete gamma function.
\n\n
It is defined as
\n\n
$$Q(a, x) = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a - 1}e^{-t} dt$$
\n\n
for \\( a > 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • a (array_like):\nPositive parameter
    • \n
  • x (array_like):\nNonnegative argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the upper incomplete gamma function
    • \n
\n\n
See Also
\n\n
gammainc:  regularized lower incomplete gamma function
\ngammaincinv:  inverse of the regularized lower incomplete gamma function
\ngammainccinv:  inverse of the regularized upper incomplete gamma function  
\n\n
Notes
\n\n
The function satisfies the relation gammainc(a, x) +\ngammaincc(a, x) = 1 where gammainc is the regularized lower\nincomplete gamma function.
\n\n
The implementation largely follows that of [boost]_.
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical functions\n          https://dlmf.nist.gov/8.2#E4\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
It is the survival function of the gamma distribution, so it\nstarts at 1 and monotonically decreases to 0.
\n\n
\n
>>> sc.gammaincc(0.5, [0, 1, 10, 100, 1000])\narray([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45,\n       0.00000000e+00])\n
\n
\n\n
It is equal to one minus the lower incomplete gamma function.
\n\n
\n
>>> a, x = 0.5, 0.4\n>>> sc.gammaincc(a, x)\n0.37109336952269756\n>>> 1 - sc.gammainc(a, x)\n0.37109336952269756\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammasgn": {"fullname": "pyerrors.special.gammasgn", "modulename": "pyerrors.special", "qualname": "gammasgn", "kind": "function", "doc": "
gammasgn(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gammasgn(x, out=None)
\n\n
Sign of the gamma function.
\n\n
It is defined as
\n\n
$$\\text{gammasgn}(x) =\n\\begin{cases}\n  +1 & \\Gamma(x) > 0 \\\n  -1 & \\Gamma(x) < 0\n\\end{cases}$$
\n\n
where \\( \\Gamma \\) is the gamma function; see gamma. This\ndefinition is complete since the gamma function is never zero;\nsee the discussion after [dlmf]_.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nReal argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Sign of the gamma function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\ngammaln:  log of the absolute value of the gamma function
\nloggamma:  analytic continuation of the log of the gamma function  
\n\n
Notes
\n\n
The gamma function can be computed as gammasgn(x) *\nnp.exp(gammaln(x)).
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import scipy.special as sc\n
\n
\n\n
It is 1 for x > 0.
\n\n
\n
>>> sc.gammasgn([1, 2, 3, 4])\narray([1., 1., 1., 1.])\n
\n
\n\n
It alternates between -1 and 1 for negative integers.
\n\n
\n
>>> sc.gammasgn([-0.5, -1.5, -2.5, -3.5])\narray([-1.,  1., -1.,  1.])\n
\n
\n\n
It can be used to compute the gamma function.
\n\n
\n
>>> x = [1.5, 0.5, -0.5, -1.5]\n>>> sc.gammasgn(x) * np.exp(sc.gammaln(x))\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n>>> sc.gamma(x)\narray([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.rgamma": {"fullname": "pyerrors.special.rgamma", "modulename": "pyerrors.special", "qualname": "rgamma", "kind": "function", "doc": "
rgamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
rgamma(z, out=None)
\n\n
Reciprocal of the gamma function.
\n\n
Defined as \\( 1 / \\Gamma(z) \\), where \\( \\Gamma \\) is the\ngamma function. For more on the gamma function see gamma.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex valued input
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Function results
    • \n
\n\n
See Also
\n\n
gamma,, gammaln,, loggamma  
\n\n
Notes
\n\n
The gamma function has no zeros and has simple poles at\nnonpositive integers, so rgamma is an entire function with zeros\nat the nonpositive integers. See the discussion in [dlmf]_ for\nmore details.
\n\n
References
\n\n
.. [dlmf] Nist, Digital Library of Mathematical functions,\n    https://dlmf.nist.gov/5.2#i
\n\n
Examples
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
It is the reciprocal of the gamma function.
\n\n
\n
>>> sc.rgamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n>>> 1 / sc.gamma([1, 2, 3, 4])\narray([1.        , 1.        , 0.5       , 0.16666667])\n
\n
\n\n
It is zero at nonpositive integers.
\n\n
\n
>>> sc.rgamma([0, -1, -2, -3])\narray([0., 0., 0., 0.])\n
\n
\n\n
It rapidly underflows to zero along the positive real axis.
\n\n
\n
>>> sc.rgamma([10, 100, 179])\narray([2.75573192e-006, 1.07151029e-156, 0.00000000e+000])\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.multigammaln": {"fullname": "pyerrors.special.multigammaln", "modulename": "pyerrors.special", "qualname": "multigammaln", "kind": "function", "doc": "
Returns the log of multivariate gamma, also sometimes called the\ngeneralized gamma.
\n\n
Parameters
\n\n
    \n
  • a (ndarray):\nThe multivariate gamma is computed for each item of a.
    • \n
  • d (int):\nThe dimension of the space of integration.
    • \n
\n\n
Returns
\n\n
    \n
  • res (ndarray):\nThe values of the log multivariate gamma at the given points a.
    • \n
\n\n
Notes
\n\n
The formal definition of the multivariate gamma of dimension d for a real\na is
\n\n
$$\\Gamma_d(a) = \\int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA$$
\n\n
with the condition \\( a > (d-1)/2 \\), and \\( A > 0 \\) being the set of\nall the positive definite matrices of dimension d.  Note that a is a\nscalar: the integrand only is multivariate, the argument is not (the\nfunction is defined over a subset of the real set).
\n\n
This can be proven to be equal to the much friendlier equation
\n\n
$$\\Gamma_d(a) = \\pi^{d(d-1)/4} \\prod_{i=1}^{d} \\Gamma(a - (i-1)/2).$$
\n\n
References
\n\n
R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in\nprobability and mathematical statistics).
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import multigammaln, gammaln\n>>> a = 23.5\n>>> d = 10\n>>> multigammaln(a, d)\n454.1488605074416\n
\n
\n\n
Verify that the result agrees with the logarithm of the equation\nshown above:
\n\n
\n
>>> d*(d-1)/4*np.log(np.pi) + gammaln(a - 0.5*np.arange(0, d)).sum()\n454.1488605074416\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.kn": {"fullname": "pyerrors.special.kn", "modulename": "pyerrors.special", "qualname": "kn", "kind": "function", "doc": "
Modified Bessel function of the second kind of integer order n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j0": {"fullname": "pyerrors.special.j0", "modulename": "pyerrors.special", "qualname": "j0", "kind": "function", "doc": "
j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
j0(x, out=None)
\n\n
Bessel function of the first kind of order 0.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 0 at x.
    • \n
\n\n
See Also
\n\n
jv:  Bessel function of real order and complex argument.
\nspherical_jn:  spherical Bessel functions.  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval the following rational approximation is used:
\n\n
$$J_0(x) \\approx (w - r_1^2)(w - r_2^2) \\frac{P_3(w)}{Q_8(w)},$$
\n\n
where \\( w = x^2 \\) and \\( r_1 \\), \\( r_2 \\) are the zeros of\n\\( J_0 \\), and \\( P_3 \\) and \\( Q_8 \\) are polynomials of degrees 3\nand 8, respectively.
\n\n
In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
\n\n
This function is a wrapper for the Cephes 1 routine j0.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import j0\n>>> j0(1.)\n0.7651976865579665\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> j0(np.array([-2., 0., 4.]))\narray([ 0.22389078,  1.        , -0.39714981])\n
\n
\n\n
Plot the function from -20 to 20.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y0": {"fullname": "pyerrors.special.y0", "modulename": "pyerrors.special", "qualname": "y0", "kind": "function", "doc": "
y0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
y0(x, out=None)
\n\n
Bessel function of the second kind of order 0.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 0 at x.
    • \n
\n\n
See Also
\n\n
j0:  Bessel function of the first kind of order 0
\nyv:  Bessel function of the first kind  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval a rational approximation \\( R(x) \\) is employed to\ncompute,
\n\n
$$Y_0(x) = R(x) + \\frac{2 \\log(x) J_0(x)}{\\pi},$$
\n\n
where \\( J_0 \\) is the Bessel function of the first kind of order 0.
\n\n
In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.
\n\n
This function is a wrapper for the Cephes 1 routine y0.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import y0\n>>> y0(1.)\n0.08825696421567697\n
\n
\n\n
Calculate at several points:
\n\n
\n
>>> import numpy as np\n>>> y0(np.array([0.5, 2., 3.]))\narray([-0.44451873,  0.51037567,  0.37685001])\n
\n
\n\n
Plot the function from 0 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.j1": {"fullname": "pyerrors.special.j1", "modulename": "pyerrors.special", "qualname": "j1", "kind": "function", "doc": "
j1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
j1(x, out=None)
\n\n
Bessel function of the first kind of order 1.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • J (scalar or ndarray):\nValue of the Bessel function of the first kind of order 1 at x.
    • \n
\n\n
See Also
\n\n
jv:  Bessel function of the first kind
\nspherical_jn:  spherical Bessel functions.  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 24 term Chebyshev expansion is used. In the second, the\nasymptotic trigonometric representation is employed using two rational\nfunctions of degree 5/5.
\n\n
This function is a wrapper for the Cephes 1 routine j1.\nIt should not be confused with the spherical Bessel functions (see\nspherical_jn).
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import j1\n>>> j1(1.)\n0.44005058574493355\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> j1(np.array([-2., 0., 4.]))\narray([-0.57672481,  0.        , -0.06604333])\n
\n
\n\n
Plot the function from -20 to 20.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-20., 20., 1000)\n>>> y = j1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.y1": {"fullname": "pyerrors.special.y1", "modulename": "pyerrors.special", "qualname": "y1", "kind": "function", "doc": "
y1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
y1(x, out=None)
\n\n
Bessel function of the second kind of order 1.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • Y (scalar or ndarray):\nValue of the Bessel function of the second kind of order 1 at x.
    • \n
\n\n
See Also
\n\n
j1:  Bessel function of the first kind of order 1
\nyn:  Bessel function of the second kind
\nyv:  Bessel function of the second kind  
\n\n
Notes
\n\n
The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 25 term Chebyshev expansion is used, and computing\n\\( J_1 \\) (the Bessel function of the first kind) is required. In the\nsecond, the asymptotic trigonometric representation is employed using two\nrational functions of degree 5/5.
\n\n
This function is a wrapper for the Cephes 1 routine y1.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import y1\n>>> y1(1.)\n-0.7812128213002888\n
\n
\n\n
Calculate at several points:
\n\n
\n
>>> import numpy as np\n>>> y1(np.array([0.5, 2., 3.]))\narray([-1.47147239, -0.10703243,  0.32467442])\n
\n
\n\n
Plot the function from 0 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> y = y1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.jn": {"fullname": "pyerrors.special.jn", "modulename": "pyerrors.special", "qualname": "jn", "kind": "function", "doc": "
jv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
jv(v, z, out=None)
\n\n
Bessel function of the first kind of real order and complex argument.
\n\n
Parameters
\n\n
    \n
  • v (array_like):\nOrder (float).
    • \n
  • z (array_like):\nArgument (float or complex).
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • J (scalar or ndarray):\nValue of the Bessel function, \\( J_v(z) \\).
    • \n
\n\n
See Also
\n\n
jve:  \\( J_v \\) with leading exponential behavior stripped off.
\nspherical_jn:  spherical Bessel functions.
\nj0:  faster version of this function for order 0.
\nj1:  faster version of this function for order 1.  
\n\n
Notes
\n\n
For positive v values, the computation is carried out using the AMOS\n1 zbesj routine, which exploits the connection to the modified\nBessel function \\( I_v \\),
\n\n
$$J_v(z) = \\exp(v\\pi\\imath/2) I_v(-\\imath z)\\qquad (\\Im z > 0)
\n\n
J_v(z) = \\exp(-v\\pi\\imath/2) I_v(\\imath z)\\qquad (\\Im z < 0)$$
\n\n
For negative v values the formula,
\n\n
$$J_{-v}(z) = J_v(z) \\cos(\\pi v) - Y_v(z) \\sin(\\pi v)$$
\n\n
is used, where \\( Y_v(z) \\) is the Bessel function of the second\nkind, computed using the AMOS routine zbesy.  Note that the second\nterm is exactly zero for integer v; to improve accuracy the second\nterm is explicitly omitted for v values such that v = floor(v).
\n\n
Not to be confused with the spherical Bessel functions (see spherical_jn).
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import jv\n>>> jv(0, 1.)\n0.7651976865579666\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> jv(0, 1.), jv(1, 1.), jv(1.5, 1.)\n(0.7651976865579666, 0.44005058574493355, 0.24029783912342725)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> jv([0, 1, 1.5], 1.)\narray([0.76519769, 0.44005059, 0.24029784])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> jv(0, points)\narray([ 0.22389078,  1.        , -0.26005195])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> jv(orders, points)\narray([[ 0.22389078,  1.        , -0.26005195],\n       [-0.57672481,  0.        ,  0.33905896]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -10 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, jv(i, x), label=f'$J_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.yn": {"fullname": "pyerrors.special.yn", "modulename": "pyerrors.special", "qualname": "yn", "kind": "function", "doc": "
yn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
yn(n, x, out=None)
\n\n
Bessel function of the second kind of integer order and real argument.
\n\n
Parameters
\n\n
    \n
  • n (array_like):\nOrder (integer).
    • \n
  • x (array_like):\nArgument (float).
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • Y (scalar or ndarray):\nValue of the Bessel function, \\( Y_n(x) \\).
    • \n
\n\n
See Also
\n\n
yv:  For real order and real or complex argument.
\ny0:  faster implementation of this function for order 0
\ny1:  faster implementation of this function for order 1  
\n\n
Notes
\n\n
Wrapper for the Cephes 1 routine yn.
\n\n
The function is evaluated by forward recurrence on n, starting with\nvalues computed by the Cephes routines y0 and y1. If n = 0 or 1,\nthe routine for y0 or y1 is called directly.
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import yn\n>>> yn(0, 1.)\n0.08825696421567697\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> yn(0, 1.), yn(1, 1.), yn(2, 1.)\n(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> yn([0, 1, 2], 1.)\narray([ 0.08825696, -0.78121282, -1.65068261])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([0.5, 3., 8.])\n>>> yn(0, points)\narray([-0.44451873,  0.37685001,  0.22352149])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> yn(orders, points)\narray([[-0.44451873,  0.37685001,  0.22352149],\n       [-1.47147239,  0.32467442, -0.15806046]])\n
\n
\n\n
Plot the functions of order 0 to 3 from 0 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(0., 10., 1000)\n>>> for i in range(4):\n...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')\n>>> ax.set_ylim(-3, 1)\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i0": {"fullname": "pyerrors.special.i0", "modulename": "pyerrors.special", "qualname": "i0", "kind": "function", "doc": "
i0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
i0(x, out=None)
\n\n
Modified Bessel function of order 0.
\n\n
Defined as,
\n\n
$$I_0(x) = \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{(k!)^2} = J_0(\\imath x),$$
\n\n
where \\( J_0 \\) is the Bessel function of the first kind of order 0.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float)
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • I (scalar or ndarray):\nValue of the modified Bessel function of order 0 at x.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of any order
\ni0e:  Exponentially scaled modified Bessel function of order 0  
\n\n
Notes
\n\n
The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
\n\n
This function is a wrapper for the Cephes 1 routine i0.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import i0\n>>> i0(1.)\n1.2660658777520082\n
\n
\n\n
Calculate at several points:
\n\n
\n
>>> import numpy as np\n>>> i0(np.array([-2., 0., 3.5]))\narray([2.2795853 , 1.        , 7.37820343])\n
\n
\n\n
Plot the function from -10 to 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i0(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.i1": {"fullname": "pyerrors.special.i1", "modulename": "pyerrors.special", "qualname": "i1", "kind": "function", "doc": "
i1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
i1(x, out=None)
\n\n
Modified Bessel function of order 1.
\n\n
Defined as,
\n\n
$$I_1(x) = \\frac{1}{2}x \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{k! (k + 1)!}\n       = -\\imath J_1(\\imath x),$$
\n\n
where \\( J_1 \\) is the Bessel function of the first kind of order 1.
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nArgument (float)
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • I (scalar or ndarray):\nValue of the modified Bessel function of order 1 at x.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of the first kind
\ni1e:  Exponentially scaled modified Bessel function of order 1  
\n\n
Notes
\n\n
The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.
\n\n
This function is a wrapper for the Cephes 1 routine i1.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import i1\n>>> i1(1.)\n0.5651591039924851\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> i1(np.array([-2., 0., 6.]))\narray([-1.59063685,  0.        , 61.34193678])\n
\n
\n\n
Plot the function between -10 and 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "
iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
iv(v, z, out=None)
\n\n
Modified Bessel function of the first kind of real order.
\n\n
Parameters
\n\n
    \n
  • v (array_like):\nOrder. If z is of real type and negative, v must be integer\nvalued.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the modified Bessel function.
    • \n
\n\n
See Also
\n\n
ive:  This function with leading exponential behavior stripped off.
\ni0:  Faster version of this function for order 0.
\ni1:  Faster version of this function for order 1.  
\n\n
Notes
\n\n
For real z and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method 1.  For larger orders, uniform asymptotic\nexpansions are applied.
\n\n
For complex z and positive v, the AMOS 2 zbesi routine is\ncalled. It uses a power series for small z, the asymptotic expansion\nfor large abs(z), the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import iv\n>>> iv(0, 1.)\n1.2660658777520084\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> iv(0, 1.), iv(1, 1.), iv(1.5, 1.)\n(1.2660658777520084, 0.565159103992485, 0.2935253263474798)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> iv([0, 1, 1.5], 1.)\narray([1.26606588, 0.5651591 , 0.29352533])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> iv(0, points)\narray([2.2795853 , 1.        , 4.88079259])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> iv(orders, points)\narray([[ 2.2795853 ,  1.        ,  4.88079259],\n       [-1.59063685,  0.        ,  3.95337022]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, iv(i, x), label=f'$I_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Temme, Journal of Computational Physics, vol 21, 343 (1976) ↩
    \n
    2. \n\n
  2. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "
ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
ive(v, z, out=None)
\n\n
Exponentially scaled modified Bessel function of the first kind.
\n\n
Defined as::
\n\n
ive(v, z) = iv(v, z) * exp(-abs(z.real))\n
\n\n
For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind iv.
\n\n
Parameters
\n\n
    \n
  • v (array_like of float):\nOrder.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the exponentially scaled modified Bessel function.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of the first kind
\ni0e:  Faster implementation of this function for order 0
\ni1e:  Faster implementation of this function for order 1  
\n\n
Notes
\n\n
For positive v, the AMOS 1 zbesi routine is called. It uses a\npower series for small z, the asymptotic expansion for large\nabs(z), the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
ive is useful for large arguments z: for these, iv easily overflows,\nwhile ive does not due to the exponential scaling.
\n\n
References
\n\n
Examples
\n\n
In the following example iv returns infinity whereas ive still returns\na finite number.
\n\n
\n
>>> from scipy.special import iv, ive\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> iv(3, 1000.), ive(3, 1000.)\n(inf, 0.01256056218254712)\n
\n
\n\n
Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> ive([0, 1, 1.5], 1.)\narray([0.46575961, 0.20791042, 0.10798193])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> points = np.array([-2., 0., 3.])\n>>> ive(0, points)\narray([0.30850832, 1.        , 0.24300035])\n
\n
\n\n
Evaluate the function at several points for different orders by\nproviding arrays for both v for z. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:
\n\n
\n
>>> ive([[0], [1], [2]], points)\narray([[ 0.30850832,  1.        ,  0.24300035],\n       [-0.21526929,  0.        ,  0.19682671],\n       [ 0.09323903,  0.        ,  0.11178255]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, ive(i, x), label=fr'$I_{i!r}(z)\\cdot e^{{-|z|}}$')\n>>> ax.legend()\n>>> ax.set_xlabel(r"$z$")\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "
erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erf(z, out=None)
\n\n
Returns the error function of complex argument.
\n\n
It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).
\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nInput array.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • res (scalar or ndarray):\nThe values of the error function at the given points x.
    • \n
\n\n
See Also
\n\n
erfc,, erfinv,, erfcinv,, wofz,, erfcx,, erfi  
\n\n
Notes
\n\n
The cumulative of the unit normal distribution is given by\nPhi(z) = 1/2[1 + erf(z/sqrt(2))].
\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erf(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erf(x)$')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfc": {"fullname": "pyerrors.special.erfc", "modulename": "pyerrors.special", "qualname": "erfc", "kind": "function", "doc": "
erfc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erfc(x, out=None)
\n\n
Complementary error function, 1 - erf(x).
\n\n
Parameters
\n\n
    \n
  • x (array_like):\nReal or complex valued argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the complementary error function
    • \n
\n\n
See Also
\n\n
erf,, erfi,, erfcx,, dawsn,, wofz  
\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erfc(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erfc(x)$')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfinv": {"fullname": "pyerrors.special.erfinv", "modulename": "pyerrors.special", "qualname": "erfinv", "kind": "function", "doc": "
erfinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erfinv(y, out=None)
\n\n
Inverse of the error function.
\n\n
Computes the inverse of the error function.
\n\n
In the complex domain, there is no unique complex number w satisfying\nerf(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, -1 < x < 1, there is a unique real\nnumber satisfying erf(erfinv(x)) = x.
\n\n
Parameters
\n\n
    \n
  • y (ndarray):\nArgument at which to evaluate. Domain: [-1, 1]
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • erfinv (scalar or ndarray):\nThe inverse of erf of y, element-wise
    • \n
\n\n
See Also
\n\n
erf:  Error function of a complex argument
\nerfc:  Complementary error function, 1 - erf(x)
\nerfcinv:  Inverse of the complementary error function  
\n\n
Notes
\n\n
This function wraps the erf_inv routine from the\nBoost Math C++ library 1.
\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfinv, erf\n
\n
\n\n
\n
>>> erfinv(0.5)\n0.4769362762044699\n
\n
\n\n
\n
>>> y = np.linspace(-1.0, 1.0, num=9)\n>>> x = erfinv(y)\n>>> x\narray([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,\n        0.22531206,  0.47693628,  0.81341985,         inf])\n
\n
\n\n
Verify that erf(erfinv(y)) is y.
\n\n
\n
>>> erf(x)\narray([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])\n
\n
\n\n
Plot the function:
\n\n
\n
>>> y = np.linspace(-1, 1, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfinv(y)')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfcinv": {"fullname": "pyerrors.special.erfcinv", "modulename": "pyerrors.special", "qualname": "erfcinv", "kind": "function", "doc": "
erfcinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
erfcinv(y, out=None)
\n\n
Inverse of the complementary error function.
\n\n
Computes the inverse of the complementary error function.
\n\n
In the complex domain, there is no unique complex number w satisfying\nerfc(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, 0 < x < 2, there is a unique real\nnumber satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).
\n\n
It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)
\n\n
Parameters
\n\n
    \n
  • y (ndarray):\nArgument at which to evaluate. Domain: [0, 2]
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • erfcinv (scalar or ndarray):\nThe inverse of erfc of y, element-wise
    • \n
\n\n
See Also
\n\n
erf:  Error function of a complex argument
\nerfc:  Complementary error function, 1 - erf(x)
\nerfinv:  Inverse of the error function  
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfcinv\n
\n
\n\n
\n
>>> erfcinv(0.5)\n0.4769362762044699\n
\n
\n\n
\n
>>> y = np.linspace(0.0, 2.0, num=11)\n>>> erfcinv(y)\narray([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,\n       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,\n              -inf])\n
\n
\n\n
Plot the function:
\n\n
\n
>>> y = np.linspace(0, 2, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfcinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfcinv(y)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logit": {"fullname": "pyerrors.special.logit", "modulename": "pyerrors.special", "qualname": "logit", "kind": "function", "doc": "
logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
logit(x, out=None)
\n\n
Logit ufunc for ndarrays.
\n\n
The logit function is defined as logit(p) = log(p/(1-p)).\nNote that logit(0) = -inf, logit(1) = inf, and logit(p)\nfor p<0 or p>1 yields nan.
\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nThe ndarray to apply logit to element-wise.
    • \n
  • out (ndarray, optional):\nOptional output array for the function results
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare logit of the corresponding entry of x.
    • \n
\n\n
See Also
\n\n
expit  
\n\n
Notes
\n\n
As a ufunc logit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
\n\n
New in version 0.10.0.
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import logit, expit\n
\n
\n\n
\n
>>> logit([0, 0.25, 0.5, 0.75, 1])\narray([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])\n
\n
\n\n
expit is the inverse of logit:
\n\n
\n
>>> expit(logit([0.1, 0.75, 0.999]))\narray([ 0.1  ,  0.75 ,  0.999])\n
\n
\n\n
Plot logit(x) for x in [0, 1]:
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(0, 1, 501)\n>>> y = logit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.ylim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('logit(x)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.expit": {"fullname": "pyerrors.special.expit", "modulename": "pyerrors.special", "qualname": "expit", "kind": "function", "doc": "
expit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
expit(x, out=None)
\n\n
Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.
\n\n
The expit function, also known as the logistic sigmoid function, is\ndefined as expit(x) = 1/(1+exp(-x)).  It is the inverse of the\nlogit function.
\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nThe ndarray to apply expit to element-wise.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare expit of the corresponding entry of x.
    • \n
\n\n
See Also
\n\n
logit  
\n\n
Notes
\n\n
As a ufunc expit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs 
\n\n
New in version 0.10.0.
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import expit, logit\n
\n
\n\n
\n
>>> expit([-np.inf, -1.5, 0, 1.5, np.inf])\narray([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])\n
\n
\n\n
logit is the inverse of expit:
\n\n
\n
>>> logit(expit([-2.5, 0, 3.1, 5.0]))\narray([-2.5,  0. ,  3.1,  5. ])\n
\n
\n\n
Plot expit(x) for x in [-6, 6]:
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-6, 6, 121)\n>>> y = expit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.xlim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('expit(x)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logsumexp": {"fullname": "pyerrors.special.logsumexp", "modulename": "pyerrors.special", "qualname": "logsumexp", "kind": "function", "doc": "
Compute the log of the sum of exponentials of input elements.
\n\n
Parameters
\n\n
    \n
  • a (array_like):\nInput array.
    • \n
  • axis (None or int or tuple of ints, optional):\nAxis or axes over which the sum is taken. By default axis is None,\nand all elements are summed.
    \n\n
    New in version 0.11.0.
    • \n
  • b (array-like, optional):\nScaling factor for exp(a) must be of the same shape as a or\nbroadcastable to a. These values may be negative in order to\nimplement subtraction.
    \n\n
    New in version 0.12.0.
    • \n
  • keepdims (bool, optional):\nIf this is set to True, the axes which are reduced are left in the\nresult as dimensions with size one. With this option, the result\nwill broadcast correctly against the original array.
    \n\n
    New in version 0.15.0.
    • \n
  • return_sign (bool, optional):\nIf this is set to True, the result will be a pair containing sign\ninformation; if False, results that are negative will be returned\nas NaN. Default is False (no sign information).
    \n\n
    New in version 0.16.0.
    • \n
\n\n
Returns
\n\n
    \n
  • res (ndarray):\nThe result, np.log(np.sum(np.exp(a))) calculated in a numerically\nmore stable way. If b is given then np.log(np.sum(b*np.exp(a)))\nis returned. If return_sign is True, res contains the log of\nthe absolute value of the argument.
    • \n
  • sgn (ndarray):\nIf return_sign is True, this will be an array of floating-point\nnumbers matching res containing +1, 0, -1 (for real-valued inputs)\nor a complex phase (for complex inputs). This gives the sign of the\nargument of the logarithm in res.\nIf return_sign is False, only one result is returned.
    • \n
\n\n
See Also
\n\n
numpy.logaddexp,, numpy.logaddexp2  
\n\n
Notes
\n\n
NumPy has a logaddexp function which is very similar to logsumexp, but\nonly handles two arguments. logaddexp.reduce is similar to this\nfunction, but may be less stable.
\n\n
The logarithm is a multivalued function: for each \\( x \\) there is an\ninfinite number of \\( z \\) such that \\( exp(z) = x \\). The convention\nis to return the \\( z \\) whose imaginary part lies in \\( (-pi, pi] \\).
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import logsumexp\n>>> a = np.arange(10)\n>>> logsumexp(a)\n9.4586297444267107\n>>> np.log(np.sum(np.exp(a)))\n9.4586297444267107\n
\n
\n\n
With weights
\n\n
\n
>>> a = np.arange(10)\n>>> b = np.arange(10, 0, -1)\n>>> logsumexp(a, b=b)\n9.9170178533034665\n>>> np.log(np.sum(b*np.exp(a)))\n9.9170178533034647\n
\n
\n\n
Returning a sign flag
\n\n
\n
>>> logsumexp([1,2],b=[1,-1],return_sign=True)\n(1.5413248546129181, -1.0)\n
\n
\n\n
Notice that logsumexp does not directly support masked arrays. To use it\non a masked array, convert the mask into zero weights:
\n\n
\n
>>> a = np.ma.array([np.log(2), 2, np.log(3)],\n...                  mask=[False, True, False])\n>>> b = (~a.mask).astype(int)\n>>> logsumexp(a.data, b=b), np.log(5)\n1.6094379124341005, 1.6094379124341005\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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