From 8f13d14131b4720cf5f5c9ed5d487bcf43b36107 Mon Sep 17 00:00:00 2001 From: fjosw Date: Tue, 25 Feb 2025 15:59:32 +0000 Subject: [PATCH] Documentation updated --- docs/pyerrors/input/dobs.html | 1418 +++--- docs/pyerrors/input/json.html | 1785 ++++---- docs/pyerrors/obs.html | 8083 +++++++++++++++++---------------- docs/search.js | 2 +- 4 files changed, 5662 insertions(+), 5626 deletions(-) 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
  3. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
  4. \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
  3. \n

    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/

    \n
  4. \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
  3. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  4. \n\n
  5. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  6. \n\n
  7. \n

    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ 

    \n
  8. \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
  3. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  4. \n\n
  5. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  6. \n\n
  7. \n

    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ 

    \n
  8. \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
  3. \n

    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ 

    \n
  4. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "

ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

\n\n

ive(v, z, out=None)

\n\n

Exponentially scaled modified Bessel function of the first kind.

\n\n

Defined as::

\n\n
ive(v, z) = iv(v, z) * exp(-abs(z.real))\n
\n\n

For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind iv.

\n\n
Parameters
\n\n
    \n
  • v (array_like of float):\nOrder.
  • \n
  • z (array_like of float or complex):\nArgument.
  • \n
  • out (ndarray, optional):\nOptional output array for the function values
  • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the exponentially scaled modified Bessel function.
  • \n
\n\n
See Also
\n\n

iv: Modified Bessel function of the first kind
\ni0e: Faster implementation of this function for order 0
\ni1e: Faster implementation of this function for order 1

\n\n
Notes
\n\n

For positive v, the AMOS 1 zbesi routine is called. It uses a\npower series for small z, the asymptotic expansion for large\nabs(z), the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.

\n\n

The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,

\n\n

$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$

\n\n

(valid when the real part of z is positive). For negative v, the\nformula

\n\n

$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$

\n\n

is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.

\n\n

ive is useful for large arguments z: for these, iv easily overflows,\nwhile ive does not due to the exponential scaling.

\n\n
References
\n\n
Examples
\n\n

In the following example iv returns infinity whereas ive still returns\na finite number.

\n\n
\n
>>> from scipy.special import iv, ive\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> iv(3, 1000.), ive(3, 1000.)\n(inf, 0.01256056218254712)\n
\n
\n\n

Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the v parameter:

\n\n
\n
>>> ive([0, 1, 1.5], 1.)\narray([0.46575961, 0.20791042, 0.10798193])\n
\n
\n\n

Evaluate the function at several points for order 0 by providing an\narray for z.

\n\n
\n
>>> points = np.array([-2., 0., 3.])\n>>> ive(0, points)\narray([0.30850832, 1.        , 0.24300035])\n
\n
\n\n

Evaluate the function at several points for different orders by\nproviding arrays for both v for z. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:

\n\n
\n
>>> ive([[0], [1], [2]], points)\narray([[ 0.30850832,  1.        ,  0.24300035],\n       [-0.21526929,  0.        ,  0.19682671],\n       [ 0.09323903,  0.        ,  0.11178255]])\n
\n
\n\n

Plot the functions of order 0 to 3 from -5 to 5.

\n\n
\n
>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, ive(i, x), label=fr'$I_{i!r}(z)\\cdot e^{{-|z|}}$')\n>>> ax.legend()\n>>> ax.set_xlabel(r"$z$")\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n

    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ 

    \n
  2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "

erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

\n\n

erf(z, out=None)

\n\n

Returns the error function of complex argument.

\n\n

It is defined as 2/sqrt(pi)*integral(exp(-t**2), t=0..z).

\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nInput array.
  • \n
  • out (ndarray, optional):\nOptional output array for the function values
  • \n
\n\n
Returns
\n\n
    \n
  • res (scalar or ndarray):\nThe values of the error function at the given points x.
  • \n
\n\n
See Also
\n\n

erfc,, erfinv,, erfcinv,, wofz,, erfcx,, erfi

\n\n
Notes
\n\n

The cumulative of the unit normal distribution is given by\nPhi(z) = 1/2[1 + erf(z/sqrt(2))].

\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erf(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erf(x)$')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfc": {"fullname": "pyerrors.special.erfc", "modulename": "pyerrors.special", "qualname": "erfc", "kind": "function", "doc": "

erfc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

\n\n

erfc(x, out=None)

\n\n

Complementary error function, 1 - erf(x).

\n\n
Parameters
\n\n
    \n
  • x (array_like):\nReal or complex valued argument
  • \n
  • out (ndarray, optional):\nOptional output array for the function results
  • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the complementary error function
  • \n
\n\n
See Also
\n\n

erf,, erfi,, erfcx,, dawsn,, wofz

\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy import special\n>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-3, 3)\n>>> plt.plot(x, special.erfc(x))\n>>> plt.xlabel('$x$')\n>>> plt.ylabel('$erfc(x)$')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfinv": {"fullname": "pyerrors.special.erfinv", "modulename": "pyerrors.special", "qualname": "erfinv", "kind": "function", "doc": "

erfinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

\n\n

erfinv(y, out=None)

\n\n

Inverse of the error function.

\n\n

Computes the inverse of the error function.

\n\n

In the complex domain, there is no unique complex number w satisfying\nerf(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, -1 < x < 1, there is a unique real\nnumber satisfying erf(erfinv(x)) = x.

\n\n
Parameters
\n\n
    \n
  • y (ndarray):\nArgument at which to evaluate. Domain: [-1, 1]
  • \n
  • out (ndarray, optional):\nOptional output array for the function values
  • \n
\n\n
Returns
\n\n
    \n
  • erfinv (scalar or ndarray):\nThe inverse of erf of y, element-wise
  • \n
\n\n
See Also
\n\n

erf: Error function of a complex argument
\nerfc: Complementary error function, 1 - erf(x)
\nerfcinv: Inverse of the complementary error function

\n\n
Notes
\n\n

This function wraps the erf_inv routine from the\nBoost Math C++ library 1.

\n\n
References
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfinv, erf\n
\n
\n\n
\n
>>> erfinv(0.5)\n0.4769362762044699\n
\n
\n\n
\n
>>> y = np.linspace(-1.0, 1.0, num=9)\n>>> x = erfinv(y)\n>>> x\narray([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,\n        0.22531206,  0.47693628,  0.81341985,         inf])\n
\n
\n\n

Verify that erf(erfinv(y)) is y.

\n\n
\n
>>> erf(x)\narray([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])\n
\n
\n\n

Plot the function:

\n\n
\n
>>> y = np.linspace(-1, 1, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfinv(y)')\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n

    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/

    \n
  2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erfcinv": {"fullname": "pyerrors.special.erfcinv", "modulename": "pyerrors.special", "qualname": "erfcinv", "kind": "function", "doc": "

erfcinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

\n\n

erfcinv(y, out=None)

\n\n

Inverse of the complementary error function.

\n\n

Computes the inverse of the complementary error function.

\n\n

In the complex domain, there is no unique complex number w satisfying\nerfc(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, 0 < x < 2, there is a unique real\nnumber satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).

\n\n

It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)

\n\n
Parameters
\n\n
    \n
  • y (ndarray):\nArgument at which to evaluate. Domain: [0, 2]
  • \n
  • out (ndarray, optional):\nOptional output array for the function values
  • \n
\n\n
Returns
\n\n
    \n
  • erfcinv (scalar or ndarray):\nThe inverse of erfc of y, element-wise
  • \n
\n\n
See Also
\n\n

erf: Error function of a complex argument
\nerfc: Complementary error function, 1 - erf(x)
\nerfinv: Inverse of the error function

\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> from scipy.special import erfcinv\n
\n
\n\n
\n
>>> erfcinv(0.5)\n0.4769362762044699\n
\n
\n\n
\n
>>> y = np.linspace(0.0, 2.0, num=11)\n>>> erfcinv(y)\narray([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,\n       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,\n              -inf])\n
\n
\n\n

Plot the function:

\n\n
\n
>>> y = np.linspace(0, 2, 200)\n>>> fig, ax = plt.subplots()\n>>> ax.plot(y, erfcinv(y))\n>>> ax.grid(True)\n>>> ax.set_xlabel('y')\n>>> ax.set_title('erfcinv(y)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logit": {"fullname": "pyerrors.special.logit", "modulename": "pyerrors.special", "qualname": "logit", "kind": "function", "doc": "

logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

\n\n

logit(x, out=None)

\n\n

Logit ufunc for ndarrays.

\n\n

The logit function is defined as logit(p) = log(p/(1-p)).\nNote that logit(0) = -inf, logit(1) = inf, and logit(p)\nfor p<0 or p>1 yields nan.

\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nThe ndarray to apply logit to element-wise.
  • \n
  • out (ndarray, optional):\nOptional output array for the function results
  • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare logit of the corresponding entry of x.
  • \n
\n\n
See Also
\n\n

expit

\n\n
Notes
\n\n

As a ufunc logit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs

\n\n

New in version 0.10.0.

\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import logit, expit\n
\n
\n\n
\n
>>> logit([0, 0.25, 0.5, 0.75, 1])\narray([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])\n
\n
\n\n

expit is the inverse of logit:

\n\n
\n
>>> expit(logit([0.1, 0.75, 0.999]))\narray([ 0.1  ,  0.75 ,  0.999])\n
\n
\n\n

Plot logit(x) for x in [0, 1]:

\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(0, 1, 501)\n>>> y = logit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.ylim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('logit(x)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.expit": {"fullname": "pyerrors.special.expit", "modulename": "pyerrors.special", "qualname": "expit", "kind": "function", "doc": "

expit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

\n\n

expit(x, out=None)

\n\n

Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.

\n\n

The expit function, also known as the logistic sigmoid function, is\ndefined as expit(x) = 1/(1+exp(-x)). It is the inverse of the\nlogit function.

\n\n
Parameters
\n\n
    \n
  • x (ndarray):\nThe ndarray to apply expit to element-wise.
  • \n
  • out (ndarray, optional):\nOptional output array for the function values
  • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: An ndarray of the same shape as x. Its entries\nare expit of the corresponding entry of x.
  • \n
\n\n
See Also
\n\n

logit

\n\n
Notes
\n\n

As a ufunc expit takes a number of optional\nkeyword arguments. For more information\nsee ufuncs

\n\n

New in version 0.10.0.

\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import expit, logit\n
\n
\n\n
\n
>>> expit([-np.inf, -1.5, 0, 1.5, np.inf])\narray([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])\n
\n
\n\n

logit is the inverse of expit:

\n\n
\n
>>> logit(expit([-2.5, 0, 3.1, 5.0]))\narray([-2.5,  0. ,  3.1,  5. ])\n
\n
\n\n

Plot expit(x) for x in [-6, 6]:

\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> x = np.linspace(-6, 6, 121)\n>>> y = expit(x)\n>>> plt.plot(x, y)\n>>> plt.grid()\n>>> plt.xlim(-6, 6)\n>>> plt.xlabel('x')\n>>> plt.title('expit(x)')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.logsumexp": {"fullname": "pyerrors.special.logsumexp", "modulename": "pyerrors.special", "qualname": "logsumexp", "kind": "function", "doc": "

Compute the log of the sum of exponentials of input elements.

\n\n
Parameters
\n\n
    \n
  • a (array_like):\nInput array.
  • \n
  • axis (None or int or tuple of ints, optional):\nAxis or axes over which the sum is taken. By default axis is None,\nand all elements are summed.

    \n\n

    New in version 0.11.0.

  • \n
  • b (array-like, optional):\nScaling factor for exp(a) must be of the same shape as a or\nbroadcastable to a. These values may be negative in order to\nimplement subtraction.

    \n\n

    New in version 0.12.0.

  • \n
  • keepdims (bool, optional):\nIf this is set to True, the axes which are reduced are left in the\nresult as dimensions with size one. With this option, the result\nwill broadcast correctly against the original array.

    \n\n

    New in version 0.15.0.

  • \n
  • return_sign (bool, optional):\nIf this is set to True, the result will be a pair containing sign\ninformation; if False, results that are negative will be returned\nas NaN. Default is False (no sign information).

    \n\n

    New in version 0.16.0.

  • \n
\n\n
Returns
\n\n
    \n
  • res (ndarray):\nThe result, np.log(np.sum(np.exp(a))) calculated in a numerically\nmore stable way. If b is given then np.log(np.sum(b*np.exp(a)))\nis returned. If return_sign is True, res contains the log of\nthe absolute value of the argument.
  • \n
  • sgn (ndarray):\nIf return_sign is True, this will be an array of floating-point\nnumbers matching res containing +1, 0, -1 (for real-valued inputs)\nor a complex phase (for complex inputs). This gives the sign of the\nargument of the logarithm in res.\nIf return_sign is False, only one result is returned.
  • \n
\n\n
See Also
\n\n

numpy.logaddexp,, numpy.logaddexp2

\n\n
Notes
\n\n

NumPy has a logaddexp function which is very similar to logsumexp, but\nonly handles two arguments. logaddexp.reduce is similar to this\nfunction, but may be less stable.

\n\n

The logarithm is a multivalued function: for each \\( x \\) there is an\ninfinite number of \\( z \\) such that \\( exp(z) = x \\). The convention\nis to return the \\( z \\) whose imaginary part lies in \\( (-pi, pi] \\).

\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import logsumexp\n>>> a = np.arange(10)\n>>> logsumexp(a)\n9.4586297444267107\n>>> np.log(np.sum(np.exp(a)))\n9.4586297444267107\n
\n
\n\n

With weights

\n\n
\n
>>> a = np.arange(10)\n>>> b = np.arange(10, 0, -1)\n>>> logsumexp(a, b=b)\n9.9170178533034665\n>>> np.log(np.sum(b*np.exp(a)))\n9.9170178533034647\n
\n
\n\n

Returning a sign flag

\n\n
\n
>>> logsumexp([1,2],b=[1,-1],return_sign=True)\n(1.5413248546129181, -1.0)\n
\n
\n\n

Notice that logsumexp does not directly support masked arrays. To use it\non a masked array, convert the mask into zero weights:

\n\n
\n
>>> a = np.ma.array([np.log(2), 2, np.log(3)],\n...                  mask=[False, True, False])\n>>> b = (~a.mask).astype(int)\n>>> logsumexp(a.data, b=b), np.log(5)\n1.6094379124341005, 1.6094379124341005\n
\n
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What is pyerrors?

\n\n

pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:

\n\n
    \n
  • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
  • \n
  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
  • \n
  • coherent error propagation for data from different Markov chains.
  • \n
  • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
  • \n
  • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
  • \n
\n\n

More detailed examples can found in the GitHub repository \"badge\".

\n\n

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

\n\n
    \n
  • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
  • \n
  • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
  • \n
  • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
  • \n
\n\n

and

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    \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:

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\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:

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\n
conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
\n
\n\n

Install the current develop version:

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\n
python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
\n
\n\n

(Also works for any feature branch).

\n\n

Basic example

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

The Obs class

\n\n

pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.

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

Error propagation

\n\n

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

\n\n

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

\n\n
\n
import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
\n
\n\n

Error estimation

\n\n

The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.

\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
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\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
  3. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
  4. \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
  3. \n

    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/

    \n
  4. \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
  3. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  4. \n\n
  5. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  6. \n\n
  7. \n

    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ 

    \n
  8. \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
  3. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  4. \n\n
  5. \n

    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 

    \n
  6. \n\n
  7. \n

    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ 

    \n
  8. \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
  3. \n

    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ 

    \n
  4. \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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