From 8811f01fb8e1c34ee57d6c80fa3d791694a197d5 Mon Sep 17 00:00:00 2001 From: fjosw Date: Tue, 25 Nov 2025 11:57:51 +0000 Subject: [PATCH] Documentation updated --- docs/pyerrors/input/sfcf.html | 2183 +++++++++++++++++---------------- docs/pyerrors/misc.html | 2 +- docs/search.js | 2 +- 3 files changed, 1114 insertions(+), 1073 deletions(-) diff --git a/docs/pyerrors/input/sfcf.html b/docs/pyerrors/input/sfcf.html index b1056afa..5329b3a4 100644 --- a/docs/pyerrors/input/sfcf.html +++ b/docs/pyerrors/input/sfcf.html @@ -89,690 +89,731 @@ 5from ..obs import Obs 6from .utils import sort_names, check_idl 7import itertools - 8 + 8import warnings 9 - 10sep = "/" - 11 + 10 + 11sep = "/" 12 - 13def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", cfg_func=None, silent=False, **kwargs): - 14 """Read sfcf files from given folder structure. - 15 - 16 Parameters - 17 ---------- - 18 path : str - 19 Path to the sfcf files. - 20 prefix : str - 21 Prefix of the sfcf files. - 22 name : str - 23 Name of the correlation function to read. - 24 quarks : str - 25 Label of the quarks used in the sfcf input file. e.g. "quark quark" - 26 for version 0.0 this does NOT need to be given with the typical " - " - 27 that is present in the output file, - 28 this is done automatically for this version - 29 corr_type : str - 30 Type of correlation function to read. Can be - 31 - 'bi' for boundary-inner - 32 - 'bb' for boundary-boundary - 33 - 'bib' for boundary-inner-boundary - 34 noffset : int - 35 Offset of the source (only relevant when wavefunctions are used) - 36 wf : int - 37 ID of wave function - 38 wf2 : int - 39 ID of the second wavefunction - 40 (only relevant for boundary-to-boundary correlation functions) - 41 im : bool - 42 if True, read imaginary instead of real part - 43 of the correlation function. - 44 names : list - 45 Alternative labeling for replicas/ensembles. - 46 Has to have the appropriate length - 47 ens_name : str - 48 replaces the name of the ensemble - 49 version: str - 50 version of SFCF, with which the measurement was done. - 51 if the compact output option (-c) was specified, - 52 append a "c" to the version (e.g. "1.0c") - 53 if the append output option (-a) was specified, - 54 append an "a" to the version - 55 cfg_separator : str - 56 String that separates the ensemble identifier from the configuration number (default 'n'). - 57 replica: list - 58 list of replica to be read, default is all - 59 files: list - 60 list of files to be read per replica, default is all. - 61 for non-compact output format, hand the folders to be read here. - 62 check_configs: list[list[int]] - 63 list of list of supposed configs, eg. [range(1,1000)] - 64 for one replicum with 1000 configs - 65 - 66 Returns - 67 ------- - 68 result: list[Obs] - 69 list of Observables with length T, observable per timeslice. - 70 bb-type correlators have length 1. - 71 """ - 72 ret = read_sfcf_multi(path, prefix, [name], quarks_list=[quarks], corr_type_list=[corr_type], - 73 noffset_list=[noffset], wf_list=[wf], wf2_list=[wf2], version=version, - 74 cfg_separator=cfg_separator, cfg_func=cfg_func, silent=silent, **kwargs) - 75 return ret[name][quarks][str(noffset)][str(wf)][str(wf2)] - 76 + 13 + 14def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", cfg_func=None, silent=False, **kwargs): + 15 """Read sfcf files from given folder structure. + 16 + 17 Parameters + 18 ---------- + 19 path : str + 20 Path to the sfcf files. + 21 prefix : str + 22 Prefix of the sfcf files. + 23 name : str + 24 Name of the correlation function to read. + 25 quarks : str + 26 Label of the quarks used in the sfcf input file. e.g. "quark quark" + 27 for version 0.0 this does NOT need to be given with the typical " - " + 28 that is present in the output file, + 29 this is done automatically for this version + 30 corr_type : str + 31 Type of correlation function to read. Can be + 32 - 'bi' for boundary-inner + 33 - 'bb' for boundary-boundary + 34 - 'bib' for boundary-inner-boundary + 35 noffset : int + 36 Offset of the source (only relevant when wavefunctions are used) + 37 wf : int + 38 ID of wave function + 39 wf2 : int + 40 ID of the second wavefunction + 41 (only relevant for boundary-to-boundary correlation functions) + 42 im : bool + 43 if True, read imaginary instead of real part + 44 of the correlation function. + 45 names : list + 46 Alternative labeling for replicas/ensembles. + 47 Has to have the appropriate length + 48 ens_name : str + 49 replaces the name of the ensemble + 50 version: str + 51 version of SFCF, with which the measurement was done. + 52 if the compact output option (-c) was specified, + 53 append a "c" to the version (e.g. "1.0c") + 54 if the append output option (-a) was specified, + 55 append an "a" to the version + 56 cfg_separator : str + 57 String that separates the ensemble identifier from the configuration number (default 'n'). + 58 replica: list + 59 list of replica to be read, default is all + 60 files: list + 61 list of files to be read per replica, default is all. + 62 for non-compact output format, hand the folders to be read here. + 63 check_configs: list[list[int]] + 64 list of list of supposed configs, eg. [range(1,1000)] + 65 for one replicum with 1000 configs + 66 + 67 Returns + 68 ------- + 69 result: list[Obs] + 70 list of Observables with length T, observable per timeslice. + 71 bb-type correlators have length 1. + 72 """ + 73 ret = read_sfcf_multi(path, prefix, [name], quarks_list=[quarks], corr_type_list=[corr_type], + 74 noffset_list=[noffset], wf_list=[wf], wf2_list=[wf2], version=version, + 75 cfg_separator=cfg_separator, cfg_func=cfg_func, silent=silent, **kwargs) + 76 return ret[name][quarks][str(noffset)][str(wf)][str(wf2)] 77 - 78def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", cfg_func=None, silent=False, keyed_out=False, **kwargs): - 79 """Read sfcf files from given folder structure. - 80 - 81 Parameters - 82 ---------- - 83 path : str - 84 Path to the sfcf files. - 85 prefix : str - 86 Prefix of the sfcf files. - 87 name : str - 88 Name of the correlation function to read. - 89 quarks_list : list[str] - 90 Label of the quarks used in the sfcf input file. e.g. "quark quark" - 91 for version 0.0 this does NOT need to be given with the typical " - " - 92 that is present in the output file, - 93 this is done automatically for this version - 94 corr_type_list : list[str] - 95 Type of correlation function to read. Can be - 96 - 'bi' for boundary-inner - 97 - 'bb' for boundary-boundary - 98 - 'bib' for boundary-inner-boundary - 99 noffset_list : list[int] -100 Offset of the source (only relevant when wavefunctions are used) -101 wf_list : int -102 ID of wave function -103 wf2_list : list[int] -104 ID of the second wavefunction -105 (only relevant for boundary-to-boundary correlation functions) -106 im : bool -107 if True, read imaginary instead of real part -108 of the correlation function. -109 names : list -110 Alternative labeling for replicas/ensembles. -111 Has to have the appropriate length -112 ens_name : str -113 replaces the name of the ensemble -114 version: str -115 version of SFCF, with which the measurement was done. -116 if the compact output option (-c) was specified, -117 append a "c" to the version (e.g. "1.0c") -118 if the append output option (-a) was specified, -119 append an "a" to the version -120 cfg_separator : str -121 String that separates the ensemble identifier from the configuration number (default 'n'). -122 replica: list -123 list of replica to be read, default is all -124 files: list[list[int]] -125 list of files to be read per replica, default is all. -126 for non-compact output format, hand the folders to be read here. -127 check_configs: list[list[int]] -128 list of list of supposed configs, eg. [range(1,1000)] -129 for one replicum with 1000 configs -130 rep_string: str -131 Separator of ensemble name and replicum. Example: In "ensAr0", "r" would be the separator string. -132 Returns -133 ------- -134 result: dict[list[Obs]] -135 dict with one of the following properties: -136 if keyed_out: -137 dict[key] = list[Obs] -138 where key has the form name/quarks/offset/wf/wf2 -139 if not keyed_out: -140 dict[name][quarks][offset][wf][wf2] = list[Obs] -141 """ -142 -143 if kwargs.get('im'): -144 im = 1 -145 part = 'imaginary' -146 else: -147 im = 0 -148 part = 'real' -149 -150 known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"] -151 -152 if version not in known_versions: -153 raise Exception("This version is not known!") -154 if (version[-1] == "c"): -155 appended = False -156 compact = True -157 version = version[:-1] -158 elif (version[-1] == "a"): -159 appended = True -160 compact = False -161 version = version[:-1] -162 else: -163 compact = False -164 appended = False -165 ls = [] -166 if "replica" in kwargs: -167 ls = kwargs.get("replica") -168 else: -169 for (dirpath, dirnames, filenames) in os.walk(path): -170 if not appended: -171 ls.extend(dirnames) -172 else: -173 ls.extend(filenames) -174 break -175 if not ls: -176 raise Exception('Error, directory not found') -177 # Exclude folders with different names -178 for exc in ls: -179 if not fnmatch.fnmatch(exc, prefix + '*'): -180 ls = list(set(ls) - set([exc])) -181 -182 if not appended: -183 ls = sort_names(ls) -184 replica = len(ls) -185 -186 else: -187 replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls])) -188 if replica == 0: -189 raise Exception('No replica found in directory') -190 if not silent: -191 print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica') -192 -193 if 'names' in kwargs: -194 new_names = kwargs.get('names') -195 if len(new_names) != len(set(new_names)): -196 raise Exception("names are not unique!") -197 if len(new_names) != replica: -198 raise Exception('names should have the length', replica) -199 -200 else: -201 ens_name = kwargs.get("ens_name") -202 if not appended: -203 new_names = _get_rep_names(ls, ens_name, rep_sep=(kwargs.get('rep_string', 'r'))) -204 else: -205 new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name, rep_sep=(kwargs.get('rep_string', 'r'))) -206 new_names = sort_names(new_names) -207 -208 idl = [] -209 -210 noffset_list = [str(x) for x in noffset_list] -211 wf_list = [str(x) for x in wf_list] -212 wf2_list = [str(x) for x in wf2_list] -213 -214 # setup dict structures -215 intern = {} -216 for name, corr_type in zip(name_list, corr_type_list): -217 intern[name] = {} -218 b2b, single = _extract_corr_type(corr_type) -219 intern[name]["b2b"] = b2b -220 intern[name]["single"] = single -221 intern[name]["spec"] = {} -222 for quarks in quarks_list: -223 intern[name]["spec"][quarks] = {} -224 for off in noffset_list: -225 intern[name]["spec"][quarks][off] = {} -226 for w in wf_list: -227 intern[name]["spec"][quarks][off][w] = {} -228 if b2b: -229 for w2 in wf2_list: -230 intern[name]["spec"][quarks][off][w][w2] = {} -231 intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks) -232 else: -233 intern[name]["spec"][quarks][off][w]["0"] = {} -234 intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks) -235 -236 internal_ret_dict = {} -237 needed_keys = [] -238 for name, corr_type in zip(name_list, corr_type_list): -239 b2b, single = _extract_corr_type(corr_type) -240 if b2b: -241 needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list)) -242 else: -243 needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"])) -244 -245 for key in needed_keys: -246 internal_ret_dict[key] = [] -247 -248 def _default_idl_func(cfg_string, cfg_sep): -249 return int(cfg_string.split(cfg_sep)[-1]) -250 -251 if cfg_func is None: -252 print("Default idl function in use.") -253 cfg_func = _default_idl_func -254 cfg_func_args = [cfg_separator] -255 else: -256 cfg_func_args = kwargs.get("cfg_func_args", []) -257 -258 if not appended: -259 for i, item in enumerate(ls): -260 rep_path = path + '/' + item -261 if "files" in kwargs: -262 files = kwargs.get("files") -263 if isinstance(files, list): -264 if all(isinstance(f, list) for f in files): -265 files = files[i] -266 elif all(isinstance(f, str) for f in files): -267 files = files -268 else: -269 raise TypeError("files has to be of type list[list[str]] or list[str]!") -270 else: -271 raise TypeError("files has to be of type list[list[str]] or list[str]!") -272 -273 else: -274 files = [] -275 sub_ls = _find_files(rep_path, prefix, compact, files) -276 rep_idl = [] -277 no_cfg = len(sub_ls) -278 for cfg in sub_ls: -279 try: -280 if compact: -281 rep_idl.append(cfg_func(cfg, *cfg_func_args)) -282 else: -283 rep_idl.append(int(cfg[3:])) -284 except Exception: -285 raise Exception("Couldn't parse idl from directory, problem with file " + cfg) -286 rep_idl.sort() -287 # maybe there is a better way to print the idls -288 if not silent: -289 print(item, ':', no_cfg, ' configurations') -290 idl.append(rep_idl) -291 # here we have found all the files we need to look into. -292 if i == 0: -293 if version != "0.0" and compact: -294 file = path + '/' + item + '/' + sub_ls[0] -295 for name_index, name in enumerate(name_list): -296 if version == "0.0" or not compact: -297 file = path + '/' + item + '/' + sub_ls[0] + '/' + name -298 if corr_type_list[name_index] == 'bi': -299 name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"]) -300 else: -301 name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list) -302 for key in name_keys: -303 specs = _key2specs(key) -304 quarks = specs[0] -305 off = specs[1] -306 w = specs[2] -307 w2 = specs[3] -308 # here, we want to find the place within the file, -309 # where the correlator we need is stored. -310 # to do so, the pattern needed is put together -311 # from the input values -312 start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent) -313 intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read -314 intern[name]["T"] = T -315 # preparing the datastructure -316 # the correlators get parsed into... -317 deltas = [] -318 for j in range(intern[name]["T"]): -319 deltas.append([]) -320 internal_ret_dict[sep.join([name, key])] = deltas -321 -322 if compact: -323 rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im) -324 for key in needed_keys: -325 name = _key2specs(key)[0] -326 for t in range(intern[name]["T"]): -327 internal_ret_dict[key][t].append(rep_deltas[key][t]) -328 else: -329 for key in needed_keys: -330 rep_data = [] -331 name = _key2specs(key)[0] -332 for subitem in sub_ls: -333 cfg_path = path + '/' + item + '/' + subitem -334 file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im) -335 rep_data.append(file_data) -336 for t in range(intern[name]["T"]): -337 internal_ret_dict[key][t].append([]) -338 for cfg in range(no_cfg): -339 internal_ret_dict[key][t][i].append(rep_data[cfg][key][t]) -340 else: -341 for key in needed_keys: -342 specs = _key2specs(key) -343 name = specs[0] -344 quarks = specs[1] -345 off = specs[2] -346 w = specs[3] -347 w2 = specs[4] -348 if "files" in kwargs: -349 if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")): -350 name_ls = kwargs.get("files") -351 else: -352 raise TypeError("In append mode, files has to be of type list[str]!") -353 else: -354 name_ls = ls -355 for exc in name_ls: -356 if not fnmatch.fnmatch(exc, prefix + '*.' + name): -357 name_ls = list(set(name_ls) - set([exc])) -358 name_ls = sort_names(name_ls) -359 pattern = intern[name]['spec'][quarks][off][w][w2]['pattern'] -360 deltas = [] -361 for rep, file in enumerate(name_ls): -362 rep_idl = [] -363 filename = path + '/' + file -364 T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], im, intern[name]['single'], cfg_func, cfg_func_args) -365 if rep == 0: -366 intern[name]['T'] = T -367 for t in range(intern[name]['T']): -368 deltas.append([]) -369 for t in range(intern[name]['T']): -370 deltas[t].append(rep_data[t]) -371 internal_ret_dict[key] = deltas -372 if name == name_list[0]: -373 idl.append(rep_idl) -374 -375 if kwargs.get("check_configs") is True: -376 if not silent: -377 print("Checking for missing configs...") -378 che = kwargs.get("check_configs") -379 if not (len(che) == len(idl)): -380 raise Exception("check_configs has to be the same length as replica!") -381 for r in range(len(idl)): -382 if not silent: -383 print("checking " + new_names[r]) -384 check_idl(idl[r], che[r]) -385 if not silent: -386 print("Done") -387 -388 result_dict = {} -389 if keyed_out: -390 for key in needed_keys: -391 name = _key2specs(key)[0] -392 result = [] -393 for t in range(intern[name]["T"]): -394 result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl)) -395 result_dict[key] = result -396 else: -397 for name, corr_type in zip(name_list, corr_type_list): -398 result_dict[name] = {} -399 for quarks in quarks_list: -400 result_dict[name][quarks] = {} -401 for off in noffset_list: -402 result_dict[name][quarks][off] = {} -403 for w in wf_list: -404 result_dict[name][quarks][off][w] = {} -405 if corr_type != 'bi': -406 for w2 in wf2_list: -407 key = _specs2key(name, quarks, off, w, w2) -408 result = [] -409 for t in range(intern[name]["T"]): -410 result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl)) -411 result_dict[name][quarks][str(off)][str(w)][str(w2)] = result -412 else: -413 key = _specs2key(name, quarks, off, w, "0") -414 result = [] -415 for t in range(intern[name]["T"]): -416 result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl)) -417 result_dict[name][quarks][str(off)][str(w)][str(0)] = result -418 return result_dict -419 + 78 + 79def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", cfg_func=None, silent=False, keyed_out=False, **kwargs): + 80 """Read sfcf files from given folder structure. + 81 + 82 Parameters + 83 ---------- + 84 path : str + 85 Path to the sfcf files. + 86 prefix : str + 87 Prefix of the sfcf files. + 88 name : str + 89 Name of the correlation function to read. + 90 quarks_list : list[str] + 91 Label of the quarks used in the sfcf input file. e.g. "quark quark" + 92 for version 0.0 this does NOT need to be given with the typical " - " + 93 that is present in the output file, + 94 this is done automatically for this version + 95 corr_type_list : list[str] + 96 Type of correlation function to read. Can be + 97 - 'bi' for boundary-inner + 98 - 'bb' for boundary-boundary + 99 - 'bib' for boundary-inner-boundary +100 noffset_list : list[int] +101 Offset of the source (only relevant when wavefunctions are used) +102 wf_list : int +103 ID of wave function +104 wf2_list : list[int] +105 ID of the second wavefunction +106 (only relevant for boundary-to-boundary correlation functions) +107 im : bool +108 if True, read imaginary instead of real part +109 of the correlation function. +110 names : list +111 Alternative labeling for replicas/ensembles. +112 Has to have the appropriate length +113 ens_name : str +114 replaces the name of the ensemble +115 version: str +116 version of SFCF, with which the measurement was done. +117 if the compact output option (-c) was specified, +118 append a "c" to the version (e.g. "1.0c") +119 if the append output option (-a) was specified, +120 append an "a" to the version +121 cfg_separator : str +122 String that separates the ensemble identifier from the configuration number (default 'n'). +123 replica: list +124 list of replica to be read, default is all +125 files: list[list[int]] +126 list of files to be read per replica, default is all. +127 for non-compact output format, hand the folders to be read here. +128 check_configs: list[list[int]] +129 list of list of supposed configs, eg. [range(1,1000)] +130 for one replicum with 1000 configs +131 rep_string: str +132 Separator of ensemble name and replicum. Example: In "ensAr0", "r" would be the separator string. +133 Returns +134 ------- +135 result: dict[list[Obs]] +136 dict with one of the following properties: +137 if keyed_out: +138 dict[key] = list[Obs] +139 where key has the form name/quarks/offset/wf/wf2 +140 if not keyed_out: +141 dict[name][quarks][offset][wf][wf2] = list[Obs] +142 """ +143 +144 if kwargs.get('im'): +145 im = 1 +146 part = 'imaginary' +147 else: +148 im = 0 +149 part = 'real' +150 +151 known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"] +152 +153 if version not in known_versions: +154 raise Exception("This version is not known!") +155 if (version[-1] == "c"): +156 appended = False +157 compact = True +158 version = version[:-1] +159 elif (version[-1] == "a"): +160 appended = True +161 compact = False +162 version = version[:-1] +163 else: +164 compact = False +165 appended = False +166 ls = [] +167 if "replica" in kwargs: +168 ls = kwargs.get("replica") +169 else: +170 for (dirpath, dirnames, filenames) in os.walk(path): +171 if not appended: +172 ls.extend(dirnames) +173 else: +174 ls.extend(filenames) +175 break +176 if not ls: +177 raise Exception('Error, directory not found') +178 # Exclude folders with different names +179 for exc in ls: +180 if not fnmatch.fnmatch(exc, prefix + '*'): +181 ls = list(set(ls) - set([exc])) +182 +183 if not appended: +184 ls = sort_names(ls) +185 replica = len(ls) +186 +187 else: +188 replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls])) +189 if replica == 0: +190 raise Exception('No replica found in directory') +191 if not silent: +192 print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica') +193 +194 if 'names' in kwargs: +195 new_names = kwargs.get('names') +196 if len(new_names) != len(set(new_names)): +197 raise Exception("names are not unique!") +198 if len(new_names) != replica: +199 raise Exception('names should have the length', replica) +200 +201 else: +202 ens_name = kwargs.get("ens_name") +203 if not appended: +204 new_names = _get_rep_names(ls, ens_name, rep_sep=(kwargs.get('rep_string', 'r'))) +205 else: +206 new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name, rep_sep=(kwargs.get('rep_string', 'r'))) +207 new_names = sort_names(new_names) +208 +209 idl = [] +210 +211 noffset_list = [str(x) for x in noffset_list] +212 wf_list = [str(x) for x in wf_list] +213 wf2_list = [str(x) for x in wf2_list] +214 +215 # setup dict structures +216 intern = {} +217 for name, corr_type in zip(name_list, corr_type_list): +218 intern[name] = {} +219 b2b, single = _extract_corr_type(corr_type) +220 intern[name]["b2b"] = b2b +221 intern[name]["single"] = single +222 intern[name]["spec"] = {} +223 for quarks in quarks_list: +224 intern[name]["spec"][quarks] = {} +225 for off in noffset_list: +226 intern[name]["spec"][quarks][off] = {} +227 for w in wf_list: +228 intern[name]["spec"][quarks][off][w] = {} +229 if b2b: +230 for w2 in wf2_list: +231 intern[name]["spec"][quarks][off][w][w2] = {} +232 intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks) +233 else: +234 intern[name]["spec"][quarks][off][w]["0"] = {} +235 intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks) +236 +237 internal_ret_dict = {} +238 needed_keys = [] +239 for name, corr_type in zip(name_list, corr_type_list): +240 b2b, single = _extract_corr_type(corr_type) +241 if b2b: +242 needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list)) +243 else: +244 needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"])) +245 +246 for key in needed_keys: +247 internal_ret_dict[key] = [] +248 +249 def _default_idl_func(cfg_string, cfg_sep): +250 return int(cfg_string.split(cfg_sep)[-1]) +251 +252 if cfg_func is None: +253 print("Default idl function in use.") +254 cfg_func = _default_idl_func +255 cfg_func_args = [cfg_separator] +256 else: +257 cfg_func_args = kwargs.get("cfg_func_args", []) +258 +259 if not appended: +260 for i, item in enumerate(ls): +261 rep_path = path + '/' + item +262 if "files" in kwargs: +263 files = kwargs.get("files") +264 if isinstance(files, list): +265 if all(isinstance(f, list) for f in files): +266 files = files[i] +267 elif all(isinstance(f, str) for f in files): +268 files = files +269 else: +270 raise TypeError("files has to be of type list[list[str]] or list[str]!") +271 else: +272 raise TypeError("files has to be of type list[list[str]] or list[str]!") +273 +274 else: +275 files = [] +276 sub_ls = _find_files(rep_path, prefix, compact, files) +277 rep_idl = [] +278 no_cfg = len(sub_ls) +279 for cfg in sub_ls: +280 try: +281 if compact: +282 rep_idl.append(cfg_func(cfg, *cfg_func_args)) +283 else: +284 rep_idl.append(int(cfg[3:])) +285 except Exception: +286 raise Exception("Couldn't parse idl from directory, problem with file " + cfg) +287 rep_idl.sort() +288 # maybe there is a better way to print the idls +289 if not silent: +290 print(item, ':', no_cfg, ' configurations') +291 idl.append(rep_idl) +292 # here we have found all the files we need to look into. +293 if i == 0: +294 if version != "0.0" and compact: +295 file = path + '/' + item + '/' + sub_ls[0] +296 for name_index, name in enumerate(name_list): +297 if version == "0.0" or not compact: +298 file = path + '/' + item + '/' + sub_ls[0] + '/' + name +299 if corr_type_list[name_index] == 'bi': +300 name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"]) +301 else: +302 name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list) +303 for key in name_keys: +304 specs = _key2specs(key) +305 quarks = specs[0] +306 off = specs[1] +307 w = specs[2] +308 w2 = specs[3] +309 # here, we want to find the place within the file, +310 # where the correlator we need is stored. +311 # to do so, the pattern needed is put together +312 # from the input values +313 start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent) +314 intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read +315 intern[name]["T"] = T +316 # preparing the datastructure +317 # the correlators get parsed into... +318 deltas = [] +319 for j in range(intern[name]["T"]): +320 deltas.append([]) +321 internal_ret_dict[sep.join([name, key])] = deltas +322 +323 if compact: +324 rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im) +325 for key in needed_keys: +326 name = _key2specs(key)[0] +327 for t in range(intern[name]["T"]): +328 internal_ret_dict[key][t].append(rep_deltas[key][t]) +329 else: +330 for key in needed_keys: +331 rep_data = [] +332 name = _key2specs(key)[0] +333 for subitem in sub_ls: +334 cfg_path = path + '/' + item + '/' + subitem +335 file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im) +336 rep_data.append(file_data) +337 for t in range(intern[name]["T"]): +338 internal_ret_dict[key][t].append([]) +339 for cfg in range(no_cfg): +340 internal_ret_dict[key][t][i].append(rep_data[cfg][key][t]) +341 else: +342 for key in needed_keys: +343 specs = _key2specs(key) +344 name = specs[0] +345 quarks = specs[1] +346 off = specs[2] +347 w = specs[3] +348 w2 = specs[4] +349 if "files" in kwargs: +350 if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")): +351 name_ls = kwargs.get("files") +352 else: +353 raise TypeError("In append mode, files has to be of type list[str]!") +354 else: +355 name_ls = ls +356 for exc in name_ls: +357 if not fnmatch.fnmatch(exc, prefix + '*.' + name): +358 name_ls = list(set(name_ls) - set([exc])) +359 name_ls = sort_names(name_ls) +360 pattern = intern[name]['spec'][quarks][off][w][w2]['pattern'] +361 deltas = [] +362 for rep, file in enumerate(name_ls): +363 rep_idl = [] +364 filename = path + '/' + file +365 T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], im, intern[name]['single'], cfg_func, cfg_func_args) +366 if rep == 0: +367 intern[name]['T'] = T +368 for t in range(intern[name]['T']): +369 deltas.append([]) +370 for t in range(intern[name]['T']): +371 deltas[t].append(rep_data[t]) +372 internal_ret_dict[key] = deltas +373 if name == name_list[0]: +374 idl.append(rep_idl) +375 +376 if kwargs.get("check_configs") is True: +377 if not silent: +378 print("Checking for missing configs...") +379 che = kwargs.get("check_configs") +380 if not (len(che) == len(idl)): +381 raise Exception("check_configs has to be the same length as replica!") +382 for r in range(len(idl)): +383 if not silent: +384 print("checking " + new_names[r]) +385 check_idl(idl[r], che[r]) +386 if not silent: +387 print("Done") +388 +389 result_dict = {} +390 if keyed_out: +391 for key in needed_keys: +392 name = _key2specs(key)[0] +393 result = [] +394 for t in range(intern[name]["T"]): +395 result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl)) +396 result_dict[key] = result +397 else: +398 for name, corr_type in zip(name_list, corr_type_list): +399 result_dict[name] = {} +400 for quarks in quarks_list: +401 result_dict[name][quarks] = {} +402 for off in noffset_list: +403 result_dict[name][quarks][off] = {} +404 for w in wf_list: +405 result_dict[name][quarks][off][w] = {} +406 if corr_type != 'bi': +407 for w2 in wf2_list: +408 key = _specs2key(name, quarks, off, w, w2) +409 result = [] +410 for t in range(intern[name]["T"]): +411 result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl)) +412 result_dict[name][quarks][str(off)][str(w)][str(w2)] = result +413 else: +414 key = _specs2key(name, quarks, off, w, "0") +415 result = [] +416 for t in range(intern[name]["T"]): +417 result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl)) +418 result_dict[name][quarks][str(off)][str(w)][str(0)] = result +419 return result_dict 420 -421def _lists2key(*lists): -422 keys = [] -423 for tup in itertools.product(*lists): -424 keys.append(sep.join(tup)) -425 return keys -426 +421 +422def _lists2key(*lists): +423 keys = [] +424 for tup in itertools.product(*lists): +425 keys.append(sep.join(tup)) +426 return keys 427 -428def _key2specs(key): -429 return key.split(sep) -430 +428 +429def _key2specs(key): +430 return key.split(sep) 431 -432def _specs2key(*specs): -433 return sep.join(specs) -434 +432 +433def _specs2key(*specs): +434 return sep.join(specs) 435 -436def _read_o_file(cfg_path, name, needed_keys, intern, version, im): -437 return_vals = {} -438 for key in needed_keys: -439 file = cfg_path + '/' + name -440 specs = _key2specs(key) -441 if specs[0] == name: -442 with open(file) as fp: -443 lines = fp.readlines() -444 quarks = specs[1] -445 off = specs[2] -446 w = specs[3] -447 w2 = specs[4] -448 T = intern[name]["T"] -449 start_read = intern[name]["spec"][quarks][off][w][w2]["start"] -450 deltas = [] -451 for line in lines[start_read:start_read + T]: -452 floats = list(map(float, line.split())) -453 if version == "0.0": -454 deltas.append(floats[im - intern[name]["single"]]) -455 else: -456 deltas.append(floats[1 + im - intern[name]["single"]]) -457 return_vals[key] = deltas -458 return return_vals -459 +436 +437def _read_o_file(cfg_path, name, needed_keys, intern, version, im): +438 return_vals = {} +439 for key in needed_keys: +440 file = cfg_path + '/' + name +441 specs = _key2specs(key) +442 if specs[0] == name: +443 with open(file) as fp: +444 lines = fp.readlines() +445 quarks = specs[1] +446 off = specs[2] +447 w = specs[3] +448 w2 = specs[4] +449 T = intern[name]["T"] +450 start_read = intern[name]["spec"][quarks][off][w][w2]["start"] +451 deltas = [] +452 for line in lines[start_read:start_read + T]: +453 floats = list(map(float, line.split())) +454 if version == "0.0": +455 deltas.append(floats[im - intern[name]["single"]]) +456 else: +457 deltas.append(floats[1 + im - intern[name]["single"]]) +458 return_vals[key] = deltas +459 return return_vals 460 -461def _extract_corr_type(corr_type): -462 if corr_type == 'bb': -463 b2b = True -464 single = True -465 elif corr_type == 'bib': -466 b2b = True -467 single = False -468 else: -469 b2b = False -470 single = False -471 return b2b, single -472 +461 +462def _extract_corr_type(corr_type): +463 if corr_type == 'bb': +464 b2b = True +465 single = True +466 elif corr_type == 'bib': +467 b2b = True +468 single = False +469 else: +470 b2b = False +471 single = False +472 return b2b, single 473 -474def _find_files(rep_path, prefix, compact, files=[]): -475 sub_ls = [] -476 if not files == []: -477 files.sort(key=lambda x: int(re.findall(r'\d+', x)[-1])) -478 else: -479 for (dirpath, dirnames, filenames) in os.walk(rep_path): -480 if compact: -481 sub_ls.extend(filenames) -482 else: -483 sub_ls.extend(dirnames) -484 break -485 if compact: -486 for exc in sub_ls: -487 if not fnmatch.fnmatch(exc, prefix + '*'): -488 sub_ls = list(set(sub_ls) - set([exc])) -489 sub_ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1])) -490 else: -491 for exc in sub_ls: -492 if not fnmatch.fnmatch(exc, 'cfg*'): -493 sub_ls = list(set(sub_ls) - set([exc])) -494 sub_ls.sort(key=lambda x: int(x[3:])) -495 files = sub_ls -496 if len(files) == 0: -497 raise FileNotFoundError("Did not find files in", rep_path, "with prefix", prefix, "and the given structure.") -498 return files -499 +474 +475def _find_files(rep_path, prefix, compact, files=[]): +476 sub_ls = [] +477 if not files == []: +478 files.sort(key=lambda x: int(re.findall(r'\d+', x)[-1])) +479 else: +480 for (dirpath, dirnames, filenames) in os.walk(rep_path): +481 if compact: +482 sub_ls.extend(filenames) +483 else: +484 sub_ls.extend(dirnames) +485 break +486 if compact: +487 for exc in sub_ls: +488 if not fnmatch.fnmatch(exc, prefix + '*'): +489 sub_ls = list(set(sub_ls) - set([exc])) +490 sub_ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1])) +491 else: +492 for exc in sub_ls: +493 if not fnmatch.fnmatch(exc, 'cfg*'): +494 sub_ls = list(set(sub_ls) - set([exc])) +495 sub_ls.sort(key=lambda x: int(x[3:])) +496 files = sub_ls +497 if len(files) == 0: +498 raise FileNotFoundError("Did not find files in", rep_path, "with prefix", prefix, "and the given structure.") +499 return files 500 -501def _make_pattern(version, name, noffset, wf, wf2, b2b, quarks): -502 if version == "0.0": -503 pattern = "# " + name + " : offset " + str(noffset) + ", wf " + str(wf) -504 if b2b: -505 pattern += ", wf_2 " + str(wf2) -506 qs = quarks.split(" ") -507 pattern += " : " + qs[0] + " - " + qs[1] -508 else: -509 pattern = 'name ' + name + '\nquarks ' + quarks + '\noffset ' + str(noffset) + '\nwf ' + str(wf) -510 if b2b: -511 pattern += '\nwf_2 ' + str(wf2) -512 return pattern -513 +501 +502def _make_pattern(version, name, noffset, wf, wf2, b2b, quarks): +503 if version == "0.0": +504 pattern = "# " + name + " : offset " + str(noffset) + ", wf " + str(wf) +505 if b2b: +506 pattern += ", wf_2 " + str(wf2) +507 qs = quarks.split(" ") +508 pattern += " : " + qs[0] + " - " + qs[1] +509 else: +510 pattern = 'name ' + name + '\nquarks ' + quarks + '\noffset ' + str(noffset) + '\nwf ' + str(wf) +511 if b2b: +512 pattern += '\nwf_2 ' + str(wf2) +513 return pattern 514 -515def _find_correlator(file_name, version, pattern, b2b, silent=False): -516 T = 0 -517 -518 with open(file_name, "r") as my_file: -519 -520 content = my_file.read() -521 match = re.search(pattern, content) -522 if match: -523 if version == "0.0": -524 start_read = content.count('\n', 0, match.start()) + 1 -525 T = content.count('\n', start_read) -526 else: -527 start_read = content.count('\n', 0, match.start()) + 5 + b2b -528 end_match = re.search(r'\n\s*\n', content[match.start():]) -529 T = content[match.start():].count('\n', 0, end_match.start()) - 4 - b2b -530 if not T > 0: -531 raise ValueError("Correlator with pattern\n" + pattern + "\nis empty!") -532 if not silent: -533 print(T, 'entries, starting to read in line', start_read) -534 -535 else: -536 raise ValueError('Correlator with pattern\n' + pattern + '\nnot found.') -537 -538 return start_read, T -539 +515 +516def _find_correlator(file_name, version, pattern, b2b, silent=False): +517 T = 0 +518 +519 with open(file_name, "r") as my_file: +520 +521 content = my_file.read() +522 match = re.search(pattern, content) +523 if match: +524 if version == "0.0": +525 start_read = content.count('\n', 0, match.start()) + 1 +526 T = content.count('\n', start_read) +527 else: +528 start_read = content.count('\n', 0, match.start()) + 5 + b2b +529 end_match = re.search(r'\n\s*\n', content[match.start():]) +530 T = content[match.start():].count('\n', 0, end_match.start()) - 4 - b2b +531 if not T > 0: +532 raise ValueError("Correlator with pattern\n" + pattern + "\nis empty!") +533 if not silent: +534 print(T, 'entries, starting to read in line', start_read) +535 +536 else: +537 raise ValueError('Correlator with pattern\n' + pattern + '\nnot found.') +538 +539 return start_read, T 540 -541def _read_compact_file(rep_path, cfg_file, intern, needed_keys, im): -542 return_vals = {} -543 with open(rep_path + cfg_file) as fp: -544 lines = fp.readlines() -545 for key in needed_keys: -546 keys = _key2specs(key) -547 name = keys[0] -548 quarks = keys[1] -549 off = keys[2] -550 w = keys[3] -551 w2 = keys[4] -552 -553 T = intern[name]["T"] -554 start_read = intern[name]["spec"][quarks][off][w][w2]["start"] -555 # check, if the correlator is in fact -556 # printed completely -557 if (start_read + T + 1 > len(lines)): -558 raise Exception("EOF before end of correlator data! Maybe " + rep_path + cfg_file + " is corrupted?") -559 corr_lines = lines[start_read - 6: start_read + T] -560 t_vals = [] -561 -562 if corr_lines[1 - intern[name]["b2b"]].strip() != 'name ' + name: -563 raise Exception('Wrong format in file', cfg_file) -564 -565 for k in range(6, T + 6): -566 floats = list(map(float, corr_lines[k].split())) -567 t_vals.append(floats[-2:][im]) -568 return_vals[key] = t_vals -569 return return_vals -570 +541 +542def _read_compact_file(rep_path, cfg_file, intern, needed_keys, im): +543 return_vals = {} +544 with open(rep_path + cfg_file) as fp: +545 lines = fp.readlines() +546 for key in needed_keys: +547 keys = _key2specs(key) +548 name = keys[0] +549 quarks = keys[1] +550 off = keys[2] +551 w = keys[3] +552 w2 = keys[4] +553 +554 T = intern[name]["T"] +555 start_read = intern[name]["spec"][quarks][off][w][w2]["start"] +556 # check, if the correlator is in fact +557 # printed completely +558 if (start_read + T + 1 > len(lines)): +559 raise Exception("EOF before end of correlator data! Maybe " + rep_path + cfg_file + " is corrupted?") +560 corr_lines = lines[start_read - 6: start_read + T] +561 t_vals = [] +562 +563 if corr_lines[1 - intern[name]["b2b"]].strip() != 'name ' + name: +564 raise Exception('Wrong format in file', cfg_file) +565 +566 for k in range(6, T + 6): +567 floats = list(map(float, corr_lines[k].split())) +568 t_vals.append(floats[-2:][im]) +569 return_vals[key] = t_vals +570 return return_vals 571 -572def _read_compact_rep(path, rep, sub_ls, intern, needed_keys, im): -573 rep_path = path + '/' + rep + '/' -574 no_cfg = len(sub_ls) -575 -576 return_vals = {} -577 for key in needed_keys: -578 name = _key2specs(key)[0] -579 deltas = [] -580 for t in range(intern[name]["T"]): -581 deltas.append(np.zeros(no_cfg)) -582 return_vals[key] = deltas -583 -584 for cfg in range(no_cfg): -585 cfg_file = sub_ls[cfg] -586 cfg_data = _read_compact_file(rep_path, cfg_file, intern, needed_keys, im) -587 for key in needed_keys: -588 name = _key2specs(key)[0] -589 for t in range(intern[name]["T"]): -590 return_vals[key][t][cfg] = cfg_data[key][t] -591 return return_vals -592 +572 +573def _read_compact_rep(path, rep, sub_ls, intern, needed_keys, im): +574 rep_path = path + '/' + rep + '/' +575 no_cfg = len(sub_ls) +576 +577 return_vals = {} +578 for key in needed_keys: +579 name = _key2specs(key)[0] +580 deltas = [] +581 for t in range(intern[name]["T"]): +582 deltas.append(np.zeros(no_cfg)) +583 return_vals[key] = deltas +584 +585 for cfg in range(no_cfg): +586 cfg_file = sub_ls[cfg] +587 cfg_data = _read_compact_file(rep_path, cfg_file, intern, needed_keys, im) +588 for key in needed_keys: +589 name = _key2specs(key)[0] +590 for t in range(intern[name]["T"]): +591 return_vals[key][t][cfg] = cfg_data[key][t] +592 return return_vals 593 -594def _read_chunk_data(chunk, start_read, T, corr_line, b2b, pattern, im, single): -595 found_pat = "" -596 data = [] -597 for li in chunk[corr_line + 1:corr_line + 6 + b2b]: -598 found_pat += li -599 if re.search(pattern, found_pat): -600 for t, line in enumerate(chunk[start_read:start_read + T]): -601 floats = list(map(float, line.split())) -602 data.append(floats[im + 1 - single]) -603 return data -604 +594 +595def _read_chunk_data(chunk, start_read, T, corr_line, b2b, pattern, im, single): +596 found_pat = "" +597 data = [] +598 for li in chunk[corr_line + 1:corr_line + 6 + b2b]: +599 found_pat += li +600 if re.search(pattern, found_pat): +601 for t, line in enumerate(chunk[start_read:start_read + T]): +602 floats = list(map(float, line.split())) +603 data.append(floats[im + 1 - single]) +604 return data 605 -606def _read_append_rep(filename, pattern, b2b, im, single, idl_func, cfg_func_args): -607 with open(filename, 'r') as fp: -608 content = fp.readlines() -609 data_starts = [] -610 for linenumber, line in enumerate(content): -611 if "[run]" in line: -612 data_starts.append(linenumber) -613 if len(set([data_starts[i] - data_starts[i - 1] for i in range(1, len(data_starts))])) > 1: -614 raise Exception("Irregularities in file structure found, not all runs have the same output length") -615 chunk = content[:data_starts[1]] -616 for linenumber, line in enumerate(chunk): -617 if line.startswith("gauge_name"): -618 gauge_line = linenumber -619 elif line.startswith("[correlator]"): -620 corr_line = linenumber -621 found_pat = "" -622 for li in chunk[corr_line + 1: corr_line + 6 + b2b]: -623 found_pat += li -624 if re.search(pattern, found_pat): -625 start_read = corr_line + 7 + b2b -626 break -627 else: -628 raise ValueError("Did not find pattern\n", pattern, "\nin\n", filename) -629 endline = corr_line + 6 + b2b -630 while not chunk[endline] == "\n": -631 endline += 1 -632 T = endline - start_read +606 +607def _check_append_rep(content, start_list): +608 data_len_list = [] +609 header_len_list = [] +610 has_regular_len_heads = True +611 for chunk_num in range(len(start_list)): +612 start = start_list[chunk_num] +613 if chunk_num == len(start_list) - 1: +614 stop = len(content) +615 else: +616 stop = start_list[chunk_num + 1] +617 chunk = content[start:stop] +618 for linenumber, line in enumerate(chunk): +619 if line.startswith("[correlator]"): +620 header_len = linenumber +621 break +622 header_len_list.append(header_len) +623 data_len_list.append(len(chunk) - header_len) +624 +625 if len(set(header_len_list)) > 1: +626 warnings.warn("Not all headers have the same length. Data parts do.") +627 has_regular_len_heads = False +628 +629 if len(set(data_len_list)) > 1: +630 raise Exception("Irregularities in file structure found, not all run data are of the same output length") +631 return has_regular_len_heads +632 633 -634 # all other chunks should follow the same structure -635 rep_idl = [] -636 rep_data = [] -637 -638 for cnfg in range(len(data_starts)): -639 start = data_starts[cnfg] -640 stop = start + data_starts[1] -641 chunk = content[start:stop] -642 try: -643 idl = idl_func(chunk[gauge_line], *cfg_func_args) -644 except Exception: -645 raise Exception("Couldn't parse idl from file", filename, ", problem with chunk of lines", start + 1, "to", stop + 1) -646 data = _read_chunk_data(chunk, start_read, T, corr_line, b2b, pattern, im, single) -647 rep_idl.append(idl) -648 rep_data.append(data) -649 -650 data = [] -651 -652 for t in range(T): -653 data.append([]) -654 for c in range(len(rep_data)): -655 data[t].append(rep_data[c][t]) -656 return T, rep_idl, data -657 -658 -659def _get_rep_names(ls, ens_name=None, rep_sep='r'): -660 new_names = [] -661 for entry in ls: -662 try: -663 idx = entry.index(rep_sep) -664 except Exception: -665 raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.") -666 -667 if ens_name: -668 new_names.append(ens_name + '|' + entry[idx:]) -669 else: -670 new_names.append(entry[:idx] + '|' + entry[idx:]) -671 return new_names -672 +634def _read_chunk_structure(chunk, pattern, b2b): +635 start_read = 0 +636 for linenumber, line in enumerate(chunk): +637 if line.startswith("gauge_name"): +638 gauge_line = linenumber +639 elif line.startswith("[correlator]"): +640 corr_line = linenumber +641 found_pat = "" +642 for li in chunk[corr_line + 1: corr_line + 6 + b2b]: +643 found_pat += li +644 if re.search(pattern, found_pat): +645 start_read = corr_line + 7 + b2b +646 break +647 if start_read == 0: +648 raise ValueError("Did not find pattern\n", pattern) +649 endline = corr_line + 6 + b2b +650 while not chunk[endline] == "\n": +651 endline += 1 +652 T = endline - start_read +653 return gauge_line, corr_line, start_read, T +654 +655 +656def _read_append_rep(filename, pattern, b2b, im, single, idl_func, cfg_func_args): +657 with open(filename, 'r') as fp: +658 content = fp.readlines() +659 chunk_start_lines = [] +660 for linenumber, line in enumerate(content): +661 if "[run]" in line: +662 chunk_start_lines.append(linenumber) +663 has_regular_len_heads = _check_append_rep(content, chunk_start_lines) +664 if has_regular_len_heads: +665 chunk = content[:chunk_start_lines[1]] +666 try: +667 gauge_line, corr_line, start_read, T = _read_chunk_structure(chunk, pattern, b2b) +668 except ValueError: +669 raise ValueError("Did not find pattern\n", pattern, "\nin\n", filename, "lines", 1, "to", chunk_start_lines[1] + 1) +670 # if has_regular_len_heads is true, all other chunks should follow the same structure +671 rep_idl = [] +672 rep_data = [] 673 -674def _get_appended_rep_names(ls, prefix, name, ens_name=None, rep_sep='r'): -675 new_names = [] -676 for exc in ls: -677 if not fnmatch.fnmatch(exc, prefix + '*.' + name): -678 ls = list(set(ls) - set([exc])) -679 ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1])) -680 for entry in ls: -681 myentry = entry[:-len(name) - 1] -682 try: -683 idx = myentry.index(rep_sep) -684 except Exception: -685 raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.") -686 -687 if ens_name: -688 new_names.append(ens_name + '|' + entry[idx:]) -689 else: -690 new_names.append(myentry[:idx] + '|' + myentry[idx:]) -691 return new_names +674 for chunk_num in range(len(chunk_start_lines)): +675 start = chunk_start_lines[chunk_num] +676 if chunk_num == len(chunk_start_lines) - 1: +677 stop = len(content) +678 else: +679 stop = chunk_start_lines[chunk_num + 1] +680 chunk = content[start:stop] +681 if not has_regular_len_heads: +682 gauge_line, corr_line, start_read, T = _read_chunk_structure(chunk, pattern, b2b) +683 try: +684 idl = idl_func(chunk[gauge_line], *cfg_func_args) +685 except Exception: +686 raise Exception("Couldn't parse idl from file", filename, ", problem with chunk of lines", start + 1, "to", stop + 1) +687 data = _read_chunk_data(chunk, start_read, T, corr_line, b2b, pattern, im, single) +688 rep_idl.append(idl) +689 rep_data.append(data) +690 +691 data = [] +692 +693 for t in range(T): +694 data.append([]) +695 for c in range(len(rep_data)): +696 data[t].append(rep_data[c][t]) +697 return T, rep_idl, data +698 +699 +700def _get_rep_names(ls, ens_name=None, rep_sep='r'): +701 new_names = [] +702 for entry in ls: +703 try: +704 idx = entry.index(rep_sep) +705 except Exception: +706 raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.") +707 +708 if ens_name: +709 new_names.append(ens_name + '|' + entry[idx:]) +710 else: +711 new_names.append(entry[:idx] + '|' + entry[idx:]) +712 return new_names +713 +714 +715def _get_appended_rep_names(ls, prefix, name, ens_name=None, rep_sep='r'): +716 new_names = [] +717 for exc in ls: +718 if not fnmatch.fnmatch(exc, prefix + '*.' + name): +719 ls = list(set(ls) - set([exc])) +720 ls.sort(key=lambda x: int(re.findall(r'\d+', x)[-1])) +721 for entry in ls: +722 myentry = entry[:-len(name) - 1] +723 try: +724 idx = myentry.index(rep_sep) +725 except Exception: +726 raise Exception("Automatic recognition of replicum failed, please enter the key word 'names'.") +727 +728 if ens_name: +729 new_names.append(ens_name + '|' + entry[idx:]) +730 else: +731 new_names.append(myentry[:idx] + '|' + myentry[idx:]) +732 return new_names @@ -800,69 +841,69 @@ - 
14def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", cfg_func=None, silent=False, **kwargs):
-15    """Read sfcf files from given folder structure.
-16
-17    Parameters
-18    ----------
-19    path : str
-20        Path to the sfcf files.
-21    prefix : str
-22        Prefix of the sfcf files.
-23    name : str
-24        Name of the correlation function to read.
-25    quarks : str
-26        Label of the quarks used in the sfcf input file. e.g. "quark quark"
-27        for version 0.0 this does NOT need to be given with the typical " - "
-28        that is present in the output file,
-29        this is done automatically for this version
-30    corr_type : str
-31        Type of correlation function to read. Can be
-32        - 'bi' for boundary-inner
-33        - 'bb' for boundary-boundary
-34        - 'bib' for boundary-inner-boundary
-35    noffset : int
-36        Offset of the source (only relevant when wavefunctions are used)
-37    wf : int
-38        ID of wave function
-39    wf2 : int
-40        ID of the second wavefunction
-41        (only relevant for boundary-to-boundary correlation functions)
-42    im : bool
-43        if True, read imaginary instead of real part
-44        of the correlation function.
-45    names : list
-46        Alternative labeling for replicas/ensembles.
-47        Has to have the appropriate length
-48    ens_name : str
-49        replaces the name of the ensemble
-50    version: str
-51        version of SFCF, with which the measurement was done.
-52        if the compact output option (-c) was specified,
-53        append a "c" to the version (e.g. "1.0c")
-54        if the append output option (-a) was specified,
-55        append an "a" to the version
-56    cfg_separator : str
-57        String that separates the ensemble identifier from the configuration number (default 'n').
-58    replica: list
-59        list of replica to be read, default is all
-60    files: list
-61        list of files to be read per replica, default is all.
-62        for non-compact output format, hand the folders to be read here.
-63    check_configs: list[list[int]]
-64        list of list of supposed configs, eg. [range(1,1000)]
-65        for one replicum with 1000 configs
-66
-67    Returns
-68    -------
-69    result: list[Obs]
-70        list of Observables with length T, observable per timeslice.
-71        bb-type correlators have length 1.
-72    """
-73    ret = read_sfcf_multi(path, prefix, [name], quarks_list=[quarks], corr_type_list=[corr_type],
-74                          noffset_list=[noffset], wf_list=[wf], wf2_list=[wf2], version=version,
-75                          cfg_separator=cfg_separator, cfg_func=cfg_func, silent=silent, **kwargs)
-76    return ret[name][quarks][str(noffset)][str(wf)][str(wf2)]
+            
15def read_sfcf(path, prefix, name, quarks='.*', corr_type="bi", noffset=0, wf=0, wf2=0, version="1.0c", cfg_separator="n", cfg_func=None, silent=False, **kwargs):
+16    """Read sfcf files from given folder structure.
+17
+18    Parameters
+19    ----------
+20    path : str
+21        Path to the sfcf files.
+22    prefix : str
+23        Prefix of the sfcf files.
+24    name : str
+25        Name of the correlation function to read.
+26    quarks : str
+27        Label of the quarks used in the sfcf input file. e.g. "quark quark"
+28        for version 0.0 this does NOT need to be given with the typical " - "
+29        that is present in the output file,
+30        this is done automatically for this version
+31    corr_type : str
+32        Type of correlation function to read. Can be
+33        - 'bi' for boundary-inner
+34        - 'bb' for boundary-boundary
+35        - 'bib' for boundary-inner-boundary
+36    noffset : int
+37        Offset of the source (only relevant when wavefunctions are used)
+38    wf : int
+39        ID of wave function
+40    wf2 : int
+41        ID of the second wavefunction
+42        (only relevant for boundary-to-boundary correlation functions)
+43    im : bool
+44        if True, read imaginary instead of real part
+45        of the correlation function.
+46    names : list
+47        Alternative labeling for replicas/ensembles.
+48        Has to have the appropriate length
+49    ens_name : str
+50        replaces the name of the ensemble
+51    version: str
+52        version of SFCF, with which the measurement was done.
+53        if the compact output option (-c) was specified,
+54        append a "c" to the version (e.g. "1.0c")
+55        if the append output option (-a) was specified,
+56        append an "a" to the version
+57    cfg_separator : str
+58        String that separates the ensemble identifier from the configuration number (default 'n').
+59    replica: list
+60        list of replica to be read, default is all
+61    files: list
+62        list of files to be read per replica, default is all.
+63        for non-compact output format, hand the folders to be read here.
+64    check_configs: list[list[int]]
+65        list of list of supposed configs, eg. [range(1,1000)]
+66        for one replicum with 1000 configs
+67
+68    Returns
+69    -------
+70    result: list[Obs]
+71        list of Observables with length T, observable per timeslice.
+72        bb-type correlators have length 1.
+73    """
+74    ret = read_sfcf_multi(path, prefix, [name], quarks_list=[quarks], corr_type_list=[corr_type],
+75                          noffset_list=[noffset], wf_list=[wf], wf2_list=[wf2], version=version,
+76                          cfg_separator=cfg_separator, cfg_func=cfg_func, silent=silent, **kwargs)
+77    return ret[name][quarks][str(noffset)][str(wf)][str(wf2)]
 

 
 
@@ -944,347 +985,347 @@ bb-type correlators have length 1.
- 
 79def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", cfg_func=None, silent=False, keyed_out=False, **kwargs):
- 80    """Read sfcf files from given folder structure.
- 81
- 82    Parameters
- 83    ----------
- 84    path : str
- 85        Path to the sfcf files.
- 86    prefix : str
- 87        Prefix of the sfcf files.
- 88    name : str
- 89        Name of the correlation function to read.
- 90    quarks_list : list[str]
- 91        Label of the quarks used in the sfcf input file. e.g. "quark quark"
- 92        for version 0.0 this does NOT need to be given with the typical " - "
- 93        that is present in the output file,
- 94        this is done automatically for this version
- 95    corr_type_list : list[str]
- 96        Type of correlation function to read. Can be
- 97        - 'bi' for boundary-inner
- 98        - 'bb' for boundary-boundary
- 99        - 'bib' for boundary-inner-boundary
-100    noffset_list : list[int]
-101        Offset of the source (only relevant when wavefunctions are used)
-102    wf_list : int
-103        ID of wave function
-104    wf2_list : list[int]
-105        ID of the second wavefunction
-106        (only relevant for boundary-to-boundary correlation functions)
-107    im : bool
-108        if True, read imaginary instead of real part
-109        of the correlation function.
-110    names : list
-111        Alternative labeling for replicas/ensembles.
-112        Has to have the appropriate length
-113    ens_name : str
-114        replaces the name of the ensemble
-115    version: str
-116        version of SFCF, with which the measurement was done.
-117        if the compact output option (-c) was specified,
-118        append a "c" to the version (e.g. "1.0c")
-119        if the append output option (-a) was specified,
-120        append an "a" to the version
-121    cfg_separator : str
-122        String that separates the ensemble identifier from the configuration number (default 'n').
-123    replica: list
-124        list of replica to be read, default is all
-125    files: list[list[int]]
-126        list of files to be read per replica, default is all.
-127        for non-compact output format, hand the folders to be read here.
-128    check_configs: list[list[int]]
-129        list of list of supposed configs, eg. [range(1,1000)]
-130        for one replicum with 1000 configs
-131    rep_string: str
-132        Separator of ensemble name and replicum. Example: In "ensAr0", "r" would be the separator string.
-133    Returns
-134    -------
-135    result: dict[list[Obs]]
-136        dict with one of the following properties:
-137        if keyed_out:
-138            dict[key] = list[Obs]
-139            where key has the form name/quarks/offset/wf/wf2
-140        if not keyed_out:
-141            dict[name][quarks][offset][wf][wf2] = list[Obs]
-142    """
-143
-144    if kwargs.get('im'):
-145        im = 1
-146        part = 'imaginary'
-147    else:
-148        im = 0
-149        part = 'real'
-150
-151    known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"]
-152
-153    if version not in known_versions:
-154        raise Exception("This version is not known!")
-155    if (version[-1] == "c"):
-156        appended = False
-157        compact = True
-158        version = version[:-1]
-159    elif (version[-1] == "a"):
-160        appended = True
-161        compact = False
-162        version = version[:-1]
-163    else:
-164        compact = False
-165        appended = False
-166    ls = []
-167    if "replica" in kwargs:
-168        ls = kwargs.get("replica")
-169    else:
-170        for (dirpath, dirnames, filenames) in os.walk(path):
-171            if not appended:
-172                ls.extend(dirnames)
-173            else:
-174                ls.extend(filenames)
-175            break
-176        if not ls:
-177            raise Exception('Error, directory not found')
-178        # Exclude folders with different names
-179        for exc in ls:
-180            if not fnmatch.fnmatch(exc, prefix + '*'):
-181                ls = list(set(ls) - set([exc]))
-182
-183    if not appended:
-184        ls = sort_names(ls)
-185        replica = len(ls)
-186
-187    else:
-188        replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls]))
-189    if replica == 0:
-190        raise Exception('No replica found in directory')
-191    if not silent:
-192        print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica')
-193
-194    if 'names' in kwargs:
-195        new_names = kwargs.get('names')
-196        if len(new_names) != len(set(new_names)):
-197            raise Exception("names are not unique!")
-198        if len(new_names) != replica:
-199            raise Exception('names should have the length', replica)
-200
-201    else:
-202        ens_name = kwargs.get("ens_name")
-203        if not appended:
-204            new_names = _get_rep_names(ls, ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
-205        else:
-206            new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
-207        new_names = sort_names(new_names)
-208
-209    idl = []
-210
-211    noffset_list = [str(x) for x in noffset_list]
-212    wf_list = [str(x) for x in wf_list]
-213    wf2_list = [str(x) for x in wf2_list]
-214
-215    # setup dict structures
-216    intern = {}
-217    for name, corr_type in zip(name_list, corr_type_list):
-218        intern[name] = {}
-219        b2b, single = _extract_corr_type(corr_type)
-220        intern[name]["b2b"] = b2b
-221        intern[name]["single"] = single
-222        intern[name]["spec"] = {}
-223        for quarks in quarks_list:
-224            intern[name]["spec"][quarks] = {}
-225            for off in noffset_list:
-226                intern[name]["spec"][quarks][off] = {}
-227                for w in wf_list:
-228                    intern[name]["spec"][quarks][off][w] = {}
-229                    if b2b:
-230                        for w2 in wf2_list:
-231                            intern[name]["spec"][quarks][off][w][w2] = {}
-232                            intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks)
-233                    else:
-234                        intern[name]["spec"][quarks][off][w]["0"] = {}
-235                        intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks)
-236
-237    internal_ret_dict = {}
-238    needed_keys = []
-239    for name, corr_type in zip(name_list, corr_type_list):
-240        b2b, single = _extract_corr_type(corr_type)
-241        if b2b:
-242            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list))
-243        else:
-244            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"]))
-245
-246    for key in needed_keys:
-247        internal_ret_dict[key] = []
-248
-249    def _default_idl_func(cfg_string, cfg_sep):
-250        return int(cfg_string.split(cfg_sep)[-1])
-251
-252    if cfg_func is None:
-253        print("Default idl function in use.")
-254        cfg_func = _default_idl_func
-255        cfg_func_args = [cfg_separator]
-256    else:
-257        cfg_func_args = kwargs.get("cfg_func_args", [])
-258
-259    if not appended:
-260        for i, item in enumerate(ls):
-261            rep_path = path + '/' + item
-262            if "files" in kwargs:
-263                files = kwargs.get("files")
-264                if isinstance(files, list):
-265                    if all(isinstance(f, list) for f in files):
-266                        files = files[i]
-267                    elif all(isinstance(f, str) for f in files):
-268                        files = files
-269                    else:
-270                        raise TypeError("files has to be of type list[list[str]] or list[str]!")
-271                else:
-272                    raise TypeError("files has to be of type list[list[str]] or list[str]!")
-273
-274            else:
-275                files = []
-276            sub_ls = _find_files(rep_path, prefix, compact, files)
-277            rep_idl = []
-278            no_cfg = len(sub_ls)
-279            for cfg in sub_ls:
-280                try:
-281                    if compact:
-282                        rep_idl.append(cfg_func(cfg, *cfg_func_args))
-283                    else:
-284                        rep_idl.append(int(cfg[3:]))
-285                except Exception:
-286                    raise Exception("Couldn't parse idl from directory, problem with file " + cfg)
-287            rep_idl.sort()
-288            # maybe there is a better way to print the idls
-289            if not silent:
-290                print(item, ':', no_cfg, ' configurations')
-291            idl.append(rep_idl)
-292            # here we have found all the files we need to look into.
-293            if i == 0:
-294                if version != "0.0" and compact:
-295                    file = path + '/' + item + '/' + sub_ls[0]
-296                for name_index, name in enumerate(name_list):
-297                    if version == "0.0" or not compact:
-298                        file = path + '/' + item + '/' + sub_ls[0] + '/' + name
-299                    if corr_type_list[name_index] == 'bi':
-300                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"])
-301                    else:
-302                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list)
-303                    for key in name_keys:
-304                        specs = _key2specs(key)
-305                        quarks = specs[0]
-306                        off = specs[1]
-307                        w = specs[2]
-308                        w2 = specs[3]
-309                        # here, we want to find the place within the file,
-310                        # where the correlator we need is stored.
-311                        # to do so, the pattern needed is put together
-312                        # from the input values
-313                        start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent)
-314                        intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read
-315                        intern[name]["T"] = T
-316                        # preparing the datastructure
-317                        # the correlators get parsed into...
-318                        deltas = []
-319                        for j in range(intern[name]["T"]):
-320                            deltas.append([])
-321                        internal_ret_dict[sep.join([name, key])] = deltas
-322
-323            if compact:
-324                rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im)
-325                for key in needed_keys:
-326                    name = _key2specs(key)[0]
-327                    for t in range(intern[name]["T"]):
-328                        internal_ret_dict[key][t].append(rep_deltas[key][t])
-329            else:
-330                for key in needed_keys:
-331                    rep_data = []
-332                    name = _key2specs(key)[0]
-333                    for subitem in sub_ls:
-334                        cfg_path = path + '/' + item + '/' + subitem
-335                        file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im)
-336                        rep_data.append(file_data)
-337                    for t in range(intern[name]["T"]):
-338                        internal_ret_dict[key][t].append([])
-339                        for cfg in range(no_cfg):
-340                            internal_ret_dict[key][t][i].append(rep_data[cfg][key][t])
-341    else:
-342        for key in needed_keys:
-343            specs = _key2specs(key)
-344            name = specs[0]
-345            quarks = specs[1]
-346            off = specs[2]
-347            w = specs[3]
-348            w2 = specs[4]
-349            if "files" in kwargs:
-350                if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")):
-351                    name_ls = kwargs.get("files")
-352                else:
-353                    raise TypeError("In append mode, files has to be of type list[str]!")
-354            else:
-355                name_ls = ls
-356                for exc in name_ls:
-357                    if not fnmatch.fnmatch(exc, prefix + '*.' + name):
-358                        name_ls = list(set(name_ls) - set([exc]))
-359            name_ls = sort_names(name_ls)
-360            pattern = intern[name]['spec'][quarks][off][w][w2]['pattern']
-361            deltas = []
-362            for rep, file in enumerate(name_ls):
-363                rep_idl = []
-364                filename = path + '/' + file
-365                T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], im, intern[name]['single'], cfg_func, cfg_func_args)
-366                if rep == 0:
-367                    intern[name]['T'] = T
-368                    for t in range(intern[name]['T']):
-369                        deltas.append([])
-370                for t in range(intern[name]['T']):
-371                    deltas[t].append(rep_data[t])
-372                internal_ret_dict[key] = deltas
-373                if name == name_list[0]:
-374                    idl.append(rep_idl)
-375
-376    if kwargs.get("check_configs") is True:
-377        if not silent:
-378            print("Checking for missing configs...")
-379        che = kwargs.get("check_configs")
-380        if not (len(che) == len(idl)):
-381            raise Exception("check_configs has to be the same length as replica!")
-382        for r in range(len(idl)):
-383            if not silent:
-384                print("checking " + new_names[r])
-385            check_idl(idl[r], che[r])
-386        if not silent:
-387            print("Done")
-388
-389    result_dict = {}
-390    if keyed_out:
-391        for key in needed_keys:
-392            name = _key2specs(key)[0]
-393            result = []
-394            for t in range(intern[name]["T"]):
-395                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-396            result_dict[key] = result
-397    else:
-398        for name, corr_type in zip(name_list, corr_type_list):
-399            result_dict[name] = {}
-400            for quarks in quarks_list:
-401                result_dict[name][quarks] = {}
-402                for off in noffset_list:
-403                    result_dict[name][quarks][off] = {}
-404                    for w in wf_list:
-405                        result_dict[name][quarks][off][w] = {}
-406                        if corr_type != 'bi':
-407                            for w2 in wf2_list:
-408                                key = _specs2key(name, quarks, off, w, w2)
-409                                result = []
-410                                for t in range(intern[name]["T"]):
-411                                    result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-412                                result_dict[name][quarks][str(off)][str(w)][str(w2)] = result
-413                        else:
-414                            key = _specs2key(name, quarks, off, w, "0")
-415                            result = []
-416                            for t in range(intern[name]["T"]):
-417                                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
-418                            result_dict[name][quarks][str(off)][str(w)][str(0)] = result
-419    return result_dict
+            
 80def read_sfcf_multi(path, prefix, name_list, quarks_list=['.*'], corr_type_list=['bi'], noffset_list=[0], wf_list=[0], wf2_list=[0], version="1.0c", cfg_separator="n", cfg_func=None, silent=False, keyed_out=False, **kwargs):
+ 81    """Read sfcf files from given folder structure.
+ 82
+ 83    Parameters
+ 84    ----------
+ 85    path : str
+ 86        Path to the sfcf files.
+ 87    prefix : str
+ 88        Prefix of the sfcf files.
+ 89    name : str
+ 90        Name of the correlation function to read.
+ 91    quarks_list : list[str]
+ 92        Label of the quarks used in the sfcf input file. e.g. "quark quark"
+ 93        for version 0.0 this does NOT need to be given with the typical " - "
+ 94        that is present in the output file,
+ 95        this is done automatically for this version
+ 96    corr_type_list : list[str]
+ 97        Type of correlation function to read. Can be
+ 98        - 'bi' for boundary-inner
+ 99        - 'bb' for boundary-boundary
+100        - 'bib' for boundary-inner-boundary
+101    noffset_list : list[int]
+102        Offset of the source (only relevant when wavefunctions are used)
+103    wf_list : int
+104        ID of wave function
+105    wf2_list : list[int]
+106        ID of the second wavefunction
+107        (only relevant for boundary-to-boundary correlation functions)
+108    im : bool
+109        if True, read imaginary instead of real part
+110        of the correlation function.
+111    names : list
+112        Alternative labeling for replicas/ensembles.
+113        Has to have the appropriate length
+114    ens_name : str
+115        replaces the name of the ensemble
+116    version: str
+117        version of SFCF, with which the measurement was done.
+118        if the compact output option (-c) was specified,
+119        append a "c" to the version (e.g. "1.0c")
+120        if the append output option (-a) was specified,
+121        append an "a" to the version
+122    cfg_separator : str
+123        String that separates the ensemble identifier from the configuration number (default 'n').
+124    replica: list
+125        list of replica to be read, default is all
+126    files: list[list[int]]
+127        list of files to be read per replica, default is all.
+128        for non-compact output format, hand the folders to be read here.
+129    check_configs: list[list[int]]
+130        list of list of supposed configs, eg. [range(1,1000)]
+131        for one replicum with 1000 configs
+132    rep_string: str
+133        Separator of ensemble name and replicum. Example: In "ensAr0", "r" would be the separator string.
+134    Returns
+135    -------
+136    result: dict[list[Obs]]
+137        dict with one of the following properties:
+138        if keyed_out:
+139            dict[key] = list[Obs]
+140            where key has the form name/quarks/offset/wf/wf2
+141        if not keyed_out:
+142            dict[name][quarks][offset][wf][wf2] = list[Obs]
+143    """
+144
+145    if kwargs.get('im'):
+146        im = 1
+147        part = 'imaginary'
+148    else:
+149        im = 0
+150        part = 'real'
+151
+152    known_versions = ["0.0", "1.0", "2.0", "1.0c", "2.0c", "1.0a", "2.0a"]
+153
+154    if version not in known_versions:
+155        raise Exception("This version is not known!")
+156    if (version[-1] == "c"):
+157        appended = False
+158        compact = True
+159        version = version[:-1]
+160    elif (version[-1] == "a"):
+161        appended = True
+162        compact = False
+163        version = version[:-1]
+164    else:
+165        compact = False
+166        appended = False
+167    ls = []
+168    if "replica" in kwargs:
+169        ls = kwargs.get("replica")
+170    else:
+171        for (dirpath, dirnames, filenames) in os.walk(path):
+172            if not appended:
+173                ls.extend(dirnames)
+174            else:
+175                ls.extend(filenames)
+176            break
+177        if not ls:
+178            raise Exception('Error, directory not found')
+179        # Exclude folders with different names
+180        for exc in ls:
+181            if not fnmatch.fnmatch(exc, prefix + '*'):
+182                ls = list(set(ls) - set([exc]))
+183
+184    if not appended:
+185        ls = sort_names(ls)
+186        replica = len(ls)
+187
+188    else:
+189        replica = len([file.split(".")[-1] for file in ls]) // len(set([file.split(".")[-1] for file in ls]))
+190    if replica == 0:
+191        raise Exception('No replica found in directory')
+192    if not silent:
+193        print('Read', part, 'part of', name_list, 'from', prefix[:-1], ',', replica, 'replica')
+194
+195    if 'names' in kwargs:
+196        new_names = kwargs.get('names')
+197        if len(new_names) != len(set(new_names)):
+198            raise Exception("names are not unique!")
+199        if len(new_names) != replica:
+200            raise Exception('names should have the length', replica)
+201
+202    else:
+203        ens_name = kwargs.get("ens_name")
+204        if not appended:
+205            new_names = _get_rep_names(ls, ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
+206        else:
+207            new_names = _get_appended_rep_names(ls, prefix, name_list[0], ens_name, rep_sep=(kwargs.get('rep_string', 'r')))
+208        new_names = sort_names(new_names)
+209
+210    idl = []
+211
+212    noffset_list = [str(x) for x in noffset_list]
+213    wf_list = [str(x) for x in wf_list]
+214    wf2_list = [str(x) for x in wf2_list]
+215
+216    # setup dict structures
+217    intern = {}
+218    for name, corr_type in zip(name_list, corr_type_list):
+219        intern[name] = {}
+220        b2b, single = _extract_corr_type(corr_type)
+221        intern[name]["b2b"] = b2b
+222        intern[name]["single"] = single
+223        intern[name]["spec"] = {}
+224        for quarks in quarks_list:
+225            intern[name]["spec"][quarks] = {}
+226            for off in noffset_list:
+227                intern[name]["spec"][quarks][off] = {}
+228                for w in wf_list:
+229                    intern[name]["spec"][quarks][off][w] = {}
+230                    if b2b:
+231                        for w2 in wf2_list:
+232                            intern[name]["spec"][quarks][off][w][w2] = {}
+233                            intern[name]["spec"][quarks][off][w][w2]["pattern"] = _make_pattern(version, name, off, w, w2, intern[name]['b2b'], quarks)
+234                    else:
+235                        intern[name]["spec"][quarks][off][w]["0"] = {}
+236                        intern[name]["spec"][quarks][off][w]["0"]["pattern"] = _make_pattern(version, name, off, w, 0, intern[name]['b2b'], quarks)
+237
+238    internal_ret_dict = {}
+239    needed_keys = []
+240    for name, corr_type in zip(name_list, corr_type_list):
+241        b2b, single = _extract_corr_type(corr_type)
+242        if b2b:
+243            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, wf2_list))
+244        else:
+245            needed_keys.extend(_lists2key([name], quarks_list, noffset_list, wf_list, ["0"]))
+246
+247    for key in needed_keys:
+248        internal_ret_dict[key] = []
+249
+250    def _default_idl_func(cfg_string, cfg_sep):
+251        return int(cfg_string.split(cfg_sep)[-1])
+252
+253    if cfg_func is None:
+254        print("Default idl function in use.")
+255        cfg_func = _default_idl_func
+256        cfg_func_args = [cfg_separator]
+257    else:
+258        cfg_func_args = kwargs.get("cfg_func_args", [])
+259
+260    if not appended:
+261        for i, item in enumerate(ls):
+262            rep_path = path + '/' + item
+263            if "files" in kwargs:
+264                files = kwargs.get("files")
+265                if isinstance(files, list):
+266                    if all(isinstance(f, list) for f in files):
+267                        files = files[i]
+268                    elif all(isinstance(f, str) for f in files):
+269                        files = files
+270                    else:
+271                        raise TypeError("files has to be of type list[list[str]] or list[str]!")
+272                else:
+273                    raise TypeError("files has to be of type list[list[str]] or list[str]!")
+274
+275            else:
+276                files = []
+277            sub_ls = _find_files(rep_path, prefix, compact, files)
+278            rep_idl = []
+279            no_cfg = len(sub_ls)
+280            for cfg in sub_ls:
+281                try:
+282                    if compact:
+283                        rep_idl.append(cfg_func(cfg, *cfg_func_args))
+284                    else:
+285                        rep_idl.append(int(cfg[3:]))
+286                except Exception:
+287                    raise Exception("Couldn't parse idl from directory, problem with file " + cfg)
+288            rep_idl.sort()
+289            # maybe there is a better way to print the idls
+290            if not silent:
+291                print(item, ':', no_cfg, ' configurations')
+292            idl.append(rep_idl)
+293            # here we have found all the files we need to look into.
+294            if i == 0:
+295                if version != "0.0" and compact:
+296                    file = path + '/' + item + '/' + sub_ls[0]
+297                for name_index, name in enumerate(name_list):
+298                    if version == "0.0" or not compact:
+299                        file = path + '/' + item + '/' + sub_ls[0] + '/' + name
+300                    if corr_type_list[name_index] == 'bi':
+301                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, ["0"])
+302                    else:
+303                        name_keys = _lists2key(quarks_list, noffset_list, wf_list, wf2_list)
+304                    for key in name_keys:
+305                        specs = _key2specs(key)
+306                        quarks = specs[0]
+307                        off = specs[1]
+308                        w = specs[2]
+309                        w2 = specs[3]
+310                        # here, we want to find the place within the file,
+311                        # where the correlator we need is stored.
+312                        # to do so, the pattern needed is put together
+313                        # from the input values
+314                        start_read, T = _find_correlator(file, version, intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["pattern"], intern[name]['b2b'], silent=silent)
+315                        intern[name]["spec"][quarks][str(off)][str(w)][str(w2)]["start"] = start_read
+316                        intern[name]["T"] = T
+317                        # preparing the datastructure
+318                        # the correlators get parsed into...
+319                        deltas = []
+320                        for j in range(intern[name]["T"]):
+321                            deltas.append([])
+322                        internal_ret_dict[sep.join([name, key])] = deltas
+323
+324            if compact:
+325                rep_deltas = _read_compact_rep(path, item, sub_ls, intern, needed_keys, im)
+326                for key in needed_keys:
+327                    name = _key2specs(key)[0]
+328                    for t in range(intern[name]["T"]):
+329                        internal_ret_dict[key][t].append(rep_deltas[key][t])
+330            else:
+331                for key in needed_keys:
+332                    rep_data = []
+333                    name = _key2specs(key)[0]
+334                    for subitem in sub_ls:
+335                        cfg_path = path + '/' + item + '/' + subitem
+336                        file_data = _read_o_file(cfg_path, name, needed_keys, intern, version, im)
+337                        rep_data.append(file_data)
+338                    for t in range(intern[name]["T"]):
+339                        internal_ret_dict[key][t].append([])
+340                        for cfg in range(no_cfg):
+341                            internal_ret_dict[key][t][i].append(rep_data[cfg][key][t])
+342    else:
+343        for key in needed_keys:
+344            specs = _key2specs(key)
+345            name = specs[0]
+346            quarks = specs[1]
+347            off = specs[2]
+348            w = specs[3]
+349            w2 = specs[4]
+350            if "files" in kwargs:
+351                if isinstance(kwargs.get("files"), list) and all(isinstance(f, str) for f in kwargs.get("files")):
+352                    name_ls = kwargs.get("files")
+353                else:
+354                    raise TypeError("In append mode, files has to be of type list[str]!")
+355            else:
+356                name_ls = ls
+357                for exc in name_ls:
+358                    if not fnmatch.fnmatch(exc, prefix + '*.' + name):
+359                        name_ls = list(set(name_ls) - set([exc]))
+360            name_ls = sort_names(name_ls)
+361            pattern = intern[name]['spec'][quarks][off][w][w2]['pattern']
+362            deltas = []
+363            for rep, file in enumerate(name_ls):
+364                rep_idl = []
+365                filename = path + '/' + file
+366                T, rep_idl, rep_data = _read_append_rep(filename, pattern, intern[name]['b2b'], im, intern[name]['single'], cfg_func, cfg_func_args)
+367                if rep == 0:
+368                    intern[name]['T'] = T
+369                    for t in range(intern[name]['T']):
+370                        deltas.append([])
+371                for t in range(intern[name]['T']):
+372                    deltas[t].append(rep_data[t])
+373                internal_ret_dict[key] = deltas
+374                if name == name_list[0]:
+375                    idl.append(rep_idl)
+376
+377    if kwargs.get("check_configs") is True:
+378        if not silent:
+379            print("Checking for missing configs...")
+380        che = kwargs.get("check_configs")
+381        if not (len(che) == len(idl)):
+382            raise Exception("check_configs has to be the same length as replica!")
+383        for r in range(len(idl)):
+384            if not silent:
+385                print("checking " + new_names[r])
+386            check_idl(idl[r], che[r])
+387        if not silent:
+388            print("Done")
+389
+390    result_dict = {}
+391    if keyed_out:
+392        for key in needed_keys:
+393            name = _key2specs(key)[0]
+394            result = []
+395            for t in range(intern[name]["T"]):
+396                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+397            result_dict[key] = result
+398    else:
+399        for name, corr_type in zip(name_list, corr_type_list):
+400            result_dict[name] = {}
+401            for quarks in quarks_list:
+402                result_dict[name][quarks] = {}
+403                for off in noffset_list:
+404                    result_dict[name][quarks][off] = {}
+405                    for w in wf_list:
+406                        result_dict[name][quarks][off][w] = {}
+407                        if corr_type != 'bi':
+408                            for w2 in wf2_list:
+409                                key = _specs2key(name, quarks, off, w, w2)
+410                                result = []
+411                                for t in range(intern[name]["T"]):
+412                                    result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+413                                result_dict[name][quarks][str(off)][str(w)][str(w2)] = result
+414                        else:
+415                            key = _specs2key(name, quarks, off, w, "0")
+416                            result = []
+417                            for t in range(intern[name]["T"]):
+418                                result.append(Obs(internal_ret_dict[key][t], new_names, idl=idl))
+419                            result_dict[name][quarks][str(off)][str(w)][str(0)] = result
+420    return result_dict
 

 
 
diff --git a/docs/pyerrors/misc.html b/docs/pyerrors/misc.html
index d8a27b6a..67022ce0 100644
--- a/docs/pyerrors/misc.html
+++ b/docs/pyerrors/misc.html
@@ -316,7 +316,7 @@
 

             
         def
-        errorbar(	x,	y,	axes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.12.11/x64/lib/python3.12/site-packages/matplotlib/pyplot.py'>,	**kwargs):
+        errorbar(	x,	y,	axes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.12.12/x64/lib/python3.12/site-packages/matplotlib/pyplot.py'>,	**kwargs):
 
                 
 
diff --git a/docs/search.js b/docs/search.js
index 914a773c..0e8a3900 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
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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\u2013Marquardt 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\u2013Marquardt) 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 = (number of y values) X (number 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_parms (int, optional):\nNumber of fit parameters. Overrides automatic detection of parameter count.\nUseful when autodetection fails. Must match the length of initial_guess or priors (if provided).
    • \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 differentiation instead of automatic differentiation to perform the error propagation (default False).
    • \n
  • n_parms (int, optional):\nNumber of fit parameters. Overrides automatic detection of parameter count.\nUseful when autodetection fails. Must match the length of initial_guess (if provided).
    • \n
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy.
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n\n
Returns
\n\n
    \n
  • fit_parameters (list[Obs]):\nLIist of fitted observables.
    • \n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n\n
For uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\n
Returns
\n\n
    \n
  • err (np.array(Obs)):\nError band for an array of sample values x
    • \n
\n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\n
Jackknife samples
\n\n
For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
Extract generic MCMC data from a bdio file
\n\n
read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • data (List[Obs]):\nExtracted data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
Write Obs to a bdio file according to ADerrors conventions
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • success (int):\nreturns 0 is successful
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
Extract mesons data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n\n
Returns
\n\n
    \n
  • data (dict):\nExtracted meson data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
Extract dSdm data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, kappa)
\n\n
read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML formatted string of the input data
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
Import a list of Obs from a string in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator |is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML string generated from the data
    • \n
\n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
Read hadrons hdf5 file and extract entry based on attributes.
\n\n
Parameters
\n\n
    \n
  • filestem (str):\nFull namestem of the files to read, including the full path.
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • group (str):\nlabel of the group to be extracted.
    • \n
  • attrs (dict or int):\nDictionary containing the attributes. For example
    \n\n
    \n
    attrs = {"gamma_snk": "Gamma5",\n         "gamma_src": "Gamma5"}\n
    \n
    \n\n
    Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
Read hadrons FlowObservables hdf5 file and extract t0
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
Read hadrons DistillationContraction hdf5 files in given directory structure
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
    • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
\n\n
An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\n
Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\n
For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n
array:  Construct an array.
\nzeros:  Create an array, each element of which is zero.
\nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype:  Create a data-type.
\nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
\n\n
Notes
\n\n
There are two modes of creating an array using __new__:
\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n
No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\n
Examples
\n\n
These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\n
First mode, buffer is None:
\n\n
\n
>>> import numpy as np\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n
\n\n
Second mode:
\n\n
\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
Gamma_5 hermitean conjugate
\n\n
Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
Read hadrons ExternalLeg hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Npr_matrix):\nread Cobs-matrix
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
Read hadrons Bilinear hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict[Npr_matrix]):\nextracted Bilinears
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • vertices (list):\nVertex functions to be extracted.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict):\nextracted fourquark matrizes
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
\n\n
Returns
\n\n
    \n
  • json_string (str):\nString for export to .json(.gz) file
    • \n
\n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • Null
    • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
Reconstruct a list of Obs or structures containing Obs from a json string.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
Import a list of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
Export a dict of Obs or structures containing Obs to a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
Import a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
    • \n
\n\n
Returns
\n\n
    \n
  • data (Obs / list / Corr):\nRead data
    • \n
  • or
    • \n
  • data (dict):\nRead data and meta-data
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
\n\n
It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
\n\n
A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
\n\n
Parameters
\n\n
    \n
  • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
    • \n
  • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
    • \n
\n\n
Returns
\n\n
    \n
  • root (Obs):\nThe root of the data series.
    • \n
\n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
Read pbp format from given folder structure.
\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of observables read
    • \n
\n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
Read rwms format from given folder structure. Returns a list of length nrw
\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
    • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
    • \n
  • version (str):\nversion of openQCD, default 2.0
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
    • \n
\n\n
Returns
\n\n
    \n
  • rwms (Obs):\nReweighting factors read
    • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • t0 (Obs):\nExtracted t0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
Extract w0/a from given .ms.dat files. Returns w0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • w0 (Obs):\nExtracted w0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
Read the topologial charge based on openQCD gradient flow measurements.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Obs):\nRead topological charge
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
\n\n
Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
Returns the projection to the topological charge sector defined by target.
\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
Constructs reweighting factors to a specified topological sector.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
    • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
\n\n
Parameters
\n\n
    \n
  • path (str):\nThe directory to search for the files in.
    • \n
  • prefix (str):\nThe prefix to match the files against.
    • \n
  • qc (str):\nThe quark combination extension to match the files against.
    • \n
  • corr (str):\nThe correlator to extract data for.
    • \n
  • sep (str, optional):\nThe separator to use when parsing the replika names.
    • \n
  • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
    \n\n
      \n
    • names (List[str]): A list of names to use for the replicas.
      • \n
    • files (List[str]): A list of files to read data from.
      • \n
    • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
      • \n
    • \n
\n\n
Returns
\n\n
    \n
  • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
    • \n
  • or
    • \n
  • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
    • \n
\n\n
Raises
\n\n
    \n
  • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
    • \n
  • IOError: If there is an error reading a file.
    • \n
  • struct.error: If there is an error unpacking binary data.
    • \n
\n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
Write DataFrame including Obs or Corr valued columns to sqlite database.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be written to the database.
    • \n
  • table_name (str):\nName of the table in the database.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
    • \n
  • gz (bool):\nIf True the json strings are gzipped.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
\n\n
Parameters
\n\n
    \n
  • sql (str):\nSQL query to be executed.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
\n\n
Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be dumped to a file.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
\n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
\n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
    • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tcfg_func=None,\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',\tcfg_func=None,\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/3.12.11/x64/lib/python3.12/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(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()`\nbeta`, `function`  \nbetaincinv()\ninverse, of, the, regularized, incomplete, beta, function
\nbetaincc()`\ncomplement`, `of`, `the`, `regularized`, `incomplete`, `beta`, `function`  \nscipy.stats.beta()\nbeta, 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
betainc(a, b, x) is treated as a two parameter family of functions\nof a single variable x, rather than as a function of three variables.\nThis impacts only the limiting cases a = 0, b = 0, a = inf,\nb = inf.
\n\n
In general
\n\n
$$\\lim_{(a, b) \\rightarrow (a_0, b_0)} \\mathrm{betainc}(a, b, x)$$
\n\n
is treated as a pointwise limit in x. Thus for example,\nbetainc(0, b, 0) equals 0 for b > 0, although it would be\nindeterminate when considering the simultaneous limit (a, x) -> (0+, 0+).
\n\n
This function wraps the ibeta routine from the\nBoost Math C++ library 2.
\n\n
betainc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u26d4
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\n\n
References
\n\n
Examples
\n\n
Let \\( B(a, b) \\) be the beta function.
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
The coefficient in terms of gamma is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).
\n\n
\n
>>> sc.betainc(0.2, 3.5, 1.0)\n1.0\n
\n
\n\n
It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function hyp2f1:
\n\n
\n
>>> a, b, x = 1.4, 3.1, 0.5\n>>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n0.8148904036225295\n>>> sc.betainc(a, b, x)\n0.8148904036225296\n
\n
\n\n
This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):
\n\n
\n
>>> sc.betainc(2.2, 3.1, 0.4)\n0.49339638807619446\n>>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n0.49339638807619446\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/8.17 ↩
    \n
    2. \n\n
  2. \n
    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "
betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
betaln(a, b, out=None)
\n\n
Natural logarithm of absolute value of beta function.
\n\n
Computes ln(abs(beta(a, b))).
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nPositive, real-valued parameters
    • \n
  • out (ndarray, optional):\nOptional output array for function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the betaln function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\nbetainc:   the regularized incomplete beta function
\nbeta:  the beta function  
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import betaln, beta\n
\n
\n\n
Verify that, for moderate values of a and b, betaln(a, b)\nis the same as log(beta(a, b)):
\n\n
\n
>>> betaln(3, 4)\n-4.0943445622221\n
\n
\n\n
\n
>>> np.log(beta(3, 4))\n-4.0943445622221\n
\n
\n\n
In the following beta(a, b) underflows to 0, so we can't compute\nthe logarithm of the actual value.
\n\n
\n
>>> a = 400\n>>> b = 900\n>>> beta(a, b)\n0.0\n
\n
\n\n
We can compute the logarithm of beta(a, b) by using betaln:
\n\n
\n
>>> betaln(a, b)\n-804.3069951764146\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "
Polygamma functions.
\n\n
Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\ndigamma function. See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • n (array_like):\nThe order of the derivative of the digamma function; must be\nintegral
    • \n
  • x (array_like):\nReal valued input
    • \n
\n\n
Returns
\n\n
    \n
  • ndarray: Function results
    • \n
\n\n
See Also
\n\n
digamma  
\n\n
References
\n\n
.. [dlmf] NIST, Digital Library of Mathematical Functions,\n    https://dlmf.nist.gov/5.15
\n\n
Examples
\n\n
\n
>>> from scipy import special\n>>> x = [2, 3, 25.5]\n>>> special.polygamma(1, x)\narray([ 0.64493407,  0.39493407,  0.03999467])\n>>> special.polygamma(0, x) == special.psi(x)\narray([ True,  True,  True], dtype=bool)\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "
gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gamma(z, out=None)
\n\n
gamma function.
\n\n
The gamma function is defined as
\n\n
$$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$
\n\n
for \\( \\Re(z) > 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex valued argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the gamma function
    • \n
\n\n
Notes
\n\n
The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).
\n\n
The gamma function has poles at non-negative integers and the sign\nof infinity as z approaches each pole depends upon the direction in\nwhich the pole is approached. For this reason, the consistent thing\nis for gamma(z) to return NaN at negative integers, and to return\n-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero\nto signify the direction in which the origin is being approached. This\nis for instance what is recommended for the gamma function in annex F\nentry 9.5.4 of the Iso C 99 standard [isoc99]_.
\n\n
Prior to SciPy version 1.15, scipy.special.gamma(z) returned +inf\nat each pole. This was fixed in version 1.15, but with the following\nconsequence. Expressions where gamma appears in the denominator\nsuch as
\n\n
gamma(u) * gamma(v) / (gamma(w) * gamma(x))
\n\n
no longer evaluate to 0 if the numerator is well defined but there is a\npole in the denominator. Instead such expressions evaluate to NaN. We\nrecommend instead using the function rgamma for the reciprocal gamma\nfunction in such cases. The above expression could for instance be written\nas
\n\n
gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1\n.. [isoc99] https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import gamma, factorial\n
\n
\n\n
\n
>>> gamma([0, 0.5, 1, 5])\narray([         inf,   1.77245385,   1.        ,  24.        ])\n
\n
\n\n
\n
>>> z = 2.5 + 1j\n>>> gamma(z)\n(0.77476210455108352+0.70763120437959293j)\n>>> gamma(z+1), z*gamma(z)  # Recurrence property\n((1.2292740569981171+2.5438401155000685j),\n (1.2292740569981158+2.5438401155000658j))\n
\n
\n\n
\n
>>> gamma(0.5)**2  # gamma(0.5) = sqrt(pi)\n3.1415926535897927\n
\n
\n\n
Plot gamma(x) for real x
\n\n
\n
>>> x = np.linspace(-3.5, 5.5, 2251)\n>>> y = gamma(x)\n
\n
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)')\n>>> k = np.arange(1, 7)\n>>> plt.plot(k, factorial(k-1), 'k*', alpha=0.6,\n...          label='(x-1)!, x = 1, 2, ...')\n>>> plt.xlim(-3.5, 5.5)\n>>> plt.ylim(-10, 25)\n>>> plt.grid()\n>>> plt.xlabel('x')\n>>> plt.legend(loc='lower right')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "
gammaln(x, out=None)
\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()`\nsign`, `of`, `the`, `gamma`, `function`  \nloggamma()\nprincipal, 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
gammaln has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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(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()`\nregularized`, `upper`, `incomplete`, `gamma`, `function`  \ngammaincinv()\ninverse, of, the, regularized, lower, incomplete, gamma, function
\n`gammainccinv()\ninverse,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
gammainc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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(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()`\nregularized`, `lower`, `incomplete`, `gamma`, `function`  \ngammaincinv()\ninverse, of, the, regularized, lower, incomplete, gamma, function
\n`gammainccinv()\ninverse,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
gammaincc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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()`\nModified`, `Bessel`, `function`, `of`, `any`, `order`  \ni0e()\nExponentially, 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
i0 has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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()`\nModified`, `Bessel`, `function`, `of`, `the`, `first`, `kind`  \ni1e()\nExponentially, 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
i1 has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import i1\n>>> i1(1.)\n0.5651591039924851\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> i1(np.array([-2., 0., 6.]))\narray([-1.59063685,  0.        , 61.34193678])\n
\n
\n\n
Plot the function between -10 and 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "
iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
iv(v, z, out=None)
\n\n
Modified Bessel function of the first kind of real order.
\n\n
Parameters
\n\n
    \n
  • v (array_like):\nOrder. If z is of real type and negative, v must be integer\nvalued.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the modified Bessel function.
    • \n
\n\n
See Also
\n\n
ive:  This function with leading exponential behavior stripped off.
\ni0:  Faster version of this function for order 0.
\ni1:  Faster version of this function for order 1.  
\n\n
Notes
\n\n
For real z and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method 1.  For larger orders, uniform asymptotic\nexpansions are applied.
\n\n
For complex z and positive v, the AMOS 2 zbesi routine is\ncalled. It uses a power series for small z, the asymptotic expansion\nfor large abs(z), the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import iv\n>>> iv(0, 1.)\n1.2660658777520084\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> iv(0, 1.), iv(1, 1.), iv(1.5, 1.)\n(1.2660658777520084, 0.565159103992485, 0.2935253263474798)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> iv([0, 1, 1.5], 1.)\narray([1.26606588, 0.5651591 , 0.29352533])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> iv(0, points)\narray([2.2795853 , 1.        , 4.88079259])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> iv(orders, points)\narray([[ 2.2795853 ,  1.        ,  4.88079259],\n       [-1.59063685,  0.        ,  3.95337022]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, iv(i, x), label=f'$I_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Temme, Journal of Computational Physics, vol 21, 343 (1976) ↩
    \n
    2. \n\n
  2. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "
ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
ive(v, z, out=None)
\n\n
Exponentially scaled modified Bessel function of the first kind.
\n\n
Defined as::
\n\n
ive(v, z) = iv(v, z) * exp(-abs(z.real))\n
\n\n
For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind iv.
\n\n
Parameters
\n\n
    \n
  • v (array_like of float):\nOrder.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the exponentially scaled modified Bessel function.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of the first kind
\ni0e:  Faster implementation of this function for order 0
\ni1e:  Faster implementation of this function for order 1  
\n\n
Notes
\n\n
For positive v, the AMOS 1 zbesi routine is called. It uses a\npower series for small z, the asymptotic expansion for large\nabs(z), the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
ive is useful for large arguments z: for these, iv easily overflows,\nwhile ive does not due to the exponential scaling.
\n\n
References
\n\n
Examples
\n\n
In the following example iv returns infinity whereas ive still returns\na finite number.
\n\n
\n
>>> from scipy.special import iv, ive\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> iv(3, 1000.), ive(3, 1000.)\n(inf, 0.01256056218254712)\n
\n
\n\n
Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> ive([0, 1, 1.5], 1.)\narray([0.46575961, 0.20791042, 0.10798193])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> points = np.array([-2., 0., 3.])\n>>> ive(0, points)\narray([0.30850832, 1.        , 0.24300035])\n
\n
\n\n
Evaluate the function at several points for different orders by\nproviding arrays for both v for z. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:
\n\n
\n
>>> ive([[0], [1], [2]], points)\narray([[ 0.30850832,  1.        ,  0.24300035],\n       [-0.21526929,  0.        ,  0.19682671],\n       [ 0.09323903,  0.        ,  0.11178255]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, ive(i, x), label=fr'$I_{i!r}(z)\\cdot e^{{-|z|}}$')\n>>> ax.legend()\n>>> ax.set_xlabel(r"$z$")\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "
erf(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\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
erf has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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\n
Notes
\n\n
erfc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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\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
logit has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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\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
expit has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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`\n..`  \nnumpy.logaddexp2\n..  
\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
logsumexp has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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": "
\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 8400}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 367}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 40, "bases": 0, "doc": 100}, "pyerrors.correlators.Corr.tag": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.content": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.T": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, 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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:
\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:
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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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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\u2013Marquardt 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\u2013Marquardt) 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 = (number of y values) X (number 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_parms (int, optional):\nNumber of fit parameters. Overrides automatic detection of parameter count.\nUseful when autodetection fails. Must match the length of initial_guess or priors (if provided).
    • \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 differentiation instead of automatic differentiation to perform the error propagation (default False).
    • \n
  • n_parms (int, optional):\nNumber of fit parameters. Overrides automatic detection of parameter count.\nUseful when autodetection fails. Must match the length of initial_guess (if provided).
    • \n
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy.
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n\n
Returns
\n\n
    \n
  • fit_parameters (list[Obs]):\nLIist of fitted observables.
    • \n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n\n
For uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\n
Returns
\n\n
    \n
  • err (np.array(Obs)):\nError band for an array of sample values x
    • \n
\n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\n
Jackknife samples
\n\n
For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
Extract generic MCMC data from a bdio file
\n\n
read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • data (List[Obs]):\nExtracted data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
Write Obs to a bdio file according to ADerrors conventions
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • success (int):\nreturns 0 is successful
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
Extract mesons data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n\n
Returns
\n\n
    \n
  • data (dict):\nExtracted meson data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
Extract dSdm data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, kappa)
\n\n
read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML formatted string of the input data
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
Import a list of Obs from a string in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator |is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML string generated from the data
    • \n
\n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
Read hadrons hdf5 file and extract entry based on attributes.
\n\n
Parameters
\n\n
    \n
  • filestem (str):\nFull namestem of the files to read, including the full path.
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • group (str):\nlabel of the group to be extracted.
    • \n
  • attrs (dict or int):\nDictionary containing the attributes. For example
    \n\n
    \n
    attrs = {"gamma_snk": "Gamma5",\n         "gamma_src": "Gamma5"}\n
    \n
    \n\n
    Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
Read hadrons FlowObservables hdf5 file and extract t0
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
Read hadrons DistillationContraction hdf5 files in given directory structure
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
    • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
\n\n
An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\n
Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\n
For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n
array:  Construct an array.
\nzeros:  Create an array, each element of which is zero.
\nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype:  Create a data-type.
\nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
\n\n
Notes
\n\n
There are two modes of creating an array using __new__:
\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n
No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\n
Examples
\n\n
These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\n
First mode, buffer is None:
\n\n
\n
>>> import numpy as np\n>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n
\n\n
Second mode:
\n\n
\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
Gamma_5 hermitean conjugate
\n\n
Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
Read hadrons ExternalLeg hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Npr_matrix):\nread Cobs-matrix
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
Read hadrons Bilinear hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict[Npr_matrix]):\nextracted Bilinears
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • vertices (list):\nVertex functions to be extracted.
    • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict):\nextracted fourquark matrizes
    • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
\n\n
Returns
\n\n
    \n
  • json_string (str):\nString for export to .json(.gz) file
    • \n
\n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • Null
    • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
Reconstruct a list of Obs or structures containing Obs from a json string.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
Import a list of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
    • \n
  • or
    • \n
  • result (Obs):\nonly one observable if the list only has one entry
    • \n
  • or
    • \n
  • result (dict):\nif full_output=True
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
Export a dict of Obs or structures containing Obs to a .json(.gz) file
\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • description (str):\nOptional string that describes the contents of the json file.
    • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
    • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
Import a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\n
The following structures are supported: Obs, list, numpy.ndarray, Corr
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • verbose (bool):\nPrint additional information that was written to the file.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
    • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
    • \n
\n\n
Returns
\n\n
    \n
  • data (Obs / list / Corr):\nRead data
    • \n
  • or
    • \n
  • data (dict):\nRead data and meta-data
    • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
\n\n
It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
\n\n
A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
\n\n
Parameters
\n\n
    \n
  • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
    • \n
  • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
    • \n
\n\n
Returns
\n\n
    \n
  • root (Obs):\nThe root of the data series.
    • \n
\n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
Read pbp format from given folder structure.
\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of observables read
    • \n
\n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
Read rwms format from given folder structure. Returns a list of length nrw
\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
    • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
    • \n
  • version (str):\nversion of openQCD, default 2.0
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
    • \n
\n\n
Returns
\n\n
    \n
  • rwms (Obs):\nReweighting factors read
    • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • t0 (Obs):\nExtracted t0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
Extract w0/a from given .ms.dat files. Returns w0 as Obs.
\n\n
It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
\n\n
It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
    • \n
  • prefix (str):\nEnsemble prefix
    • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
    • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
    • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
    • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
    • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
    • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
    • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
    • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
    • \n
\n\n
Returns
\n\n
    \n
  • w0 (Obs):\nExtracted w0
    • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
Read the topologial charge based on openQCD gradient flow measurements.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
    • \n
\n\n
Returns
\n\n
    \n
  • result (Obs):\nRead topological charge
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
\n\n
Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
    • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
    • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
    • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
Returns the projection to the topological charge sector defined by target.
\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
Constructs reweighting factors to a specified topological sector.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
    • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
    • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
    • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
    • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
    • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
    • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
    • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
    • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
    • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
    • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
    • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
    • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
\n\n
Parameters
\n\n
    \n
  • path (str):\nThe directory to search for the files in.
    • \n
  • prefix (str):\nThe prefix to match the files against.
    • \n
  • qc (str):\nThe quark combination extension to match the files against.
    • \n
  • corr (str):\nThe correlator to extract data for.
    • \n
  • sep (str, optional):\nThe separator to use when parsing the replika names.
    • \n
  • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
    \n\n
      \n
    • names (List[str]): A list of names to use for the replicas.
      • \n
    • files (List[str]): A list of files to read data from.
      • \n
    • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
      • \n
    • \n
\n\n
Returns
\n\n
    \n
  • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
    • \n
  • or
    • \n
  • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
    • \n
\n\n
Raises
\n\n
    \n
  • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
    • \n
  • IOError: If there is an error reading a file.
    • \n
  • struct.error: If there is an error unpacking binary data.
    • \n
\n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
Write DataFrame including Obs or Corr valued columns to sqlite database.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be written to the database.
    • \n
  • table_name (str):\nName of the table in the database.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
    • \n
  • gz (bool):\nIf True the json strings are gzipped.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
\n\n
Parameters
\n\n
    \n
  • sql (str):\nSQL query to be executed.
    • \n
  • db (str):\nPath to the sqlite database.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
\n\n
Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be dumped to a file.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
    • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
    • \n
\n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
\n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
\n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
    • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tcfg_func=None,\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',\tcfg_func=None,\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/3.12.12/x64/lib/python3.12/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(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()`\nbeta`, `function`  \nbetaincinv()\ninverse, of, the, regularized, incomplete, beta, function
\nbetaincc()`\ncomplement`, `of`, `the`, `regularized`, `incomplete`, `beta`, `function`  \nscipy.stats.beta()\nbeta, 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
betainc(a, b, x) is treated as a two parameter family of functions\nof a single variable x, rather than as a function of three variables.\nThis impacts only the limiting cases a = 0, b = 0, a = inf,\nb = inf.
\n\n
In general
\n\n
$$\\lim_{(a, b) \\rightarrow (a_0, b_0)} \\mathrm{betainc}(a, b, x)$$
\n\n
is treated as a pointwise limit in x. Thus for example,\nbetainc(0, b, 0) equals 0 for b > 0, although it would be\nindeterminate when considering the simultaneous limit (a, x) -> (0+, 0+).
\n\n
This function wraps the ibeta routine from the\nBoost Math C++ library 2.
\n\n
betainc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u26d4
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\n\n
References
\n\n
Examples
\n\n
Let \\( B(a, b) \\) be the beta function.
\n\n
\n
>>> import scipy.special as sc\n
\n
\n\n
The coefficient in terms of gamma is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).
\n\n
\n
>>> sc.betainc(0.2, 3.5, 1.0)\n1.0\n
\n
\n\n
It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function hyp2f1:
\n\n
\n
>>> a, b, x = 1.4, 3.1, 0.5\n>>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))\n0.8148904036225295\n>>> sc.betainc(a, b, x)\n0.8148904036225296\n
\n
\n\n
This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):
\n\n
\n
>>> sc.betainc(2.2, 3.1, 0.4)\n0.49339638807619446\n>>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)\n0.49339638807619446\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/8.17 ↩
    \n
    2. \n\n
  2. \n
    The Boost Developers. \"Boost C++ Libraries\". https://www.boost.org/. ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "
betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
betaln(a, b, out=None)
\n\n
Natural logarithm of absolute value of beta function.
\n\n
Computes ln(abs(beta(a, b))).
\n\n
Parameters
\n\n
    \n
  • a, b (array_like):\nPositive, real-valued parameters
    • \n
  • out (ndarray, optional):\nOptional output array for function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Value of the betaln function
    • \n
\n\n
See Also
\n\n
gamma:  the gamma function
\nbetainc:   the regularized incomplete beta function
\nbeta:  the beta function  
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import betaln, beta\n
\n
\n\n
Verify that, for moderate values of a and b, betaln(a, b)\nis the same as log(beta(a, b)):
\n\n
\n
>>> betaln(3, 4)\n-4.0943445622221\n
\n
\n\n
\n
>>> np.log(beta(3, 4))\n-4.0943445622221\n
\n
\n\n
In the following beta(a, b) underflows to 0, so we can't compute\nthe logarithm of the actual value.
\n\n
\n
>>> a = 400\n>>> b = 900\n>>> beta(a, b)\n0.0\n
\n
\n\n
We can compute the logarithm of beta(a, b) by using betaln:
\n\n
\n
>>> betaln(a, b)\n-804.3069951764146\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "
Polygamma functions.
\n\n
Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\ndigamma function. See [dlmf]_ for details.
\n\n
Parameters
\n\n
    \n
  • n (array_like):\nThe order of the derivative of the digamma function; must be\nintegral
    • \n
  • x (array_like):\nReal valued input
    • \n
\n\n
Returns
\n\n
    \n
  • ndarray: Function results
    • \n
\n\n
See Also
\n\n
digamma  
\n\n
References
\n\n
.. [dlmf] NIST, Digital Library of Mathematical Functions,\n    https://dlmf.nist.gov/5.15
\n\n
Examples
\n\n
\n
>>> from scipy import special\n>>> x = [2, 3, 25.5]\n>>> special.polygamma(1, x)\narray([ 0.64493407,  0.39493407,  0.03999467])\n>>> special.polygamma(0, x) == special.psi(x)\narray([ True,  True,  True], dtype=bool)\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "
psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
psi(z, out=None)
\n\n
The digamma function.
\n\n
The logarithmic derivative of the gamma function evaluated at z.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex argument.
    • \n
  • out (ndarray, optional):\nArray for the computed values of psi.
    • \n
\n\n
Returns
\n\n
    \n
  • digamma (scalar or ndarray):\nComputed values of psi.
    • \n
\n\n
Notes
\n\n
For large values not close to the negative real axis, psi is\ncomputed using the asymptotic series (5.11.2) from 1. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from 2 is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from 3 is\nused first. Note that psi has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using 4, so the\nfunction should maintain full accuracy around the origin.
\n\n
References
\n\n
Examples
\n\n
\n
>>> from scipy.special import psi\n>>> z = 3 + 4j\n>>> psi(z)\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
Verify psi(z) = psi(z + 1) - 1/z:
\n\n
\n
>>> psi(z + 1) - 1/z\n(1.55035981733341+1.0105022091860445j)\n
\n
\n\n
\n
\n
    \n
  1. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    2. \n\n
  2. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    3. \n\n
  3. \n
    NIST Digital Library of Mathematical Functions\nhttps://dlmf.nist.gov/5 ↩
    \n
    4. \n\n
  4. \n
    Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) http://mpmath.org/ ↩
    \n
    5. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "
gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
gamma(z, out=None)
\n\n
gamma function.
\n\n
The gamma function is defined as
\n\n
$$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$
\n\n
for \\( \\Re(z) > 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.
\n\n
Parameters
\n\n
    \n
  • z (array_like):\nReal or complex valued argument
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the gamma function
    • \n
\n\n
Notes
\n\n
The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).
\n\n
The gamma function has poles at non-negative integers and the sign\nof infinity as z approaches each pole depends upon the direction in\nwhich the pole is approached. For this reason, the consistent thing\nis for gamma(z) to return NaN at negative integers, and to return\n-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero\nto signify the direction in which the origin is being approached. This\nis for instance what is recommended for the gamma function in annex F\nentry 9.5.4 of the Iso C 99 standard [isoc99]_.
\n\n
Prior to SciPy version 1.15, scipy.special.gamma(z) returned +inf\nat each pole. This was fixed in version 1.15, but with the following\nconsequence. Expressions where gamma appears in the denominator\nsuch as
\n\n
gamma(u) * gamma(v) / (gamma(w) * gamma(x))
\n\n
no longer evaluate to 0 if the numerator is well defined but there is a\npole in the denominator. Instead such expressions evaluate to NaN. We\nrecommend instead using the function rgamma for the reciprocal gamma\nfunction in such cases. The above expression could for instance be written\nas
\n\n
gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))
\n\n
References
\n\n
.. [dlmf] NIST Digital Library of Mathematical Functions\n          https://dlmf.nist.gov/5.2#E1\n.. [isoc99] https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf
\n\n
Examples
\n\n
\n
>>> import numpy as np\n>>> from scipy.special import gamma, factorial\n
\n
\n\n
\n
>>> gamma([0, 0.5, 1, 5])\narray([         inf,   1.77245385,   1.        ,  24.        ])\n
\n
\n\n
\n
>>> z = 2.5 + 1j\n>>> gamma(z)\n(0.77476210455108352+0.70763120437959293j)\n>>> gamma(z+1), z*gamma(z)  # Recurrence property\n((1.2292740569981171+2.5438401155000685j),\n (1.2292740569981158+2.5438401155000658j))\n
\n
\n\n
\n
>>> gamma(0.5)**2  # gamma(0.5) = sqrt(pi)\n3.1415926535897927\n
\n
\n\n
Plot gamma(x) for real x
\n\n
\n
>>> x = np.linspace(-3.5, 5.5, 2251)\n>>> y = gamma(x)\n
\n
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> plt.plot(x, y, 'b', alpha=0.6, label='gamma(x)')\n>>> k = np.arange(1, 7)\n>>> plt.plot(k, factorial(k-1), 'k*', alpha=0.6,\n...          label='(x-1)!, x = 1, 2, ...')\n>>> plt.xlim(-3.5, 5.5)\n>>> plt.ylim(-10, 25)\n>>> plt.grid()\n>>> plt.xlabel('x')\n>>> plt.legend(loc='lower right')\n>>> plt.show()\n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "
gammaln(x, out=None)
\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()`\nsign`, `of`, `the`, `gamma`, `function`  \nloggamma()\nprincipal, 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
gammaln has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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(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()`\nregularized`, `upper`, `incomplete`, `gamma`, `function`  \ngammaincinv()\ninverse, of, the, regularized, lower, incomplete, gamma, function
\n`gammainccinv()\ninverse,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
gammainc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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(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()`\nregularized`, `lower`, `incomplete`, `gamma`, `function`  \ngammaincinv()\ninverse, of, the, regularized, lower, incomplete, gamma, function
\n`gammainccinv()\ninverse,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
gammaincc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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()`\nModified`, `Bessel`, `function`, `of`, `any`, `order`  \ni0e()\nExponentially, 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
i0 has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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()`\nModified`, `Bessel`, `function`, `of`, `the`, `first`, `kind`  \ni1e()\nExponentially, 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
i1 has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\n\n
References
\n\n
Examples
\n\n
Calculate the function at one point:
\n\n
\n
>>> from scipy.special import i1\n>>> i1(1.)\n0.5651591039924851\n
\n
\n\n
Calculate the function at several points:
\n\n
\n
>>> import numpy as np\n>>> i1(np.array([-2., 0., 6.]))\narray([-1.59063685,  0.        , 61.34193678])\n
\n
\n\n
Plot the function between -10 and 10.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-10., 10., 1000)\n>>> y = i1(x)\n>>> ax.plot(x, y)\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Cephes Mathematical Functions Library,\nhttp://www.netlib.org/cephes/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "
iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
iv(v, z, out=None)
\n\n
Modified Bessel function of the first kind of real order.
\n\n
Parameters
\n\n
    \n
  • v (array_like):\nOrder. If z is of real type and negative, v must be integer\nvalued.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the modified Bessel function.
    • \n
\n\n
See Also
\n\n
ive:  This function with leading exponential behavior stripped off.
\ni0:  Faster version of this function for order 0.
\ni1:  Faster version of this function for order 1.  
\n\n
Notes
\n\n
For real z and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method 1.  For larger orders, uniform asymptotic\nexpansions are applied.
\n\n
For complex z and positive v, the AMOS 2 zbesi routine is\ncalled. It uses a power series for small z, the asymptotic expansion\nfor large abs(z), the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
References
\n\n
Examples
\n\n
Evaluate the function of order 0 at one point.
\n\n
\n
>>> from scipy.special import iv\n>>> iv(0, 1.)\n1.2660658777520084\n
\n
\n\n
Evaluate the function at one point for different orders.
\n\n
\n
>>> iv(0, 1.), iv(1, 1.), iv(1.5, 1.)\n(1.2660658777520084, 0.565159103992485, 0.2935253263474798)\n
\n
\n\n
The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> iv([0, 1, 1.5], 1.)\narray([1.26606588, 0.5651591 , 0.29352533])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> import numpy as np\n>>> points = np.array([-2., 0., 3.])\n>>> iv(0, points)\narray([2.2795853 , 1.        , 4.88079259])\n
\n
\n\n
If z is an array, the order parameter v must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:
\n\n
\n
>>> orders = np.array([[0], [1]])\n>>> orders.shape\n(2, 1)\n
\n
\n\n
\n
>>> iv(orders, points)\narray([[ 2.2795853 ,  1.        ,  4.88079259],\n       [-1.59063685,  0.        ,  3.95337022]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> import matplotlib.pyplot as plt\n>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, iv(i, x), label=f'$I_{i!r}$')\n>>> ax.legend()\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Temme, Journal of Computational Physics, vol 21, 343 (1976) ↩
    \n
    2. \n\n
  2. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    3. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "
ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
\n\n
ive(v, z, out=None)
\n\n
Exponentially scaled modified Bessel function of the first kind.
\n\n
Defined as::
\n\n
ive(v, z) = iv(v, z) * exp(-abs(z.real))\n
\n\n
For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind iv.
\n\n
Parameters
\n\n
    \n
  • v (array_like of float):\nOrder.
    • \n
  • z (array_like of float or complex):\nArgument.
    • \n
  • out (ndarray, optional):\nOptional output array for the function values
    • \n
\n\n
Returns
\n\n
    \n
  • scalar or ndarray: Values of the exponentially scaled modified Bessel function.
    • \n
\n\n
See Also
\n\n
iv:  Modified Bessel function of the first kind
\ni0e:  Faster implementation of this function for order 0
\ni1e:  Faster implementation of this function for order 1  
\n\n
Notes
\n\n
For positive v, the AMOS 1 zbesi routine is called. It uses a\npower series for small z, the asymptotic expansion for large\nabs(z), the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.
\n\n
The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,
\n\n
$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$
\n\n
(valid when the real part of z is positive).  For negative v, the\nformula
\n\n
$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$
\n\n
is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine zbesk.
\n\n
ive is useful for large arguments z: for these, iv easily overflows,\nwhile ive does not due to the exponential scaling.
\n\n
References
\n\n
Examples
\n\n
In the following example iv returns infinity whereas ive still returns\na finite number.
\n\n
\n
>>> from scipy.special import iv, ive\n>>> import numpy as np\n>>> import matplotlib.pyplot as plt\n>>> iv(3, 1000.), ive(3, 1000.)\n(inf, 0.01256056218254712)\n
\n
\n\n
Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the v parameter:
\n\n
\n
>>> ive([0, 1, 1.5], 1.)\narray([0.46575961, 0.20791042, 0.10798193])\n
\n
\n\n
Evaluate the function at several points for order 0 by providing an\narray for z.
\n\n
\n
>>> points = np.array([-2., 0., 3.])\n>>> ive(0, points)\narray([0.30850832, 1.        , 0.24300035])\n
\n
\n\n
Evaluate the function at several points for different orders by\nproviding arrays for both v for z. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:
\n\n
\n
>>> ive([[0], [1], [2]], points)\narray([[ 0.30850832,  1.        ,  0.24300035],\n       [-0.21526929,  0.        ,  0.19682671],\n       [ 0.09323903,  0.        ,  0.11178255]])\n
\n
\n\n
Plot the functions of order 0 to 3 from -5 to 5.
\n\n
\n
>>> fig, ax = plt.subplots()\n>>> x = np.linspace(-5., 5., 1000)\n>>> for i in range(4):\n...     ax.plot(x, ive(i, x), label=fr'$I_{i!r}(z)\\cdot e^{{-|z|}}$')\n>>> ax.legend()\n>>> ax.set_xlabel(r"$z$")\n>>> plt.show()\n
\n
\n\n
\n
\n
    \n
  1. \n
    Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\nhttp://netlib.org/amos/ ↩
    \n
    2. \n
\n
\n", "signature": "(*args, **kwargs):", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "
erf(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\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
erf has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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\n
Notes
\n\n
erfc has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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\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
logit has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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)
\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\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
expit has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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`\n..`  \nnumpy.logaddexp2\n..  
\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
logsumexp has experimental support for Python Array API Standard compatible\nbackends in addition to NumPy. Please consider testing these features\nby setting an environment variable SCIPY_ARRAY_API=1 and providing\nCuPy, PyTorch, JAX, or Dask arrays as array arguments. The following\ncombinations of backend and device (or other capability) are supported.
\n\n
====================  ====================  ====================\nLibrary               CPU                   GPU\n====================  ====================  ====================\nNumPy                 \u2705                     n/a
\nCuPy                  n/a                   \u2705
\nPyTorch               \u2705                     \u2705
\nJAX                   \u2705                     \u2705
\nDask                  \u2705                     n/a
\n====================  ====================  ====================
\n\n
See :ref:dev-arrayapi for more information.
\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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