diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html index d933ff5d..d7796d68 100644 --- a/docs/pyerrors/obs.html +++ b/docs/pyerrors/obs.html @@ -1369,715 +1369,710 @@ 1039 return np.vectorize(lambda o: o.gm(**kwargs))(x) 1040 1041 -1042def gm(x, **kwargs): -1043 """Short version of the vectorized gamma_method. +1042gm = gamma_method +1043 1044 -1045 See docstring of pe.Obs.gamma_method for details -1046 """ -1047 return gamma_method(x, **kwargs) -1048 -1049 -1050def _format_uncertainty(value, dvalue, significance=2): -1051 """Creates a string of a value and its error in paranthesis notation, e.g., 13.02(45)""" -1052 if dvalue == 0.0 or (not np.isfinite(dvalue)): -1053 return str(value) -1054 if not isinstance(significance, int): -1055 raise TypeError("significance needs to be an integer.") -1056 if significance < 1: -1057 raise ValueError("significance needs to be larger than zero.") -1058 fexp = np.floor(np.log10(dvalue)) -1059 if fexp < 0.0: -1060 return '{:{form}}({:1.0f})'.format(value, dvalue * 10 ** (-fexp + significance - 1), form='.' + str(-int(fexp) + significance - 1) + 'f') -1061 elif fexp == 0.0: -1062 return f"{value:.{significance - 1}f}({dvalue:1.{significance - 1}f})" -1063 else: -1064 return f"{value:.{max(0, int(significance - fexp - 1))}f}({dvalue:2.{max(0, int(significance - fexp - 1))}f})" -1065 +1045def _format_uncertainty(value, dvalue, significance=2): +1046 """Creates a string of a value and its error in paranthesis notation, e.g., 13.02(45)""" +1047 if dvalue == 0.0 or (not np.isfinite(dvalue)): +1048 return str(value) +1049 if not isinstance(significance, int): +1050 raise TypeError("significance needs to be an integer.") +1051 if significance < 1: +1052 raise ValueError("significance needs to be larger than zero.") +1053 fexp = np.floor(np.log10(dvalue)) +1054 if fexp < 0.0: +1055 return '{:{form}}({:1.0f})'.format(value, dvalue * 10 ** (-fexp + significance - 1), form='.' + str(-int(fexp) + significance - 1) + 'f') +1056 elif fexp == 0.0: +1057 return f"{value:.{significance - 1}f}({dvalue:1.{significance - 1}f})" +1058 else: +1059 return f"{value:.{max(0, int(significance - fexp - 1))}f}({dvalue:2.{max(0, int(significance - fexp - 1))}f})" +1060 +1061 +1062def _expand_deltas(deltas, idx, shape, gapsize): +1063 """Expand deltas defined on idx to a regular range with spacing gapsize between two +1064 configurations and where holes are filled by 0. +1065 If idx is of type range, the deltas are not changed if the idx.step == gapsize. 1066 -1067def _expand_deltas(deltas, idx, shape, gapsize): -1068 """Expand deltas defined on idx to a regular range with spacing gapsize between two -1069 configurations and where holes are filled by 0. -1070 If idx is of type range, the deltas are not changed if the idx.step == gapsize. -1071 -1072 Parameters -1073 ---------- -1074 deltas : list -1075 List of fluctuations -1076 idx : list -1077 List or range of configs on which the deltas are defined, has to be sorted in ascending order. -1078 shape : int -1079 Number of configs in idx. -1080 gapsize : int -1081 The target distance between two configurations. If longer distances -1082 are found in idx, the data is expanded. -1083 """ -1084 if isinstance(idx, range): -1085 if (idx.step == gapsize): -1086 return deltas -1087 ret = np.zeros((idx[-1] - idx[0] + gapsize) // gapsize) -1088 for i in range(shape): -1089 ret[(idx[i] - idx[0]) // gapsize] = deltas[i] -1090 return ret -1091 -1092 -1093def _merge_idx(idl): -1094 """Returns the union of all lists in idl as range or sorted list -1095 -1096 Parameters -1097 ---------- -1098 idl : list -1099 List of lists or ranges. -1100 """ +1067 Parameters +1068 ---------- +1069 deltas : list +1070 List of fluctuations +1071 idx : list +1072 List or range of configs on which the deltas are defined, has to be sorted in ascending order. +1073 shape : int +1074 Number of configs in idx. +1075 gapsize : int +1076 The target distance between two configurations. If longer distances +1077 are found in idx, the data is expanded. +1078 """ +1079 if isinstance(idx, range): +1080 if (idx.step == gapsize): +1081 return deltas +1082 ret = np.zeros((idx[-1] - idx[0] + gapsize) // gapsize) +1083 for i in range(shape): +1084 ret[(idx[i] - idx[0]) // gapsize] = deltas[i] +1085 return ret +1086 +1087 +1088def _merge_idx(idl): +1089 """Returns the union of all lists in idl as range or sorted list +1090 +1091 Parameters +1092 ---------- +1093 idl : list +1094 List of lists or ranges. +1095 """ +1096 +1097 if _check_lists_equal(idl): +1098 return idl[0] +1099 +1100 idunion = sorted(set().union(*idl)) 1101 -1102 if _check_lists_equal(idl): -1103 return idl[0] -1104 -1105 idunion = sorted(set().union(*idl)) -1106 -1107 # Check whether idunion can be expressed as range -1108 idrange = range(idunion[0], idunion[-1] + 1, idunion[1] - idunion[0]) -1109 idtest = [list(idrange), idunion] -1110 if _check_lists_equal(idtest): -1111 return idrange -1112 -1113 return idunion -1114 -1115 -1116def _intersection_idx(idl): -1117 """Returns the intersection of all lists in idl as range or sorted list -1118 -1119 Parameters -1120 ---------- -1121 idl : list -1122 List of lists or ranges. -1123 """ +1102 # Check whether idunion can be expressed as range +1103 idrange = range(idunion[0], idunion[-1] + 1, idunion[1] - idunion[0]) +1104 idtest = [list(idrange), idunion] +1105 if _check_lists_equal(idtest): +1106 return idrange +1107 +1108 return idunion +1109 +1110 +1111def _intersection_idx(idl): +1112 """Returns the intersection of all lists in idl as range or sorted list +1113 +1114 Parameters +1115 ---------- +1116 idl : list +1117 List of lists or ranges. +1118 """ +1119 +1120 if _check_lists_equal(idl): +1121 return idl[0] +1122 +1123 idinter = sorted(set.intersection(*[set(o) for o in idl])) 1124 -1125 if _check_lists_equal(idl): -1126 return idl[0] -1127 -1128 idinter = sorted(set.intersection(*[set(o) for o in idl])) -1129 -1130 # Check whether idinter can be expressed as range -1131 try: -1132 idrange = range(idinter[0], idinter[-1] + 1, idinter[1] - idinter[0]) -1133 idtest = [list(idrange), idinter] -1134 if _check_lists_equal(idtest): -1135 return idrange -1136 except IndexError: -1137 pass -1138 -1139 return idinter -1140 +1125 # Check whether idinter can be expressed as range +1126 try: +1127 idrange = range(idinter[0], idinter[-1] + 1, idinter[1] - idinter[0]) +1128 idtest = [list(idrange), idinter] +1129 if _check_lists_equal(idtest): +1130 return idrange +1131 except IndexError: +1132 pass +1133 +1134 return idinter +1135 +1136 +1137def _expand_deltas_for_merge(deltas, idx, shape, new_idx): +1138 """Expand deltas defined on idx to the list of configs that is defined by new_idx. +1139 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest +1140 common divisor of the step sizes is used as new step size. 1141 -1142def _expand_deltas_for_merge(deltas, idx, shape, new_idx): -1143 """Expand deltas defined on idx to the list of configs that is defined by new_idx. -1144 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest -1145 common divisor of the step sizes is used as new step size. -1146 -1147 Parameters -1148 ---------- -1149 deltas : list -1150 List of fluctuations -1151 idx : list -1152 List or range of configs on which the deltas are defined. -1153 Has to be a subset of new_idx and has to be sorted in ascending order. -1154 shape : list -1155 Number of configs in idx. -1156 new_idx : list -1157 List of configs that defines the new range, has to be sorted in ascending order. -1158 """ -1159 -1160 if type(idx) is range and type(new_idx) is range: -1161 if idx == new_idx: -1162 return deltas -1163 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) -1164 for i in range(shape): -1165 ret[idx[i] - new_idx[0]] = deltas[i] -1166 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) * len(new_idx) / len(idx) -1167 -1168 -1169def derived_observable(func, data, array_mode=False, **kwargs): -1170 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. -1171 -1172 Parameters -1173 ---------- -1174 func : object -1175 arbitrary function of the form func(data, **kwargs). For the -1176 automatic differentiation to work, all numpy functions have to have -1177 the autograd wrapper (use 'import autograd.numpy as anp'). -1178 data : list -1179 list of Obs, e.g. [obs1, obs2, obs3]. -1180 num_grad : bool -1181 if True, numerical derivatives are used instead of autograd -1182 (default False). To control the numerical differentiation the -1183 kwargs of numdifftools.step_generators.MaxStepGenerator -1184 can be used. -1185 man_grad : list -1186 manually supply a list or an array which contains the jacobian -1187 of func. Use cautiously, supplying the wrong derivative will -1188 not be intercepted. +1142 Parameters +1143 ---------- +1144 deltas : list +1145 List of fluctuations +1146 idx : list +1147 List or range of configs on which the deltas are defined. +1148 Has to be a subset of new_idx and has to be sorted in ascending order. +1149 shape : list +1150 Number of configs in idx. +1151 new_idx : list +1152 List of configs that defines the new range, has to be sorted in ascending order. +1153 """ +1154 +1155 if type(idx) is range and type(new_idx) is range: +1156 if idx == new_idx: +1157 return deltas +1158 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) +1159 for i in range(shape): +1160 ret[idx[i] - new_idx[0]] = deltas[i] +1161 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) * len(new_idx) / len(idx) +1162 +1163 +1164def derived_observable(func, data, array_mode=False, **kwargs): +1165 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. +1166 +1167 Parameters +1168 ---------- +1169 func : object +1170 arbitrary function of the form func(data, **kwargs). For the +1171 automatic differentiation to work, all numpy functions have to have +1172 the autograd wrapper (use 'import autograd.numpy as anp'). +1173 data : list +1174 list of Obs, e.g. [obs1, obs2, obs3]. +1175 num_grad : bool +1176 if True, numerical derivatives are used instead of autograd +1177 (default False). To control the numerical differentiation the +1178 kwargs of numdifftools.step_generators.MaxStepGenerator +1179 can be used. +1180 man_grad : list +1181 manually supply a list or an array which contains the jacobian +1182 of func. Use cautiously, supplying the wrong derivative will +1183 not be intercepted. +1184 +1185 Notes +1186 ----- +1187 For simple mathematical operations it can be practical to use anonymous +1188 functions. For the ratio of two observables one can e.g. use 1189 -1190 Notes -1191 ----- -1192 For simple mathematical operations it can be practical to use anonymous -1193 functions. For the ratio of two observables one can e.g. use -1194 -1195 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) -1196 """ -1197 -1198 data = np.asarray(data) -1199 raveled_data = data.ravel() -1200 -1201 # Workaround for matrix operations containing non Obs data -1202 if not all(isinstance(x, Obs) for x in raveled_data): -1203 for i in range(len(raveled_data)): -1204 if isinstance(raveled_data[i], (int, float)): -1205 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") -1206 -1207 allcov = {} -1208 for o in raveled_data: -1209 for name in o.cov_names: -1210 if name in allcov: -1211 if not np.allclose(allcov[name], o.covobs[name].cov): -1212 raise Exception('Inconsistent covariance matrices for %s!' % (name)) -1213 else: -1214 allcov[name] = o.covobs[name].cov +1190 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) +1191 """ +1192 +1193 data = np.asarray(data) +1194 raveled_data = data.ravel() +1195 +1196 # Workaround for matrix operations containing non Obs data +1197 if not all(isinstance(x, Obs) for x in raveled_data): +1198 for i in range(len(raveled_data)): +1199 if isinstance(raveled_data[i], (int, float)): +1200 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") +1201 +1202 allcov = {} +1203 for o in raveled_data: +1204 for name in o.cov_names: +1205 if name in allcov: +1206 if not np.allclose(allcov[name], o.covobs[name].cov): +1207 raise Exception('Inconsistent covariance matrices for %s!' % (name)) +1208 else: +1209 allcov[name] = o.covobs[name].cov +1210 +1211 n_obs = len(raveled_data) +1212 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) +1213 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) +1214 new_sample_names = sorted(set(new_names) - set(new_cov_names)) 1215 -1216 n_obs = len(raveled_data) -1217 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) -1218 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) -1219 new_sample_names = sorted(set(new_names) - set(new_cov_names)) -1220 -1221 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 +1216 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 +1217 +1218 if data.ndim == 1: +1219 values = np.array([o.value for o in data]) +1220 else: +1221 values = np.vectorize(lambda x: x.value)(data) 1222 -1223 if data.ndim == 1: -1224 values = np.array([o.value for o in data]) -1225 else: -1226 values = np.vectorize(lambda x: x.value)(data) -1227 -1228 new_values = func(values, **kwargs) -1229 -1230 multi = int(isinstance(new_values, np.ndarray)) -1231 -1232 new_r_values = {} -1233 new_idl_d = {} -1234 for name in new_sample_names: -1235 idl = [] -1236 tmp_values = np.zeros(n_obs) -1237 for i, item in enumerate(raveled_data): -1238 tmp_values[i] = item.r_values.get(name, item.value) -1239 tmp_idl = item.idl.get(name) -1240 if tmp_idl is not None: -1241 idl.append(tmp_idl) -1242 if multi > 0: -1243 tmp_values = np.array(tmp_values).reshape(data.shape) -1244 new_r_values[name] = func(tmp_values, **kwargs) -1245 new_idl_d[name] = _merge_idx(idl) -1246 -1247 if 'man_grad' in kwargs: -1248 deriv = np.asarray(kwargs.get('man_grad')) -1249 if new_values.shape + data.shape != deriv.shape: -1250 raise Exception('Manual derivative does not have correct shape.') -1251 elif kwargs.get('num_grad') is True: -1252 if multi > 0: -1253 raise Exception('Multi mode currently not supported for numerical derivative') -1254 options = { -1255 'base_step': 0.1, -1256 'step_ratio': 2.5} -1257 for key in options.keys(): -1258 kwarg = kwargs.get(key) -1259 if kwarg is not None: -1260 options[key] = kwarg -1261 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) -1262 if tmp_df.size == 1: -1263 deriv = np.array([tmp_df.real]) -1264 else: -1265 deriv = tmp_df.real -1266 else: -1267 deriv = jacobian(func)(values, **kwargs) -1268 -1269 final_result = np.zeros(new_values.shape, dtype=object) -1270 -1271 if array_mode is True: -1272 -1273 class _Zero_grad(): -1274 def __init__(self, N): -1275 self.grad = np.zeros((N, 1)) -1276 -1277 new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x])) -1278 d_extracted = {} -1279 g_extracted = {} -1280 for name in new_sample_names: -1281 d_extracted[name] = [] -1282 ens_length = len(new_idl_d[name]) +1223 new_values = func(values, **kwargs) +1224 +1225 multi = int(isinstance(new_values, np.ndarray)) +1226 +1227 new_r_values = {} +1228 new_idl_d = {} +1229 for name in new_sample_names: +1230 idl = [] +1231 tmp_values = np.zeros(n_obs) +1232 for i, item in enumerate(raveled_data): +1233 tmp_values[i] = item.r_values.get(name, item.value) +1234 tmp_idl = item.idl.get(name) +1235 if tmp_idl is not None: +1236 idl.append(tmp_idl) +1237 if multi > 0: +1238 tmp_values = np.array(tmp_values).reshape(data.shape) +1239 new_r_values[name] = func(tmp_values, **kwargs) +1240 new_idl_d[name] = _merge_idx(idl) +1241 +1242 if 'man_grad' in kwargs: +1243 deriv = np.asarray(kwargs.get('man_grad')) +1244 if new_values.shape + data.shape != deriv.shape: +1245 raise Exception('Manual derivative does not have correct shape.') +1246 elif kwargs.get('num_grad') is True: +1247 if multi > 0: +1248 raise Exception('Multi mode currently not supported for numerical derivative') +1249 options = { +1250 'base_step': 0.1, +1251 'step_ratio': 2.5} +1252 for key in options.keys(): +1253 kwarg = kwargs.get(key) +1254 if kwarg is not None: +1255 options[key] = kwarg +1256 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) +1257 if tmp_df.size == 1: +1258 deriv = np.array([tmp_df.real]) +1259 else: +1260 deriv = tmp_df.real +1261 else: +1262 deriv = jacobian(func)(values, **kwargs) +1263 +1264 final_result = np.zeros(new_values.shape, dtype=object) +1265 +1266 if array_mode is True: +1267 +1268 class _Zero_grad(): +1269 def __init__(self, N): +1270 self.grad = np.zeros((N, 1)) +1271 +1272 new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x])) +1273 d_extracted = {} +1274 g_extracted = {} +1275 for name in new_sample_names: +1276 d_extracted[name] = [] +1277 ens_length = len(new_idl_d[name]) +1278 for i_dat, dat in enumerate(data): +1279 d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, ))) +1280 for name in new_cov_names: +1281 g_extracted[name] = [] +1282 zero_grad = _Zero_grad(new_covobs_lengths[name]) 1283 for i_dat, dat in enumerate(data): -1284 d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, ))) -1285 for name in new_cov_names: -1286 g_extracted[name] = [] -1287 zero_grad = _Zero_grad(new_covobs_lengths[name]) -1288 for i_dat, dat in enumerate(data): -1289 g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1))) -1290 -1291 for i_val, new_val in np.ndenumerate(new_values): -1292 new_deltas = {} -1293 new_grad = {} -1294 if array_mode is True: -1295 for name in new_sample_names: -1296 ens_length = d_extracted[name][0].shape[-1] -1297 new_deltas[name] = np.zeros(ens_length) -1298 for i_dat, dat in enumerate(d_extracted[name]): -1299 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1300 for name in new_cov_names: -1301 new_grad[name] = 0 -1302 for i_dat, dat in enumerate(g_extracted[name]): -1303 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1304 else: -1305 for j_obs, obs in np.ndenumerate(data): -1306 for name in obs.names: -1307 if name in obs.cov_names: -1308 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad -1309 else: -1310 new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name]) -1311 -1312 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} -1313 -1314 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): -1315 raise Exception('The same name has been used for deltas and covobs!') -1316 new_samples = [] -1317 new_means = [] -1318 new_idl = [] -1319 new_names_obs = [] -1320 for name in new_names: -1321 if name not in new_covobs: -1322 new_samples.append(new_deltas[name]) -1323 new_idl.append(new_idl_d[name]) -1324 new_means.append(new_r_values[name][i_val]) -1325 new_names_obs.append(name) -1326 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) -1327 for name in new_covobs: -1328 final_result[i_val].names.append(name) -1329 final_result[i_val]._covobs = new_covobs -1330 final_result[i_val]._value = new_val -1331 final_result[i_val].reweighted = reweighted +1284 g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1))) +1285 +1286 for i_val, new_val in np.ndenumerate(new_values): +1287 new_deltas = {} +1288 new_grad = {} +1289 if array_mode is True: +1290 for name in new_sample_names: +1291 ens_length = d_extracted[name][0].shape[-1] +1292 new_deltas[name] = np.zeros(ens_length) +1293 for i_dat, dat in enumerate(d_extracted[name]): +1294 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1295 for name in new_cov_names: +1296 new_grad[name] = 0 +1297 for i_dat, dat in enumerate(g_extracted[name]): +1298 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1299 else: +1300 for j_obs, obs in np.ndenumerate(data): +1301 for name in obs.names: +1302 if name in obs.cov_names: +1303 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad +1304 else: +1305 new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name]) +1306 +1307 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} +1308 +1309 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): +1310 raise Exception('The same name has been used for deltas and covobs!') +1311 new_samples = [] +1312 new_means = [] +1313 new_idl = [] +1314 new_names_obs = [] +1315 for name in new_names: +1316 if name not in new_covobs: +1317 new_samples.append(new_deltas[name]) +1318 new_idl.append(new_idl_d[name]) +1319 new_means.append(new_r_values[name][i_val]) +1320 new_names_obs.append(name) +1321 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) +1322 for name in new_covobs: +1323 final_result[i_val].names.append(name) +1324 final_result[i_val]._covobs = new_covobs +1325 final_result[i_val]._value = new_val +1326 final_result[i_val].reweighted = reweighted +1327 +1328 if multi == 0: +1329 final_result = final_result.item() +1330 +1331 return final_result 1332 -1333 if multi == 0: -1334 final_result = final_result.item() -1335 -1336 return final_result -1337 -1338 -1339def _reduce_deltas(deltas, idx_old, idx_new): -1340 """Extract deltas defined on idx_old on all configs of idx_new. -1341 -1342 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they -1343 are ordered in an ascending order. -1344 -1345 Parameters -1346 ---------- -1347 deltas : list -1348 List of fluctuations -1349 idx_old : list -1350 List or range of configs on which the deltas are defined -1351 idx_new : list -1352 List of configs for which we want to extract the deltas. -1353 Has to be a subset of idx_old. -1354 """ -1355 if not len(deltas) == len(idx_old): -1356 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) -1357 if type(idx_old) is range and type(idx_new) is range: -1358 if idx_old == idx_new: -1359 return deltas -1360 if _check_lists_equal([idx_old, idx_new]): -1361 return deltas -1362 indices = np.intersect1d(idx_old, idx_new, assume_unique=True, return_indices=True)[1] -1363 if len(indices) < len(idx_new): -1364 raise Exception('Error in _reduce_deltas: Config of idx_new not in idx_old') -1365 return np.array(deltas)[indices] -1366 -1367 -1368def reweight(weight, obs, **kwargs): -1369 """Reweight a list of observables. -1370 -1371 Parameters -1372 ---------- -1373 weight : Obs -1374 Reweighting factor. An Observable that has to be defined on a superset of the -1375 configurations in obs[i].idl for all i. -1376 obs : list -1377 list of Obs, e.g. [obs1, obs2, obs3]. -1378 all_configs : bool -1379 if True, the reweighted observables are normalized by the average of -1380 the reweighting factor on all configurations in weight.idl and not -1381 on the configurations in obs[i].idl. Default False. -1382 """ -1383 result = [] -1384 for i in range(len(obs)): -1385 if len(obs[i].cov_names): -1386 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') -1387 if not set(obs[i].names).issubset(weight.names): -1388 raise Exception('Error: Ensembles do not fit') -1389 for name in obs[i].names: -1390 if not set(obs[i].idl[name]).issubset(weight.idl[name]): -1391 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) -1392 new_samples = [] -1393 w_deltas = {} -1394 for name in sorted(obs[i].names): -1395 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) -1396 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) -1397 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) +1333 +1334def _reduce_deltas(deltas, idx_old, idx_new): +1335 """Extract deltas defined on idx_old on all configs of idx_new. +1336 +1337 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they +1338 are ordered in an ascending order. +1339 +1340 Parameters +1341 ---------- +1342 deltas : list +1343 List of fluctuations +1344 idx_old : list +1345 List or range of configs on which the deltas are defined +1346 idx_new : list +1347 List of configs for which we want to extract the deltas. +1348 Has to be a subset of idx_old. +1349 """ +1350 if not len(deltas) == len(idx_old): +1351 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) +1352 if type(idx_old) is range and type(idx_new) is range: +1353 if idx_old == idx_new: +1354 return deltas +1355 if _check_lists_equal([idx_old, idx_new]): +1356 return deltas +1357 indices = np.intersect1d(idx_old, idx_new, assume_unique=True, return_indices=True)[1] +1358 if len(indices) < len(idx_new): +1359 raise Exception('Error in _reduce_deltas: Config of idx_new not in idx_old') +1360 return np.array(deltas)[indices] +1361 +1362 +1363def reweight(weight, obs, **kwargs): +1364 """Reweight a list of observables. +1365 +1366 Parameters +1367 ---------- +1368 weight : Obs +1369 Reweighting factor. An Observable that has to be defined on a superset of the +1370 configurations in obs[i].idl for all i. +1371 obs : list +1372 list of Obs, e.g. [obs1, obs2, obs3]. +1373 all_configs : bool +1374 if True, the reweighted observables are normalized by the average of +1375 the reweighting factor on all configurations in weight.idl and not +1376 on the configurations in obs[i].idl. Default False. +1377 """ +1378 result = [] +1379 for i in range(len(obs)): +1380 if len(obs[i].cov_names): +1381 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') +1382 if not set(obs[i].names).issubset(weight.names): +1383 raise Exception('Error: Ensembles do not fit') +1384 for name in obs[i].names: +1385 if not set(obs[i].idl[name]).issubset(weight.idl[name]): +1386 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) +1387 new_samples = [] +1388 w_deltas = {} +1389 for name in sorted(obs[i].names): +1390 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) +1391 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) +1392 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) +1393 +1394 if kwargs.get('all_configs'): +1395 new_weight = weight +1396 else: +1397 new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) 1398 -1399 if kwargs.get('all_configs'): -1400 new_weight = weight -1401 else: -1402 new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) +1399 result.append(tmp_obs / new_weight) +1400 result[-1].reweighted = True +1401 +1402 return result 1403 -1404 result.append(tmp_obs / new_weight) -1405 result[-1].reweighted = True -1406 -1407 return result -1408 -1409 -1410def correlate(obs_a, obs_b): -1411 """Correlate two observables. -1412 -1413 Parameters -1414 ---------- -1415 obs_a : Obs -1416 First observable -1417 obs_b : Obs -1418 Second observable -1419 -1420 Notes -1421 ----- -1422 Keep in mind to only correlate primary observables which have not been reweighted -1423 yet. The reweighting has to be applied after correlating the observables. -1424 Currently only works if ensembles are identical (this is not strictly necessary). -1425 """ -1426 -1427 if sorted(obs_a.names) != sorted(obs_b.names): -1428 raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}") -1429 if len(obs_a.cov_names) or len(obs_b.cov_names): -1430 raise Exception('Error: Not possible to correlate Obs that contain covobs!') -1431 for name in obs_a.names: -1432 if obs_a.shape[name] != obs_b.shape[name]: -1433 raise Exception('Shapes of ensemble', name, 'do not fit') -1434 if obs_a.idl[name] != obs_b.idl[name]: -1435 raise Exception('idl of ensemble', name, 'do not fit') +1404 +1405def correlate(obs_a, obs_b): +1406 """Correlate two observables. +1407 +1408 Parameters +1409 ---------- +1410 obs_a : Obs +1411 First observable +1412 obs_b : Obs +1413 Second observable +1414 +1415 Notes +1416 ----- +1417 Keep in mind to only correlate primary observables which have not been reweighted +1418 yet. The reweighting has to be applied after correlating the observables. +1419 Currently only works if ensembles are identical (this is not strictly necessary). +1420 """ +1421 +1422 if sorted(obs_a.names) != sorted(obs_b.names): +1423 raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}") +1424 if len(obs_a.cov_names) or len(obs_b.cov_names): +1425 raise Exception('Error: Not possible to correlate Obs that contain covobs!') +1426 for name in obs_a.names: +1427 if obs_a.shape[name] != obs_b.shape[name]: +1428 raise Exception('Shapes of ensemble', name, 'do not fit') +1429 if obs_a.idl[name] != obs_b.idl[name]: +1430 raise Exception('idl of ensemble', name, 'do not fit') +1431 +1432 if obs_a.reweighted is True: +1433 warnings.warn("The first observable is already reweighted.", RuntimeWarning) +1434 if obs_b.reweighted is True: +1435 warnings.warn("The second observable is already reweighted.", RuntimeWarning) 1436 -1437 if obs_a.reweighted is True: -1438 warnings.warn("The first observable is already reweighted.", RuntimeWarning) -1439 if obs_b.reweighted is True: -1440 warnings.warn("The second observable is already reweighted.", RuntimeWarning) -1441 -1442 new_samples = [] -1443 new_idl = [] -1444 for name in sorted(obs_a.names): -1445 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) -1446 new_idl.append(obs_a.idl[name]) +1437 new_samples = [] +1438 new_idl = [] +1439 for name in sorted(obs_a.names): +1440 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) +1441 new_idl.append(obs_a.idl[name]) +1442 +1443 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) +1444 o.reweighted = obs_a.reweighted or obs_b.reweighted +1445 return o +1446 1447 -1448 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) -1449 o.reweighted = obs_a.reweighted or obs_b.reweighted -1450 return o -1451 -1452 -1453def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): -1454 r'''Calculates the error covariance matrix of a set of observables. +1448def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): +1449 r'''Calculates the error covariance matrix of a set of observables. +1450 +1451 WARNING: This function should be used with care, especially for observables with support on multiple +1452 ensembles with differing autocorrelations. See the notes below for details. +1453 +1454 The gamma method has to be applied first to all observables. 1455 -1456 WARNING: This function should be used with care, especially for observables with support on multiple -1457 ensembles with differing autocorrelations. See the notes below for details. -1458 -1459 The gamma method has to be applied first to all observables. -1460 -1461 Parameters -1462 ---------- -1463 obs : list or numpy.ndarray -1464 List or one dimensional array of Obs -1465 visualize : bool -1466 If True plots the corresponding normalized correlation matrix (default False). -1467 correlation : bool -1468 If True the correlation matrix instead of the error covariance matrix is returned (default False). -1469 smooth : None or int -1470 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue -1471 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the -1472 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely -1473 small ones. -1474 -1475 Notes -1476 ----- -1477 The error covariance is defined such that it agrees with the squared standard error for two identical observables -1478 $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$ -1479 in the absence of autocorrelation. -1480 The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite -1481 $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. -1482 For observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements. -1483 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ -1484 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). -1485 ''' -1486 -1487 length = len(obs) -1488 -1489 max_samples = np.max([o.N for o in obs]) -1490 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: -1491 warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning) -1492 -1493 cov = np.zeros((length, length)) -1494 for i in range(length): -1495 for j in range(i, length): -1496 cov[i, j] = _covariance_element(obs[i], obs[j]) -1497 cov = cov + cov.T - np.diag(np.diag(cov)) +1456 Parameters +1457 ---------- +1458 obs : list or numpy.ndarray +1459 List or one dimensional array of Obs +1460 visualize : bool +1461 If True plots the corresponding normalized correlation matrix (default False). +1462 correlation : bool +1463 If True the correlation matrix instead of the error covariance matrix is returned (default False). +1464 smooth : None or int +1465 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue +1466 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the +1467 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely +1468 small ones. +1469 +1470 Notes +1471 ----- +1472 The error covariance is defined such that it agrees with the squared standard error for two identical observables +1473 $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$ +1474 in the absence of autocorrelation. +1475 The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite +1476 $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. +1477 For observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements. +1478 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ +1479 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). +1480 ''' +1481 +1482 length = len(obs) +1483 +1484 max_samples = np.max([o.N for o in obs]) +1485 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: +1486 warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning) +1487 +1488 cov = np.zeros((length, length)) +1489 for i in range(length): +1490 for j in range(i, length): +1491 cov[i, j] = _covariance_element(obs[i], obs[j]) +1492 cov = cov + cov.T - np.diag(np.diag(cov)) +1493 +1494 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) +1495 +1496 if isinstance(smooth, int): +1497 corr = _smooth_eigenvalues(corr, smooth) 1498 -1499 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) -1500 -1501 if isinstance(smooth, int): -1502 corr = _smooth_eigenvalues(corr, smooth) -1503 -1504 if visualize: -1505 plt.matshow(corr, vmin=-1, vmax=1) -1506 plt.set_cmap('RdBu') -1507 plt.colorbar() -1508 plt.draw() -1509 -1510 if correlation is True: -1511 return corr -1512 -1513 errors = [o.dvalue for o in obs] -1514 cov = np.diag(errors) @ corr @ np.diag(errors) -1515 -1516 eigenvalues = np.linalg.eigh(cov)[0] -1517 if not np.all(eigenvalues >= 0): -1518 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) -1519 -1520 return cov -1521 -1522 -1523def _smooth_eigenvalues(corr, E): -1524 """Eigenvalue smoothing as described in hep-lat/9412087 -1525 -1526 corr : np.ndarray -1527 correlation matrix -1528 E : integer -1529 Number of eigenvalues to be left substantially unchanged -1530 """ -1531 if not (2 < E < corr.shape[0] - 1): -1532 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") -1533 vals, vec = np.linalg.eigh(corr) -1534 lambda_min = np.mean(vals[:-E]) -1535 vals[vals < lambda_min] = lambda_min -1536 vals /= np.mean(vals) -1537 return vec @ np.diag(vals) @ vec.T -1538 -1539 -1540def _covariance_element(obs1, obs2): -1541 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" +1499 if visualize: +1500 plt.matshow(corr, vmin=-1, vmax=1) +1501 plt.set_cmap('RdBu') +1502 plt.colorbar() +1503 plt.draw() +1504 +1505 if correlation is True: +1506 return corr +1507 +1508 errors = [o.dvalue for o in obs] +1509 cov = np.diag(errors) @ corr @ np.diag(errors) +1510 +1511 eigenvalues = np.linalg.eigh(cov)[0] +1512 if not np.all(eigenvalues >= 0): +1513 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) +1514 +1515 return cov +1516 +1517 +1518def _smooth_eigenvalues(corr, E): +1519 """Eigenvalue smoothing as described in hep-lat/9412087 +1520 +1521 corr : np.ndarray +1522 correlation matrix +1523 E : integer +1524 Number of eigenvalues to be left substantially unchanged +1525 """ +1526 if not (2 < E < corr.shape[0] - 1): +1527 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") +1528 vals, vec = np.linalg.eigh(corr) +1529 lambda_min = np.mean(vals[:-E]) +1530 vals[vals < lambda_min] = lambda_min +1531 vals /= np.mean(vals) +1532 return vec @ np.diag(vals) @ vec.T +1533 +1534 +1535def _covariance_element(obs1, obs2): +1536 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" +1537 +1538 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): +1539 deltas1 = _reduce_deltas(deltas1, idx1, new_idx) +1540 deltas2 = _reduce_deltas(deltas2, idx2, new_idx) +1541 return np.sum(deltas1 * deltas2) 1542 -1543 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): -1544 deltas1 = _reduce_deltas(deltas1, idx1, new_idx) -1545 deltas2 = _reduce_deltas(deltas2, idx2, new_idx) -1546 return np.sum(deltas1 * deltas2) -1547 -1548 if set(obs1.names).isdisjoint(set(obs2.names)): -1549 return 0.0 +1543 if set(obs1.names).isdisjoint(set(obs2.names)): +1544 return 0.0 +1545 +1546 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): +1547 raise Exception('The gamma method has to be applied to both Obs first.') +1548 +1549 dvalue = 0.0 1550 -1551 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): -1552 raise Exception('The gamma method has to be applied to both Obs first.') -1553 -1554 dvalue = 0.0 +1551 for e_name in obs1.mc_names: +1552 +1553 if e_name not in obs2.mc_names: +1554 continue 1555 -1556 for e_name in obs1.mc_names: -1557 -1558 if e_name not in obs2.mc_names: -1559 continue -1560 -1561 idl_d = {} -1562 for r_name in obs1.e_content[e_name]: -1563 if r_name not in obs2.e_content[e_name]: -1564 continue -1565 idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]]) -1566 -1567 gamma = 0.0 -1568 -1569 for r_name in obs1.e_content[e_name]: -1570 if r_name not in obs2.e_content[e_name]: -1571 continue -1572 if len(idl_d[r_name]) == 0: -1573 continue -1574 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) -1575 -1576 if gamma == 0.0: -1577 continue -1578 -1579 gamma_div = 0.0 -1580 for r_name in obs1.e_content[e_name]: -1581 if r_name not in obs2.e_content[e_name]: -1582 continue -1583 if len(idl_d[r_name]) == 0: -1584 continue -1585 gamma_div += np.sqrt(calc_gamma(obs1.deltas[r_name], obs1.deltas[r_name], obs1.idl[r_name], obs1.idl[r_name], idl_d[r_name]) * calc_gamma(obs2.deltas[r_name], obs2.deltas[r_name], obs2.idl[r_name], obs2.idl[r_name], idl_d[r_name])) -1586 gamma /= gamma_div -1587 -1588 dvalue += gamma +1556 idl_d = {} +1557 for r_name in obs1.e_content[e_name]: +1558 if r_name not in obs2.e_content[e_name]: +1559 continue +1560 idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]]) +1561 +1562 gamma = 0.0 +1563 +1564 for r_name in obs1.e_content[e_name]: +1565 if r_name not in obs2.e_content[e_name]: +1566 continue +1567 if len(idl_d[r_name]) == 0: +1568 continue +1569 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) +1570 +1571 if gamma == 0.0: +1572 continue +1573 +1574 gamma_div = 0.0 +1575 for r_name in obs1.e_content[e_name]: +1576 if r_name not in obs2.e_content[e_name]: +1577 continue +1578 if len(idl_d[r_name]) == 0: +1579 continue +1580 gamma_div += np.sqrt(calc_gamma(obs1.deltas[r_name], obs1.deltas[r_name], obs1.idl[r_name], obs1.idl[r_name], idl_d[r_name]) * calc_gamma(obs2.deltas[r_name], obs2.deltas[r_name], obs2.idl[r_name], obs2.idl[r_name], idl_d[r_name])) +1581 gamma /= gamma_div +1582 +1583 dvalue += gamma +1584 +1585 for e_name in obs1.cov_names: +1586 +1587 if e_name not in obs2.cov_names: +1588 continue 1589 -1590 for e_name in obs1.cov_names: +1590 dvalue += np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad)).item() 1591 -1592 if e_name not in obs2.cov_names: -1593 continue +1592 return dvalue +1593 1594 -1595 dvalue += np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad)).item() -1596 -1597 return dvalue -1598 -1599 -1600def import_jackknife(jacks, name, idl=None): -1601 """Imports jackknife samples and returns an Obs -1602 -1603 Parameters -1604 ---------- -1605 jacks : numpy.ndarray -1606 numpy array containing the mean value as zeroth entry and -1607 the N jackknife samples as first to Nth entry. -1608 name : str -1609 name of the ensemble the samples are defined on. -1610 """ -1611 length = len(jacks) - 1 -1612 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) -1613 samples = jacks[1:] @ prj -1614 mean = np.mean(samples) -1615 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) -1616 new_obs._value = jacks[0] -1617 return new_obs -1618 -1619 -1620def import_bootstrap(boots, name, random_numbers): -1621 """Imports bootstrap samples and returns an Obs -1622 -1623 Parameters -1624 ---------- -1625 boots : numpy.ndarray -1626 numpy array containing the mean value as zeroth entry and -1627 the N bootstrap samples as first to Nth entry. -1628 name : str -1629 name of the ensemble the samples are defined on. -1630 random_numbers : np.ndarray -1631 Array of shape (samples, length) containing the random numbers to generate the bootstrap samples, -1632 where samples is the number of bootstrap samples and length is the length of the original Monte Carlo -1633 chain to be reconstructed. -1634 """ -1635 samples, length = random_numbers.shape -1636 if samples != len(boots) - 1: -1637 raise ValueError("Random numbers do not have the correct shape.") +1595def import_jackknife(jacks, name, idl=None): +1596 """Imports jackknife samples and returns an Obs +1597 +1598 Parameters +1599 ---------- +1600 jacks : numpy.ndarray +1601 numpy array containing the mean value as zeroth entry and +1602 the N jackknife samples as first to Nth entry. +1603 name : str +1604 name of the ensemble the samples are defined on. +1605 """ +1606 length = len(jacks) - 1 +1607 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) +1608 samples = jacks[1:] @ prj +1609 mean = np.mean(samples) +1610 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) +1611 new_obs._value = jacks[0] +1612 return new_obs +1613 +1614 +1615def import_bootstrap(boots, name, random_numbers): +1616 """Imports bootstrap samples and returns an Obs +1617 +1618 Parameters +1619 ---------- +1620 boots : numpy.ndarray +1621 numpy array containing the mean value as zeroth entry and +1622 the N bootstrap samples as first to Nth entry. +1623 name : str +1624 name of the ensemble the samples are defined on. +1625 random_numbers : np.ndarray +1626 Array of shape (samples, length) containing the random numbers to generate the bootstrap samples, +1627 where samples is the number of bootstrap samples and length is the length of the original Monte Carlo +1628 chain to be reconstructed. +1629 """ +1630 samples, length = random_numbers.shape +1631 if samples != len(boots) - 1: +1632 raise ValueError("Random numbers do not have the correct shape.") +1633 +1634 if samples < length: +1635 raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.") +1636 +1637 proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length 1638 -1639 if samples < length: -1640 raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.") -1641 -1642 proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length +1639 samples = scipy.linalg.lstsq(proj, boots[1:])[0] +1640 ret = Obs([samples], [name]) +1641 ret._value = boots[0] +1642 return ret 1643 -1644 samples = scipy.linalg.lstsq(proj, boots[1:])[0] -1645 ret = Obs([samples], [name]) -1646 ret._value = boots[0] -1647 return ret -1648 -1649 -1650def merge_obs(list_of_obs): -1651 """Combine all observables in list_of_obs into one new observable +1644 +1645def merge_obs(list_of_obs): +1646 """Combine all observables in list_of_obs into one new observable +1647 +1648 Parameters +1649 ---------- +1650 list_of_obs : list +1651 list of the Obs object to be combined 1652 -1653 Parameters -1654 ---------- -1655 list_of_obs : list -1656 list of the Obs object to be combined -1657 -1658 Notes -1659 ----- -1660 It is not possible to combine obs which are based on the same replicum -1661 """ -1662 replist = [item for obs in list_of_obs for item in obs.names] -1663 if (len(replist) == len(set(replist))) is False: -1664 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) -1665 if any([len(o.cov_names) for o in list_of_obs]): -1666 raise Exception('Not possible to merge data that contains covobs!') -1667 new_dict = {} -1668 idl_dict = {} -1669 for o in list_of_obs: -1670 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) -1671 for key in set(o.deltas) | set(o.r_values)}) -1672 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) +1653 Notes +1654 ----- +1655 It is not possible to combine obs which are based on the same replicum +1656 """ +1657 replist = [item for obs in list_of_obs for item in obs.names] +1658 if (len(replist) == len(set(replist))) is False: +1659 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) +1660 if any([len(o.cov_names) for o in list_of_obs]): +1661 raise Exception('Not possible to merge data that contains covobs!') +1662 new_dict = {} +1663 idl_dict = {} +1664 for o in list_of_obs: +1665 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) +1666 for key in set(o.deltas) | set(o.r_values)}) +1667 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) +1668 +1669 names = sorted(new_dict.keys()) +1670 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) +1671 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) +1672 return o 1673 -1674 names = sorted(new_dict.keys()) -1675 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) -1676 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) -1677 return o -1678 -1679 -1680def cov_Obs(means, cov, name, grad=None): -1681 """Create an Obs based on mean(s) and a covariance matrix -1682 -1683 Parameters -1684 ---------- -1685 mean : list of floats or float -1686 N mean value(s) of the new Obs -1687 cov : list or array -1688 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance -1689 name : str -1690 identifier for the covariance matrix -1691 grad : list or array -1692 Gradient of the Covobs wrt. the means belonging to cov. -1693 """ -1694 -1695 def covobs_to_obs(co): -1696 """Make an Obs out of a Covobs -1697 -1698 Parameters -1699 ---------- -1700 co : Covobs -1701 Covobs to be embedded into the Obs -1702 """ -1703 o = Obs([], [], means=[]) -1704 o._value = co.value -1705 o.names.append(co.name) -1706 o._covobs[co.name] = co -1707 o._dvalue = np.sqrt(co.errsq()) -1708 return o -1709 -1710 ol = [] -1711 if isinstance(means, (float, int)): -1712 means = [means] -1713 -1714 for i in range(len(means)): -1715 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) -1716 if ol[0].covobs[name].N != len(means): -1717 raise Exception('You have to provide %d mean values!' % (ol[0].N)) -1718 if len(ol) == 1: -1719 return ol[0] -1720 return ol -1721 -1722 -1723def _determine_gap(o, e_content, e_name): -1724 gaps = [] -1725 for r_name in e_content[e_name]: -1726 if isinstance(o.idl[r_name], range): -1727 gaps.append(o.idl[r_name].step) -1728 else: -1729 gaps.append(np.min(np.diff(o.idl[r_name]))) -1730 -1731 gap = min(gaps) -1732 if not np.all([gi % gap == 0 for gi in gaps]): -1733 raise Exception(f"Replica for ensemble {e_name} do not have a common spacing.", gaps) -1734 -1735 return gap -1736 +1674 +1675def cov_Obs(means, cov, name, grad=None): +1676 """Create an Obs based on mean(s) and a covariance matrix +1677 +1678 Parameters +1679 ---------- +1680 mean : list of floats or float +1681 N mean value(s) of the new Obs +1682 cov : list or array +1683 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance +1684 name : str +1685 identifier for the covariance matrix +1686 grad : list or array +1687 Gradient of the Covobs wrt. the means belonging to cov. +1688 """ +1689 +1690 def covobs_to_obs(co): +1691 """Make an Obs out of a Covobs +1692 +1693 Parameters +1694 ---------- +1695 co : Covobs +1696 Covobs to be embedded into the Obs +1697 """ +1698 o = Obs([], [], means=[]) +1699 o._value = co.value +1700 o.names.append(co.name) +1701 o._covobs[co.name] = co +1702 o._dvalue = np.sqrt(co.errsq()) +1703 return o +1704 +1705 ol = [] +1706 if isinstance(means, (float, int)): +1707 means = [means] +1708 +1709 for i in range(len(means)): +1710 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) +1711 if ol[0].covobs[name].N != len(means): +1712 raise Exception('You have to provide %d mean values!' % (ol[0].N)) +1713 if len(ol) == 1: +1714 return ol[0] +1715 return ol +1716 +1717 +1718def _determine_gap(o, e_content, e_name): +1719 gaps = [] +1720 for r_name in e_content[e_name]: +1721 if isinstance(o.idl[r_name], range): +1722 gaps.append(o.idl[r_name].step) +1723 else: +1724 gaps.append(np.min(np.diff(o.idl[r_name]))) +1725 +1726 gap = min(gaps) +1727 if not np.all([gi % gap == 0 for gi in gaps]): +1728 raise Exception(f"Replica for ensemble {e_name} do not have a common spacing.", gaps) +1729 +1730 return gap +1731 +1732 +1733def _check_lists_equal(idl): +1734 ''' +1735 Use groupby to efficiently check whether all elements of idl are identical. +1736 Returns True if all elements are equal, otherwise False. 1737 -1738def _check_lists_equal(idl): -1739 ''' -1740 Use groupby to efficiently check whether all elements of idl are identical. -1741 Returns True if all elements are equal, otherwise False. -1742 -1743 Parameters -1744 ---------- -1745 idl : list of lists, ranges or np.ndarrays -1746 ''' -1747 g = groupby([np.nditer(el) if isinstance(el, np.ndarray) else el for el in idl]) -1748 if next(g, True) and not next(g, False): -1749 return True -1750 return False +1738 Parameters +1739 ---------- +1740 idl : list of lists, ranges or np.ndarrays +1741 ''' +1742 g = groupby([np.nditer(el) if isinstance(el, np.ndarray) else el for el in idl]) +1743 if next(g, True) and not next(g, False): +1744 return True +1745 return False @@ -5177,18 +5172,18 @@ should agree with samples from a full bootstrap analysis up to O(1/N). - 
1043def gm(x, **kwargs):
-1044    """Short version of the vectorized gamma_method.
-1045
-1046    See docstring of pe.Obs.gamma_method for details
-1047    """
-1048    return gamma_method(x, **kwargs)
+            
1035def gamma_method(x, **kwargs):
+1036    """Vectorized version of the gamma_method applicable to lists or arrays of Obs.
+1037
+1038    See docstring of pe.Obs.gamma_method for details.
+1039    """
+1040    return np.vectorize(lambda o: o.gm(**kwargs))(x)
 

 
 
-            
Short version of the vectorized gamma_method.

+            
Vectorized version of the gamma_method applicable to lists or arrays of Obs.

 
-
See docstring of pe.Obs.gamma_method for details

+
See docstring of pe.Obs.gamma_method for details.

 

 
 
@@ -5204,174 +5199,174 @@ should agree with samples from a full bootstrap analysis up to O(1/N).
 
     

     
-            
1170def derived_observable(func, data, array_mode=False, **kwargs):
-1171    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
-1172
-1173    Parameters
-1174    ----------
-1175    func : object
-1176        arbitrary function of the form func(data, **kwargs). For the
-1177        automatic differentiation to work, all numpy functions have to have
-1178        the autograd wrapper (use 'import autograd.numpy as anp').
-1179    data : list
-1180        list of Obs, e.g. [obs1, obs2, obs3].
-1181    num_grad : bool
-1182        if True, numerical derivatives are used instead of autograd
-1183        (default False). To control the numerical differentiation the
-1184        kwargs of numdifftools.step_generators.MaxStepGenerator
-1185        can be used.
-1186    man_grad : list
-1187        manually supply a list or an array which contains the jacobian
-1188        of func. Use cautiously, supplying the wrong derivative will
-1189        not be intercepted.
+            
1165def derived_observable(func, data, array_mode=False, **kwargs):
+1166    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
+1167
+1168    Parameters
+1169    ----------
+1170    func : object
+1171        arbitrary function of the form func(data, **kwargs). For the
+1172        automatic differentiation to work, all numpy functions have to have
+1173        the autograd wrapper (use 'import autograd.numpy as anp').
+1174    data : list
+1175        list of Obs, e.g. [obs1, obs2, obs3].
+1176    num_grad : bool
+1177        if True, numerical derivatives are used instead of autograd
+1178        (default False). To control the numerical differentiation the
+1179        kwargs of numdifftools.step_generators.MaxStepGenerator
+1180        can be used.
+1181    man_grad : list
+1182        manually supply a list or an array which contains the jacobian
+1183        of func. Use cautiously, supplying the wrong derivative will
+1184        not be intercepted.
+1185
+1186    Notes
+1187    -----
+1188    For simple mathematical operations it can be practical to use anonymous
+1189    functions. For the ratio of two observables one can e.g. use
 1190
-1191    Notes
-1192    -----
-1193    For simple mathematical operations it can be practical to use anonymous
-1194    functions. For the ratio of two observables one can e.g. use
-1195
-1196    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
-1197    """
-1198
-1199    data = np.asarray(data)
-1200    raveled_data = data.ravel()
-1201
-1202    # Workaround for matrix operations containing non Obs data
-1203    if not all(isinstance(x, Obs) for x in raveled_data):
-1204        for i in range(len(raveled_data)):
-1205            if isinstance(raveled_data[i], (int, float)):
-1206                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
-1207
-1208    allcov = {}
-1209    for o in raveled_data:
-1210        for name in o.cov_names:
-1211            if name in allcov:
-1212                if not np.allclose(allcov[name], o.covobs[name].cov):
-1213                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
-1214            else:
-1215                allcov[name] = o.covobs[name].cov
+1191    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
+1192    """
+1193
+1194    data = np.asarray(data)
+1195    raveled_data = data.ravel()
+1196
+1197    # Workaround for matrix operations containing non Obs data
+1198    if not all(isinstance(x, Obs) for x in raveled_data):
+1199        for i in range(len(raveled_data)):
+1200            if isinstance(raveled_data[i], (int, float)):
+1201                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
+1202
+1203    allcov = {}
+1204    for o in raveled_data:
+1205        for name in o.cov_names:
+1206            if name in allcov:
+1207                if not np.allclose(allcov[name], o.covobs[name].cov):
+1208                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
+1209            else:
+1210                allcov[name] = o.covobs[name].cov
+1211
+1212    n_obs = len(raveled_data)
+1213    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
+1214    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
+1215    new_sample_names = sorted(set(new_names) - set(new_cov_names))
 1216
-1217    n_obs = len(raveled_data)
-1218    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
-1219    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
-1220    new_sample_names = sorted(set(new_names) - set(new_cov_names))
-1221
-1222    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1217    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1218
+1219    if data.ndim == 1:
+1220        values = np.array([o.value for o in data])
+1221    else:
+1222        values = np.vectorize(lambda x: x.value)(data)
 1223
-1224    if data.ndim == 1:
-1225        values = np.array([o.value for o in data])
-1226    else:
-1227        values = np.vectorize(lambda x: x.value)(data)
-1228
-1229    new_values = func(values, **kwargs)
-1230
-1231    multi = int(isinstance(new_values, np.ndarray))
-1232
-1233    new_r_values = {}
-1234    new_idl_d = {}
-1235    for name in new_sample_names:
-1236        idl = []
-1237        tmp_values = np.zeros(n_obs)
-1238        for i, item in enumerate(raveled_data):
-1239            tmp_values[i] = item.r_values.get(name, item.value)
-1240            tmp_idl = item.idl.get(name)
-1241            if tmp_idl is not None:
-1242                idl.append(tmp_idl)
-1243        if multi > 0:
-1244            tmp_values = np.array(tmp_values).reshape(data.shape)
-1245        new_r_values[name] = func(tmp_values, **kwargs)
-1246        new_idl_d[name] = _merge_idx(idl)
-1247
-1248    if 'man_grad' in kwargs:
-1249        deriv = np.asarray(kwargs.get('man_grad'))
-1250        if new_values.shape + data.shape != deriv.shape:
-1251            raise Exception('Manual derivative does not have correct shape.')
-1252    elif kwargs.get('num_grad') is True:
-1253        if multi > 0:
-1254            raise Exception('Multi mode currently not supported for numerical derivative')
-1255        options = {
-1256            'base_step': 0.1,
-1257            'step_ratio': 2.5}
-1258        for key in options.keys():
-1259            kwarg = kwargs.get(key)
-1260            if kwarg is not None:
-1261                options[key] = kwarg
-1262        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
-1263        if tmp_df.size == 1:
-1264            deriv = np.array([tmp_df.real])
-1265        else:
-1266            deriv = tmp_df.real
-1267    else:
-1268        deriv = jacobian(func)(values, **kwargs)
-1269
-1270    final_result = np.zeros(new_values.shape, dtype=object)
-1271
-1272    if array_mode is True:
-1273
-1274        class _Zero_grad():
-1275            def __init__(self, N):
-1276                self.grad = np.zeros((N, 1))
-1277
-1278        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
-1279        d_extracted = {}
-1280        g_extracted = {}
-1281        for name in new_sample_names:
-1282            d_extracted[name] = []
-1283            ens_length = len(new_idl_d[name])
+1224    new_values = func(values, **kwargs)
+1225
+1226    multi = int(isinstance(new_values, np.ndarray))
+1227
+1228    new_r_values = {}
+1229    new_idl_d = {}
+1230    for name in new_sample_names:
+1231        idl = []
+1232        tmp_values = np.zeros(n_obs)
+1233        for i, item in enumerate(raveled_data):
+1234            tmp_values[i] = item.r_values.get(name, item.value)
+1235            tmp_idl = item.idl.get(name)
+1236            if tmp_idl is not None:
+1237                idl.append(tmp_idl)
+1238        if multi > 0:
+1239            tmp_values = np.array(tmp_values).reshape(data.shape)
+1240        new_r_values[name] = func(tmp_values, **kwargs)
+1241        new_idl_d[name] = _merge_idx(idl)
+1242
+1243    if 'man_grad' in kwargs:
+1244        deriv = np.asarray(kwargs.get('man_grad'))
+1245        if new_values.shape + data.shape != deriv.shape:
+1246            raise Exception('Manual derivative does not have correct shape.')
+1247    elif kwargs.get('num_grad') is True:
+1248        if multi > 0:
+1249            raise Exception('Multi mode currently not supported for numerical derivative')
+1250        options = {
+1251            'base_step': 0.1,
+1252            'step_ratio': 2.5}
+1253        for key in options.keys():
+1254            kwarg = kwargs.get(key)
+1255            if kwarg is not None:
+1256                options[key] = kwarg
+1257        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
+1258        if tmp_df.size == 1:
+1259            deriv = np.array([tmp_df.real])
+1260        else:
+1261            deriv = tmp_df.real
+1262    else:
+1263        deriv = jacobian(func)(values, **kwargs)
+1264
+1265    final_result = np.zeros(new_values.shape, dtype=object)
+1266
+1267    if array_mode is True:
+1268
+1269        class _Zero_grad():
+1270            def __init__(self, N):
+1271                self.grad = np.zeros((N, 1))
+1272
+1273        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
+1274        d_extracted = {}
+1275        g_extracted = {}
+1276        for name in new_sample_names:
+1277            d_extracted[name] = []
+1278            ens_length = len(new_idl_d[name])
+1279            for i_dat, dat in enumerate(data):
+1280                d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
+1281        for name in new_cov_names:
+1282            g_extracted[name] = []
+1283            zero_grad = _Zero_grad(new_covobs_lengths[name])
 1284            for i_dat, dat in enumerate(data):
-1285                d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
-1286        for name in new_cov_names:
-1287            g_extracted[name] = []
-1288            zero_grad = _Zero_grad(new_covobs_lengths[name])
-1289            for i_dat, dat in enumerate(data):
-1290                g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1)))
-1291
-1292    for i_val, new_val in np.ndenumerate(new_values):
-1293        new_deltas = {}
-1294        new_grad = {}
-1295        if array_mode is True:
-1296            for name in new_sample_names:
-1297                ens_length = d_extracted[name][0].shape[-1]
-1298                new_deltas[name] = np.zeros(ens_length)
-1299                for i_dat, dat in enumerate(d_extracted[name]):
-1300                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1301            for name in new_cov_names:
-1302                new_grad[name] = 0
-1303                for i_dat, dat in enumerate(g_extracted[name]):
-1304                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1305        else:
-1306            for j_obs, obs in np.ndenumerate(data):
-1307                for name in obs.names:
-1308                    if name in obs.cov_names:
-1309                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
-1310                    else:
-1311                        new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name])
-1312
-1313        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
-1314
-1315        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
-1316            raise Exception('The same name has been used for deltas and covobs!')
-1317        new_samples = []
-1318        new_means = []
-1319        new_idl = []
-1320        new_names_obs = []
-1321        for name in new_names:
-1322            if name not in new_covobs:
-1323                new_samples.append(new_deltas[name])
-1324                new_idl.append(new_idl_d[name])
-1325                new_means.append(new_r_values[name][i_val])
-1326                new_names_obs.append(name)
-1327        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
-1328        for name in new_covobs:
-1329            final_result[i_val].names.append(name)
-1330        final_result[i_val]._covobs = new_covobs
-1331        final_result[i_val]._value = new_val
-1332        final_result[i_val].reweighted = reweighted
-1333
-1334    if multi == 0:
-1335        final_result = final_result.item()
-1336
-1337    return final_result
+1285                g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1)))
+1286
+1287    for i_val, new_val in np.ndenumerate(new_values):
+1288        new_deltas = {}
+1289        new_grad = {}
+1290        if array_mode is True:
+1291            for name in new_sample_names:
+1292                ens_length = d_extracted[name][0].shape[-1]
+1293                new_deltas[name] = np.zeros(ens_length)
+1294                for i_dat, dat in enumerate(d_extracted[name]):
+1295                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1296            for name in new_cov_names:
+1297                new_grad[name] = 0
+1298                for i_dat, dat in enumerate(g_extracted[name]):
+1299                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1300        else:
+1301            for j_obs, obs in np.ndenumerate(data):
+1302                for name in obs.names:
+1303                    if name in obs.cov_names:
+1304                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
+1305                    else:
+1306                        new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name])
+1307
+1308        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1309
+1310        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
+1311            raise Exception('The same name has been used for deltas and covobs!')
+1312        new_samples = []
+1313        new_means = []
+1314        new_idl = []
+1315        new_names_obs = []
+1316        for name in new_names:
+1317            if name not in new_covobs:
+1318                new_samples.append(new_deltas[name])
+1319                new_idl.append(new_idl_d[name])
+1320                new_means.append(new_r_values[name][i_val])
+1321                new_names_obs.append(name)
+1322        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
+1323        for name in new_covobs:
+1324            final_result[i_val].names.append(name)
+1325        final_result[i_val]._covobs = new_covobs
+1326        final_result[i_val]._value = new_val
+1327        final_result[i_val].reweighted = reweighted
+1328
+1329    if multi == 0:
+1330        final_result = final_result.item()
+1331
+1332    return final_result
 

 
 
@@ -5418,46 +5413,46 @@ functions. For the ratio of two observables one can e.g. use

 
     

     
-            
1369def reweight(weight, obs, **kwargs):
-1370    """Reweight a list of observables.
-1371
-1372    Parameters
-1373    ----------
-1374    weight : Obs
-1375        Reweighting factor. An Observable that has to be defined on a superset of the
-1376        configurations in obs[i].idl for all i.
-1377    obs : list
-1378        list of Obs, e.g. [obs1, obs2, obs3].
-1379    all_configs : bool
-1380        if True, the reweighted observables are normalized by the average of
-1381        the reweighting factor on all configurations in weight.idl and not
-1382        on the configurations in obs[i].idl. Default False.
-1383    """
-1384    result = []
-1385    for i in range(len(obs)):
-1386        if len(obs[i].cov_names):
-1387            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
-1388        if not set(obs[i].names).issubset(weight.names):
-1389            raise Exception('Error: Ensembles do not fit')
-1390        for name in obs[i].names:
-1391            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
-1392                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
-1393        new_samples = []
-1394        w_deltas = {}
-1395        for name in sorted(obs[i].names):
-1396            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
-1397            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
-1398        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+            
1364def reweight(weight, obs, **kwargs):
+1365    """Reweight a list of observables.
+1366
+1367    Parameters
+1368    ----------
+1369    weight : Obs
+1370        Reweighting factor. An Observable that has to be defined on a superset of the
+1371        configurations in obs[i].idl for all i.
+1372    obs : list
+1373        list of Obs, e.g. [obs1, obs2, obs3].
+1374    all_configs : bool
+1375        if True, the reweighted observables are normalized by the average of
+1376        the reweighting factor on all configurations in weight.idl and not
+1377        on the configurations in obs[i].idl. Default False.
+1378    """
+1379    result = []
+1380    for i in range(len(obs)):
+1381        if len(obs[i].cov_names):
+1382            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
+1383        if not set(obs[i].names).issubset(weight.names):
+1384            raise Exception('Error: Ensembles do not fit')
+1385        for name in obs[i].names:
+1386            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
+1387                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
+1388        new_samples = []
+1389        w_deltas = {}
+1390        for name in sorted(obs[i].names):
+1391            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
+1392            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
+1393        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1394
+1395        if kwargs.get('all_configs'):
+1396            new_weight = weight
+1397        else:
+1398            new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
 1399
-1400        if kwargs.get('all_configs'):
-1401            new_weight = weight
-1402        else:
-1403            new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1404
-1405        result.append(tmp_obs / new_weight)
-1406        result[-1].reweighted = True
-1407
-1408    return result
+1400        result.append(tmp_obs / new_weight)
+1401        result[-1].reweighted = True
+1402
+1403    return result
 

 
 
@@ -5491,47 +5486,47 @@ on the configurations in obs[i].idl. Default False.
 
     

     
-            
1411def correlate(obs_a, obs_b):
-1412    """Correlate two observables.
-1413
-1414    Parameters
-1415    ----------
-1416    obs_a : Obs
-1417        First observable
-1418    obs_b : Obs
-1419        Second observable
-1420
-1421    Notes
-1422    -----
-1423    Keep in mind to only correlate primary observables which have not been reweighted
-1424    yet. The reweighting has to be applied after correlating the observables.
-1425    Currently only works if ensembles are identical (this is not strictly necessary).
-1426    """
-1427
-1428    if sorted(obs_a.names) != sorted(obs_b.names):
-1429        raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
-1430    if len(obs_a.cov_names) or len(obs_b.cov_names):
-1431        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
-1432    for name in obs_a.names:
-1433        if obs_a.shape[name] != obs_b.shape[name]:
-1434            raise Exception('Shapes of ensemble', name, 'do not fit')
-1435        if obs_a.idl[name] != obs_b.idl[name]:
-1436            raise Exception('idl of ensemble', name, 'do not fit')
+            
1406def correlate(obs_a, obs_b):
+1407    """Correlate two observables.
+1408
+1409    Parameters
+1410    ----------
+1411    obs_a : Obs
+1412        First observable
+1413    obs_b : Obs
+1414        Second observable
+1415
+1416    Notes
+1417    -----
+1418    Keep in mind to only correlate primary observables which have not been reweighted
+1419    yet. The reweighting has to be applied after correlating the observables.
+1420    Currently only works if ensembles are identical (this is not strictly necessary).
+1421    """
+1422
+1423    if sorted(obs_a.names) != sorted(obs_b.names):
+1424        raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
+1425    if len(obs_a.cov_names) or len(obs_b.cov_names):
+1426        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
+1427    for name in obs_a.names:
+1428        if obs_a.shape[name] != obs_b.shape[name]:
+1429            raise Exception('Shapes of ensemble', name, 'do not fit')
+1430        if obs_a.idl[name] != obs_b.idl[name]:
+1431            raise Exception('idl of ensemble', name, 'do not fit')
+1432
+1433    if obs_a.reweighted is True:
+1434        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
+1435    if obs_b.reweighted is True:
+1436        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
 1437
-1438    if obs_a.reweighted is True:
-1439        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
-1440    if obs_b.reweighted is True:
-1441        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
-1442
-1443    new_samples = []
-1444    new_idl = []
-1445    for name in sorted(obs_a.names):
-1446        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
-1447        new_idl.append(obs_a.idl[name])
-1448
-1449    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
-1450    o.reweighted = obs_a.reweighted or obs_b.reweighted
-1451    return o
+1438    new_samples = []
+1439    new_idl = []
+1440    for name in sorted(obs_a.names):
+1441        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
+1442        new_idl.append(obs_a.idl[name])
+1443
+1444    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
+1445    o.reweighted = obs_a.reweighted or obs_b.reweighted
+1446    return o
 

 
 
@@ -5566,74 +5561,74 @@ Currently only works if ensembles are identical (this is not strictly necessary)
 
     

     
-            
1454def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
-1455    r'''Calculates the error covariance matrix of a set of observables.
+            
1449def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+1450    r'''Calculates the error covariance matrix of a set of observables.
+1451
+1452    WARNING: This function should be used with care, especially for observables with support on multiple
+1453             ensembles with differing autocorrelations. See the notes below for details.
+1454
+1455    The gamma method has to be applied first to all observables.
 1456
-1457    WARNING: This function should be used with care, especially for observables with support on multiple
-1458             ensembles with differing autocorrelations. See the notes below for details.
-1459
-1460    The gamma method has to be applied first to all observables.
-1461
-1462    Parameters
-1463    ----------
-1464    obs : list or numpy.ndarray
-1465        List or one dimensional array of Obs
-1466    visualize : bool
-1467        If True plots the corresponding normalized correlation matrix (default False).
-1468    correlation : bool
-1469        If True the correlation matrix instead of the error covariance matrix is returned (default False).
-1470    smooth : None or int
-1471        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
-1472        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
-1473        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
-1474        small ones.
-1475
-1476    Notes
-1477    -----
-1478    The error covariance is defined such that it agrees with the squared standard error for two identical observables
-1479    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
-1480    in the absence of autocorrelation.
-1481    The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite
-1482    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
-1483    For observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.
-1484    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
-1485    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
-1486    '''
-1487
-1488    length = len(obs)
-1489
-1490    max_samples = np.max([o.N for o in obs])
-1491    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
-1492        warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning)
-1493
-1494    cov = np.zeros((length, length))
-1495    for i in range(length):
-1496        for j in range(i, length):
-1497            cov[i, j] = _covariance_element(obs[i], obs[j])
-1498    cov = cov + cov.T - np.diag(np.diag(cov))
+1457    Parameters
+1458    ----------
+1459    obs : list or numpy.ndarray
+1460        List or one dimensional array of Obs
+1461    visualize : bool
+1462        If True plots the corresponding normalized correlation matrix (default False).
+1463    correlation : bool
+1464        If True the correlation matrix instead of the error covariance matrix is returned (default False).
+1465    smooth : None or int
+1466        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
+1467        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
+1468        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
+1469        small ones.
+1470
+1471    Notes
+1472    -----
+1473    The error covariance is defined such that it agrees with the squared standard error for two identical observables
+1474    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
+1475    in the absence of autocorrelation.
+1476    The error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite
+1477    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
+1478    For observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.
+1479    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
+1480    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
+1481    '''
+1482
+1483    length = len(obs)
+1484
+1485    max_samples = np.max([o.N for o in obs])
+1486    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
+1487        warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning)
+1488
+1489    cov = np.zeros((length, length))
+1490    for i in range(length):
+1491        for j in range(i, length):
+1492            cov[i, j] = _covariance_element(obs[i], obs[j])
+1493    cov = cov + cov.T - np.diag(np.diag(cov))
+1494
+1495    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
+1496
+1497    if isinstance(smooth, int):
+1498        corr = _smooth_eigenvalues(corr, smooth)
 1499
-1500    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
-1501
-1502    if isinstance(smooth, int):
-1503        corr = _smooth_eigenvalues(corr, smooth)
-1504
-1505    if visualize:
-1506        plt.matshow(corr, vmin=-1, vmax=1)
-1507        plt.set_cmap('RdBu')
-1508        plt.colorbar()
-1509        plt.draw()
-1510
-1511    if correlation is True:
-1512        return corr
-1513
-1514    errors = [o.dvalue for o in obs]
-1515    cov = np.diag(errors) @ corr @ np.diag(errors)
-1516
-1517    eigenvalues = np.linalg.eigh(cov)[0]
-1518    if not np.all(eigenvalues >= 0):
-1519        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
-1520
-1521    return cov
+1500    if visualize:
+1501        plt.matshow(corr, vmin=-1, vmax=1)
+1502        plt.set_cmap('RdBu')
+1503        plt.colorbar()
+1504        plt.draw()
+1505
+1506    if correlation is True:
+1507        return corr
+1508
+1509    errors = [o.dvalue for o in obs]
+1510    cov = np.diag(errors) @ corr @ np.diag(errors)
+1511
+1512    eigenvalues = np.linalg.eigh(cov)[0]
+1513    if not np.all(eigenvalues >= 0):
+1514        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
+1515
+1516    return cov
 

 
 
@@ -5685,24 +5680,24 @@ This construction ensures that the estimated covariance matrix is positive semi-
 
     

     
-            
1601def import_jackknife(jacks, name, idl=None):
-1602    """Imports jackknife samples and returns an Obs
-1603
-1604    Parameters
-1605    ----------
-1606    jacks : numpy.ndarray
-1607        numpy array containing the mean value as zeroth entry and
-1608        the N jackknife samples as first to Nth entry.
-1609    name : str
-1610        name of the ensemble the samples are defined on.
-1611    """
-1612    length = len(jacks) - 1
-1613    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
-1614    samples = jacks[1:] @ prj
-1615    mean = np.mean(samples)
-1616    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
-1617    new_obs._value = jacks[0]
-1618    return new_obs
+            
1596def import_jackknife(jacks, name, idl=None):
+1597    """Imports jackknife samples and returns an Obs
+1598
+1599    Parameters
+1600    ----------
+1601    jacks : numpy.ndarray
+1602        numpy array containing the mean value as zeroth entry and
+1603        the N jackknife samples as first to Nth entry.
+1604    name : str
+1605        name of the ensemble the samples are defined on.
+1606    """
+1607    length = len(jacks) - 1
+1608    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
+1609    samples = jacks[1:] @ prj
+1610    mean = np.mean(samples)
+1611    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
+1612    new_obs._value = jacks[0]
+1613    return new_obs
 

 
 
@@ -5732,34 +5727,34 @@ name of the ensemble the samples are defined on.
 
     

     
-            
1621def import_bootstrap(boots, name, random_numbers):
-1622    """Imports bootstrap samples and returns an Obs
-1623
-1624    Parameters
-1625    ----------
-1626    boots : numpy.ndarray
-1627        numpy array containing the mean value as zeroth entry and
-1628        the N bootstrap samples as first to Nth entry.
-1629    name : str
-1630        name of the ensemble the samples are defined on.
-1631    random_numbers : np.ndarray
-1632        Array of shape (samples, length) containing the random numbers to generate the bootstrap samples,
-1633        where samples is the number of bootstrap samples and length is the length of the original Monte Carlo
-1634        chain to be reconstructed.
-1635    """
-1636    samples, length = random_numbers.shape
-1637    if samples != len(boots) - 1:
-1638        raise ValueError("Random numbers do not have the correct shape.")
+            
1616def import_bootstrap(boots, name, random_numbers):
+1617    """Imports bootstrap samples and returns an Obs
+1618
+1619    Parameters
+1620    ----------
+1621    boots : numpy.ndarray
+1622        numpy array containing the mean value as zeroth entry and
+1623        the N bootstrap samples as first to Nth entry.
+1624    name : str
+1625        name of the ensemble the samples are defined on.
+1626    random_numbers : np.ndarray
+1627        Array of shape (samples, length) containing the random numbers to generate the bootstrap samples,
+1628        where samples is the number of bootstrap samples and length is the length of the original Monte Carlo
+1629        chain to be reconstructed.
+1630    """
+1631    samples, length = random_numbers.shape
+1632    if samples != len(boots) - 1:
+1633        raise ValueError("Random numbers do not have the correct shape.")
+1634
+1635    if samples < length:
+1636        raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.")
+1637
+1638    proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
 1639
-1640    if samples < length:
-1641        raise ValueError("Obs can't be reconstructed if there are fewer bootstrap samples than Monte Carlo data points.")
-1642
-1643    proj = np.vstack([np.bincount(o, minlength=length) for o in random_numbers]) / length
-1644
-1645    samples = scipy.linalg.lstsq(proj, boots[1:])[0]
-1646    ret = Obs([samples], [name])
-1647    ret._value = boots[0]
-1648    return ret
+1640    samples = scipy.linalg.lstsq(proj, boots[1:])[0]
+1641    ret = Obs([samples], [name])
+1642    ret._value = boots[0]
+1643    return ret
 

 
 
@@ -5793,34 +5788,34 @@ chain to be reconstructed.
 
     

     
-            
1651def merge_obs(list_of_obs):
-1652    """Combine all observables in list_of_obs into one new observable
+            
1646def merge_obs(list_of_obs):
+1647    """Combine all observables in list_of_obs into one new observable
+1648
+1649    Parameters
+1650    ----------
+1651    list_of_obs : list
+1652        list of the Obs object to be combined
 1653
-1654    Parameters
-1655    ----------
-1656    list_of_obs : list
-1657        list of the Obs object to be combined
-1658
-1659    Notes
-1660    -----
-1661    It is not possible to combine obs which are based on the same replicum
-1662    """
-1663    replist = [item for obs in list_of_obs for item in obs.names]
-1664    if (len(replist) == len(set(replist))) is False:
-1665        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
-1666    if any([len(o.cov_names) for o in list_of_obs]):
-1667        raise Exception('Not possible to merge data that contains covobs!')
-1668    new_dict = {}
-1669    idl_dict = {}
-1670    for o in list_of_obs:
-1671        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
-1672                        for key in set(o.deltas) | set(o.r_values)})
-1673        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
-1674
-1675    names = sorted(new_dict.keys())
-1676    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
-1677    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
-1678    return o
+1654    Notes
+1655    -----
+1656    It is not possible to combine obs which are based on the same replicum
+1657    """
+1658    replist = [item for obs in list_of_obs for item in obs.names]
+1659    if (len(replist) == len(set(replist))) is False:
+1660        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
+1661    if any([len(o.cov_names) for o in list_of_obs]):
+1662        raise Exception('Not possible to merge data that contains covobs!')
+1663    new_dict = {}
+1664    idl_dict = {}
+1665    for o in list_of_obs:
+1666        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
+1667                        for key in set(o.deltas) | set(o.r_values)})
+1668        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
+1669
+1670    names = sorted(new_dict.keys())
+1671    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
+1672    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
+1673    return o
 

 
 
@@ -5851,47 +5846,47 @@ list of the Obs object to be combined
 
     

     
-            
1681def cov_Obs(means, cov, name, grad=None):
-1682    """Create an Obs based on mean(s) and a covariance matrix
-1683
-1684    Parameters
-1685    ----------
-1686    mean : list of floats or float
-1687        N mean value(s) of the new Obs
-1688    cov : list or array
-1689        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
-1690    name : str
-1691        identifier for the covariance matrix
-1692    grad : list or array
-1693        Gradient of the Covobs wrt. the means belonging to cov.
-1694    """
-1695
-1696    def covobs_to_obs(co):
-1697        """Make an Obs out of a Covobs
-1698
-1699        Parameters
-1700        ----------
-1701        co : Covobs
-1702            Covobs to be embedded into the Obs
-1703        """
-1704        o = Obs([], [], means=[])
-1705        o._value = co.value
-1706        o.names.append(co.name)
-1707        o._covobs[co.name] = co
-1708        o._dvalue = np.sqrt(co.errsq())
-1709        return o
-1710
-1711    ol = []
-1712    if isinstance(means, (float, int)):
-1713        means = [means]
-1714
-1715    for i in range(len(means)):
-1716        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
-1717    if ol[0].covobs[name].N != len(means):
-1718        raise Exception('You have to provide %d mean values!' % (ol[0].N))
-1719    if len(ol) == 1:
-1720        return ol[0]
-1721    return ol
+            
1676def cov_Obs(means, cov, name, grad=None):
+1677    """Create an Obs based on mean(s) and a covariance matrix
+1678
+1679    Parameters
+1680    ----------
+1681    mean : list of floats or float
+1682        N mean value(s) of the new Obs
+1683    cov : list or array
+1684        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
+1685    name : str
+1686        identifier for the covariance matrix
+1687    grad : list or array
+1688        Gradient of the Covobs wrt. the means belonging to cov.
+1689    """
+1690
+1691    def covobs_to_obs(co):
+1692        """Make an Obs out of a Covobs
+1693
+1694        Parameters
+1695        ----------
+1696        co : Covobs
+1697            Covobs to be embedded into the Obs
+1698        """
+1699        o = Obs([], [], means=[])
+1700        o._value = co.value
+1701        o.names.append(co.name)
+1702        o._covobs[co.name] = co
+1703        o._dvalue = np.sqrt(co.errsq())
+1704        return o
+1705
+1706    ol = []
+1707    if isinstance(means, (float, int)):
+1708        means = [means]
+1709
+1710    for i in range(len(means)):
+1711        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
+1712    if ol[0].covobs[name].N != len(means):
+1713        raise Exception('You have to provide %d mean values!' % (ol[0].N))
+1714    if len(ol) == 1:
+1715        return ol[0]
+1716    return ol
 

 
 
diff --git a/docs/search.js b/docs/search.js
index 0e824b7e..5a5d7835 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
\n\n
    \n
  • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
    • \n
  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
    • \n
  • coherent error propagation for data from different Markov chains.
    • \n
  • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
    • \n
  • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
    • \n
\n\n
More detailed examples can found in the GitHub repository \"badge\".
\n\n
If you use pyerrors for research that leads to a publication please consider citing:
\n\n
    \n
  • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
    • \n
  • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
    • \n
  • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
    • \n
\n\n
and
\n\n
    \n
  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
    • \n
\n\n
where applicable.
\n\n
There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
\n\n
Installation
\n\n
Install the most recent release using pip and pypi:
\n\n
\n
python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
\n
\n\n
Install the most recent release using conda and conda-forge:
\n\n
\n
conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
\n
\n\n
Install the current develop version:
\n\n
\n
python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
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(Also works for any feature branch).
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Basic example
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import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
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The Obs class
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pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
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import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
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Error propagation
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When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
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The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
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import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
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Error estimation
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The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
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my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
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We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
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my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
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If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
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Exponential tails
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Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
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my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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For the full API see pyerrors.obs.Obs.gamma_method.
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Multiple ensembles/replica
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Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
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obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
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Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
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pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
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obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
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Error estimation for multiple ensembles
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In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
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pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
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In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
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Irregular Monte Carlo chains
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Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
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# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
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Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
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Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
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For the full API see pyerrors.obs.Obs.
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Correlators
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When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
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my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
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In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
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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
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The individual entries of a correlator can be accessed via slicing
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print(my_corr[3])\n> 0.3227(33)\n
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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.
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my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
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pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
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  • Corr.gamma_method applies the gamma method to all entries of the correlator.
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  • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
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  • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
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  • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
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  • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
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  • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
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  • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
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  • Corr.plateau extracts a plateau value from the correlator in a given range.
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  • Corr.roll periodically shifts the correlator.
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  • Corr.reverse reverses the time ordering of the correlator.
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  • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
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  • Corr.reweight reweights the correlator.
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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).
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For the full API see pyerrors.correlators.Corr.
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Complex valued observables
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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.
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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
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Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
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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
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The Covobs class
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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.
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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.
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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
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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.
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Correlated auxiliary data is defined similarly to above, e.g., via
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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
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where RAP now is a list of two Obs that contains the two correlated parameters.
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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
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o.covobs[k].grad\n
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Error propagation in iterative algorithms
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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.
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Least squares fits
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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.
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Fit functions have to be of the following form
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import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
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It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
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Fits can then be performed via
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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
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where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
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Data stored in Corr objects can be fitted directly using the Corr.fit method.
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my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
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this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
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For fit functions with multiple independent variables the fit function can be of the form
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def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
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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.
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For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
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Total least squares fits
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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.
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For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
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Matrix operations
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pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
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  • inv for the matrix inverse.
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  • cholseky for the Cholesky decomposition.
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  • det for the matrix determinant.
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  • eigh for eigenvalues and eigenvectors of hermitean matrices.
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  • eig for eigenvalues of general matrices.
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  • pinv for the Moore-Penrose pseudoinverse.
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  • svd for the singular-value-decomposition.
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For the full API see pyerrors.linalg.
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Export data
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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:
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  • What observables are stored? Possibly: How exactly are they defined.
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  • How does each single ensemble or external quantity contribute to the error of the observable?
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  • Who did write the file when and on which machine?
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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
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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
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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.
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json.gz format specification
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The first entries of the file provide optional auxiliary information:
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  • 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.
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  • 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.
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  • 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
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The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
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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:
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  • 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.
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  • 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.
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  • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
    • \n
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The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
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  • id, a string that contains the name of the ensemble
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  • replica, an array that contains an entry per replica of the ensemble.
    • \n
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Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
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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.
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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:
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  • id, a string that identifies the covariance matrix
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  • 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.
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  • 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
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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.
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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).
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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.
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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.
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The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.
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Initialization
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A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs
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corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
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A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects
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matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
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\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.
      • \n
    • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
      • \n
    • \n
\n\n
Other Parameters
\n\n
    \n
  • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
    • \n
\n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "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'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
Constructs an NxN Hankel matrix
\n\n
C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
\n\n
Parameters
\n\n
    \n
  • N (int):\nDimension of the Hankel matrix
    • \n
  • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
    • \n
\n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
Periodically shift the correlator by dt timeslices
\n\n
Parameters
\n\n
    \n
  • dt (int):\nnumber of timeslices
    • \n
\n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
Reverse the time ordering of the Corr
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
Thin out a correlator to suppress correlations
\n\n
Parameters
\n\n
    \n
  • spacing (int):\nKeep only every 'spacing'th entry of the correlator
    • \n
  • offset (int):\nOffset the equal spacing
    • \n
\n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
Correlate the correlator with another correlator or Obs
\n\n
Parameters
\n\n
    \n
  • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
    • \n
\n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
Reweight the correlator.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
Return the time symmetry average of the correlator and its partner
\n\n
Parameters
\n\n
    \n
  • partner (Corr):\nTime symmetry partner of the Corr
    • \n
  • parity (int):\nParity quantum number of the correlator, can be +1 or -1
    • \n
\n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
Return the first derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
Return the second derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
Returns the effective mass of the correlator as correlator object
\n\n
Parameters
\n\n
    \n
  • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
    • \n
  • guess (float):\nguess for the root finder, only relevant for the root variant
    • \n
\n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
Fits function to the data
\n\n
Parameters
\n\n
    \n
  • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
    • \n
  • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
    • \n
  • silent (bool):\nDecides whether output is printed to the standard output.
    • \n
\n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
Extract a plateau value from a Corr object
\n\n
Parameters
\n\n
    \n
  • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
    • \n
  • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
    • \n
  • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
    • \n
\n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
Sets the attribute prange of the Corr object.
\n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
Plots the correlator using the tag of the correlator as label if available.
\n\n
Parameters
\n\n
    \n
  • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
    • \n
  • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
    • \n
  • logscale (bool):\nSets y-axis to logscale.
    • \n
  • plateau (Obs):\nPlateau value to be visualized in the figure.
    • \n
  • fit_res (Fit_result):\nFit_result object to be visualized.
    • \n
  • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
    • \n
  • ylabel (str):\nLabel for the y-axis.
    • \n
  • save (str):\npath to file in which the figure should be saved.
    • \n
  • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
    • \n
  • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
    • \n
  • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
    • \n
  • title (string):\nOptional title of the figure.
    • \n
\n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\n
Parameters
\n\n
    \n
  • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
    • \n
\n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
Dumps the Corr into a file of chosen type
\n\n
Parameters
\n\n
    \n
  • filename (str):\nName of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
\n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
Project large correlation matrix to lowest states
\n\n
This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
\n\n
Parameters
\n\n
    \n
  • Ntrunc (int):\nRank of the target matrix.
    • \n
  • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
    • \n
  • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
    • \n
  • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
    • \n
\n\n
Notes
\n\n
We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
Initialize Covobs object.
\n\n
Parameters
\n\n
    \n
  • mean (float):\nMean value of the new Obs
    • \n
  • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
Return the variance (= square of the error) of the Covobs
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
\n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
\n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
\n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
\n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
\n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
Rank-3 epsilon tensor
\n\n
Based on https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
    • \n
\n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
Rank-4 epsilon tensor
\n\n
Extension of https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
    • \n
\n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
Represents fit results.
\n\n
Attributes
\n\n
    \n
  • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
    • \n
  • chisquare_by_dof (float):\nreduced chisquare.
    • \n
  • p_value (float):\np-value of the fit
    • \n
  • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
    • \n
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
\n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x).\n    ```
\n\n
Parameters
\n\n
    \n
  • For an uncombined fit:
    • \n
  • x (list):\nlist of floats.
    • \n
  • y (list):\nlist of Obs.
    • \n
  • func (object):\nfit function, has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • OR For a combined fit:
    • \n
  • x (dict):\ndict of lists.
    • \n
  • y (dict):\ndict of lists of Obs.
    • \n
  • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
    \n\n
    def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
    \n\n
    def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
    • \n
  • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
    • \n
  • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
    • \n
  • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
    • \n
  • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
    • \n
  • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
    • \n
  • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of Obs, or a tuple of lists of Obs
    • \n
  • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
    • \n
  • func (object):\nfunc has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
    • \n
  • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy.
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n\n
Returns
\n\n
    \n
  • fit_parameters (list[Obs]):\nLIist of fitted observables.
    • \n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n\n
For uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\n
Returns
\n\n
    \n
  • err (np.array(Obs)):\nError band for an array of sample values x
    • \n
\n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\n
Jackknife samples
\n\n
For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
Extract generic MCMC data from a bdio file
\n\n
read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • data (List[Obs]):\nExtracted data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
Write Obs to a bdio file according to ADerrors conventions
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • success (int):\nreturns 0 is successful
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
Extract mesons data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n\n
Returns
\n\n
    \n
  • data (dict):\nExtracted meson data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
Extract dSdm data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, kappa)
\n\n
read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML formatted string of the input data
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
Import a list of Obs from a string in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator |is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML string generated from the data
    • \n
\n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
Read hadrons hdf5 file and extract entry based on attributes.
\n\n
Parameters
\n\n
    \n
  • filestem (str):\nFull namestem of the files to read, including the full path.
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • group (str):\nlabel of the group to be extracted.
    • \n
  • attrs (dict or int):\nDictionary containing the attributes. For example
    \n\n
    \n
    attrs = {"gamma_snk": "Gamma5",\n        "gamma_src": "Gamma5"}\n
    \n
    \n\n
    Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
Read hadrons FlowObservables hdf5 file and extract t0
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
Read hadrons DistillationContraction hdf5 files in given directory structure
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
    • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
\n\n
An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\n
Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\n
For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n
array:  Construct an array. 
\nzeros:  Create an array, each element of which is zero. 
\nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
\ndtype:  Create a data-type. 
\nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
\n\n
Notes
\n\n
There are two modes of creating an array using __new__:
\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n
No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\n
Examples
\n\n
These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\n
First mode, buffer is None:
\n\n
\n
>>> 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.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
    • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
\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.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.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
Computes the singular value decomposition of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
Print information about version of python, pyerrors and dependencies.
\n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
pyerrors wrapper for the errorbars method of matplotlib
\n\n
Parameters
\n\n
    \n
  • x (list):\nA list of x-values which can be Obs.
    • \n
  • y (list):\nA list of y-values which can be Obs.
    • \n
  • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
    • \n
\n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
Dump object into pickle file.
\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
    • \n
  • name (str):\nname of the file
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
Load object from pickle file.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n\n
Returns
\n\n
    \n
  • object (Obs):\nLoaded Object
    • \n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
Generate an Obs object with given value, dvalue and name for test purposes
\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
    • \n
  • dvalue (float):\nerror of the Obs to be generated.
    • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
    • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nGenerated Observable
    • \n
\n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
Generate observables with given covariance and autocorrelation times.
\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
    • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
    • \n
  • name (str):\nensemble name for the data to be geneated.
    • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
    • \n
  • samples (int):\nnumber of samples to be generated for each observable.
    • \n
\n\n
Returns
\n\n
    \n
  • corr_obs (list[Obs]):\nGenerated observable list
    • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
Matrix pencil method to extract k energy levels from data
\n\n
Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
    • \n
  • k (int):\nNumber of states to extract (default 1).
    • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
    • \n
\n\n
Returns
\n\n
    \n
  • energy_levels (list[Obs]):\nExtracted energy levels
    • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
Class for a general observable.
\n\n
Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
    • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
    • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
    • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
    • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
Initialize Obs object.
\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
    • \n
  • names (list):\nlist of strings labeling the individual samples
    • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
    • \n
\n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
Output detailed properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
    • \n
\n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
Reweight the obs with given rewighting factors.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
Checks whether the observable is zero within 'sigma' standard errors.
\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
    • \n
  • Works only properly when the gamma method was run.
    • \n
\n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
Checks whether the observable is zero within a given tolerance.
\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
    • \n
\n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
Plot integrated autocorrelation time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
Plot normalized autocorrelation function time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
Plot replica distribution for each ensemble with more than one replicum.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
Plot derived Monte Carlo history for each ensemble
\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
    • \n
\n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
Dump the Obs to a file 'name' of chosen format.
\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
Export jackknife samples from the Obs
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
    • \n
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
Export bootstrap samples from the Obs
\n\n
Parameters
\n\n
    \n
  • samples (int):\nNumber of bootstrap samples to generate.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
    • \n
  • save_rng (str):\nSave the random numbers to a file if a path is specified.
    • \n
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
    • \n
\n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
\n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
Executes the gamma_method for the real and the imaginary part.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
Checks whether both real and imaginary part are zero within machine precision.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
Vectorized version of the gamma_method applicable to lists or arrays of Obs.
\n\n
See docstring of pe.Obs.gamma_method for details.
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
Short version of the vectorized gamma_method.
\n\n
See docstring of pe.Obs.gamma_method for details
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
\n\n
Parameters
\n\n
    \n
  • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
    • \n
  • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
    • \n
  • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
    • \n
\n\n
Notes
\n\n
For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\n
new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
\n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
Reweight a list of observables.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
Correlate two observables.
\n\n
Parameters
\n\n
    \n
  • obs_a (Obs):\nFirst observable
    • \n
  • obs_b (Obs):\nSecond observable
    • \n
\n\n
Notes
\n\n
Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
\n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
Calculates the error covariance matrix of a set of observables.
\n\n
WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
\n\n
The gamma method has to be applied first to all observables.
\n\n
Parameters
\n\n
    \n
  • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
    • \n
  • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
    • \n
  • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
    • \n
  • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
    • \n
\n\n
Notes
\n\n
The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
Imports jackknife samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
\n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
Imports bootstrap samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
    • \n
\n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
Combine all observables in list_of_obs into one new observable
\n\n
Parameters
\n\n
    \n
  • list_of_obs (list):\nlist of the Obs object to be combined
    • \n
\n\n
Notes
\n\n
It is not possible to combine obs which are based on the same replicum
\n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
Create an Obs based on mean(s) and a covariance matrix
\n\n
Parameters
\n\n
    \n
  • mean (list of floats or float):\nN mean value(s) of the new Obs
    • \n
  • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
Finds the root of the function func(x, d) where d is an Obs.
\n\n
Parameters
\n\n
    \n
  • d (Obs):\nObs passed to the function.
    • \n
  • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
    \n\n
    \n
    import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
    \n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nObs valued root of the function.
    • \n
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What is pyerrors?
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pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
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  • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
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  • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
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  • coherent error propagation for data from different Markov chains.
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  • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
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  • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
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More detailed examples can found in the GitHub repository \"badge\".
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If you use pyerrors for research that leads to a publication please consider citing:
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  • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
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  • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
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  • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
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and
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  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
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where applicable.
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There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
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Installation
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Install the most recent release using pip and pypi:
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python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
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Install the most recent release using conda and conda-forge:
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conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
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Install the current develop version:
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python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
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(Also works for any feature branch).
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Basic example
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import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
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The Obs class
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pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
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import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
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Error propagation
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When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
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The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
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import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
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Error estimation
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The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
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my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
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We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
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my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
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If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
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Exponential tails
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Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
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my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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For the full API see pyerrors.obs.Obs.gamma_method.
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Multiple ensembles/replica
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Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
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obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
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Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
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pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
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obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
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Error estimation for multiple ensembles
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In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
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pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
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In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
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Irregular Monte Carlo chains
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Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
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# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
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Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
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Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
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For the full API see pyerrors.obs.Obs.
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Correlators
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When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
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my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
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In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
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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
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The individual entries of a correlator can be accessed via slicing
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print(my_corr[3])\n> 0.3227(33)\n
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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.
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my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
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pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
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  • Corr.gamma_method applies the gamma method to all entries of the correlator.
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  • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
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  • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
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  • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
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  • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
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  • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
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  • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
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  • Corr.plateau extracts a plateau value from the correlator in a given range.
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  • Corr.roll periodically shifts the correlator.
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  • Corr.reverse reverses the time ordering of the correlator.
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  • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
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  • Corr.reweight reweights the correlator.
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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).
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For the full API see pyerrors.correlators.Corr.
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Complex valued observables
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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.
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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
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Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
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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
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The Covobs class
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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.
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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.
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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
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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.
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Correlated auxiliary data is defined similarly to above, e.g., via
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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
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where RAP now is a list of two Obs that contains the two correlated parameters.
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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
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o.covobs[k].grad\n
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Error propagation in iterative algorithms
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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.
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Least squares fits
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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.
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Fit functions have to be of the following form
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import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
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It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
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Fits can then be performed via
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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
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where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
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Data stored in Corr objects can be fitted directly using the Corr.fit method.
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my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
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this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
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For fit functions with multiple independent variables the fit function can be of the form
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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.
      • \n
    • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
      • \n
    • \n
\n\n
Other Parameters
\n\n
    \n
  • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
    • \n
\n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "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'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
Constructs an NxN Hankel matrix
\n\n
C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
\n\n
Parameters
\n\n
    \n
  • N (int):\nDimension of the Hankel matrix
    • \n
  • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
    • \n
\n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
Periodically shift the correlator by dt timeslices
\n\n
Parameters
\n\n
    \n
  • dt (int):\nnumber of timeslices
    • \n
\n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
Reverse the time ordering of the Corr
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
Thin out a correlator to suppress correlations
\n\n
Parameters
\n\n
    \n
  • spacing (int):\nKeep only every 'spacing'th entry of the correlator
    • \n
  • offset (int):\nOffset the equal spacing
    • \n
\n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
Correlate the correlator with another correlator or Obs
\n\n
Parameters
\n\n
    \n
  • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
    • \n
\n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
Reweight the correlator.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
    • \n
\n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
Return the time symmetry average of the correlator and its partner
\n\n
Parameters
\n\n
    \n
  • partner (Corr):\nTime symmetry partner of the Corr
    • \n
  • parity (int):\nParity quantum number of the correlator, can be +1 or -1
    • \n
\n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
Return the first derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
Return the second derivative of the correlator with respect to x0.
\n\n
Parameters
\n\n
    \n
  • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
    • \n
\n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
Returns the effective mass of the correlator as correlator object
\n\n
Parameters
\n\n
    \n
  • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
    • \n
  • guess (float):\nguess for the root finder, only relevant for the root variant
    • \n
\n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
Fits function to the data
\n\n
Parameters
\n\n
    \n
  • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
    • \n
  • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
    • \n
  • silent (bool):\nDecides whether output is printed to the standard output.
    • \n
\n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
Extract a plateau value from a Corr object
\n\n
Parameters
\n\n
    \n
  • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
    • \n
  • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
    • \n
  • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
    • \n
\n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
Sets the attribute prange of the Corr object.
\n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
Plots the correlator using the tag of the correlator as label if available.
\n\n
Parameters
\n\n
    \n
  • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
    • \n
  • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
    • \n
  • logscale (bool):\nSets y-axis to logscale.
    • \n
  • plateau (Obs):\nPlateau value to be visualized in the figure.
    • \n
  • fit_res (Fit_result):\nFit_result object to be visualized.
    • \n
  • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
    • \n
  • ylabel (str):\nLabel for the y-axis.
    • \n
  • save (str):\npath to file in which the figure should be saved.
    • \n
  • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
    • \n
  • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
    • \n
  • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
    • \n
  • title (string):\nOptional title of the figure.
    • \n
\n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\n
Parameters
\n\n
    \n
  • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
    • \n
\n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
Dumps the Corr into a file of chosen type
\n\n
Parameters
\n\n
    \n
  • filename (str):\nName of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
\n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
Project large correlation matrix to lowest states
\n\n
This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
\n\n
Parameters
\n\n
    \n
  • Ntrunc (int):\nRank of the target matrix.
    • \n
  • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
    • \n
  • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
    • \n
  • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
    • \n
\n\n
Notes
\n\n
We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
\n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
Initialize Covobs object.
\n\n
Parameters
\n\n
    \n
  • mean (float):\nMean value of the new Obs
    • \n
  • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
Return the variance (= square of the error) of the Covobs
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
\n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
\n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
\n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
\n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
\n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
Rank-3 epsilon tensor
\n\n
Based on https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
    • \n
\n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
Rank-4 epsilon tensor
\n\n
Extension of https://codegolf.stackexchange.com/a/160375
\n\n
Returns
\n\n
    \n
  • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
    • \n
\n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
Returns gamma matrix in Grid labeling.
\n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
Represents fit results.
\n\n
Attributes
\n\n
    \n
  • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
    • \n
  • chisquare_by_dof (float):\nreduced chisquare.
    • \n
  • p_value (float):\np-value of the fit
    • \n
  • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
    • \n
\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
\n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
Apply the gamma method to all fit parameters
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x).\n    ```
\n\n
Parameters
\n\n
    \n
  • For an uncombined fit:
    • \n
  • x (list):\nlist of floats.
    • \n
  • y (list):\nlist of Obs.
    • \n
  • func (object):\nfit function, has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • OR For a combined fit:
    • \n
  • x (dict):\ndict of lists.
    • \n
  • y (dict):\ndict of lists of Obs.
    • \n
  • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
    \n\n
    def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
    \n\n
    def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
    • \n
  • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
    • \n
  • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
    • \n
  • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
    • \n
  • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
    • \n
  • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
    • \n
  • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\n
Parameters
\n\n
    \n
  • x (list):\nlist of Obs, or a tuple of lists of Obs
    • \n
  • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
    • \n
  • func (object):\nfunc has to be of the form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
    \n
    \n\n
    For multiple x values func can be of the form
    \n\n
    \n
    def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
    • \n
  • silent (bool, optional):\nIf true all output to the console is omitted (default False).
    • \n
  • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
    • \n
  • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
    • \n
  • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
    • \n
\n\n
Notes
\n\n
Based on the orthogonal distance regression module of scipy.
\n\n
Returns
\n\n
    \n
  • output (Fit_result):\nParameters and information on the fitted result.
    • \n
\n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
Performs a linear fit to y = n + m * x and returns two Obs n, m.
\n\n
Parameters
\n\n
    \n
  • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
    • \n
  • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
    • \n
\n\n
Returns
\n\n
    \n
  • fit_parameters (list[Obs]):\nLIist of fitted observables.
    • \n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
Generates a plot which compares the fit to the data and displays the corresponding residuals
\n\n
For uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\n
Returns
\n\n
    \n
  • err (np.array(Obs)):\nError band for an array of sample values x
    • \n
\n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\n
Parameters
\n\n
    \n
  • objects (list):\nList of fit results to include in the analysis (optional).
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
\n\n
Jackknife samples
\n\n
For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
Extract generic MCMC data from a bdio file
\n\n
read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • data (List[Obs]):\nExtracted data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
Write Obs to a bdio file according to ADerrors conventions
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path -- path to the bdio file
    • \n
  • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
\n\n
Returns
\n\n
    \n
  • success (int):\nreturns 0 is successful
    • \n
\n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
Extract mesons data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\n
read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n\n
Returns
\n\n
    \n
  • data (dict):\nExtracted meson data
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
Extract dSdm data from a bdio file and return it as a dictionary
\n\n
The dictionary can be accessed with a tuple consisting of (type, kappa)
\n\n
read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
\n\n
all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\n
Parameters
\n\n
    \n
  • file_path (str):\npath to the bdio file
    • \n
  • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
    • \n
  • start (int):\nThe first configuration to be read (default 1)
    • \n
  • stop (int):\nThe last configuration to be read (default None)
    • \n
  • step (int):\nFixed step size between two measurements (default 1)
    • \n
  • alternative_ensemble_name (str):\nManually overwrite ensemble name
    • \n
\n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML formatted string of the input data
    • \n
\n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
Import a list of Obs from a string in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • content (str):\nXML string containing the data
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically.
\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
    • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
    • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
    • \n
  • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
    • \n
\n\n
Returns
\n\n
    \n
  • res (list[Obs]):\nImported data
    • \n
  • or
    • \n
  • res (dict):\nImported data and meta-data
    • \n
\n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator |is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
\n\n
Returns
\n\n
    \n
  • xml_str (str):\nXML string generated from the data
    • \n
\n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\n
Tags are not written or recovered automatically. The separator | is removed from the replica names.
\n\n
Parameters
\n\n
    \n
  • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
    • \n
  • fname (str):\nFilename of the output file.
    • \n
  • name (str):\nThe name of the observable.
    • \n
  • spec (str):\nOptional string that describes the contents of the file.
    • \n
  • origin (str):\nSpecify where the data has its origin.
    • \n
  • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
    • \n
  • who (str):\nProvide the name of the person that exports the data.
    • \n
  • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
    • \n
  • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
Read hadrons hdf5 file and extract entry based on attributes.
\n\n
Parameters
\n\n
    \n
  • filestem (str):\nFull namestem of the files to read, including the full path.
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • group (str):\nlabel of the group to be extracted.
    • \n
  • attrs (dict or int):\nDictionary containing the attributes. For example
    \n\n
    \n
    attrs = {"gamma_snk": "Gamma5",\n        "gamma_src": "Gamma5"}\n
    \n
    \n\n
    Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
Read hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
    • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
    • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
Read hadrons FlowObservables hdf5 file and extract t0
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
    • \n
  • filestem (str):\nnamestem of the files to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
    • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
    • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
Read hadrons DistillationContraction hdf5 files in given directory structure
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
    • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
    • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
    • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
    • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
    • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
\n\n
An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
\n\n
Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
\n\n
For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
    • \n
  • shape (tuple of ints):\nShape of created array.
    • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
    • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
    • \n
  • offset (int, optional):\nOffset of array data in buffer.
    • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
    • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
    • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
    • \n
  • data (buffer):\nThe array's elements, in memory.
    • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
    • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
    • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
    • \n
  • imag (ndarray):\nImaginary part of the array.
    • \n
  • real (ndarray):\nReal part of the array.
    • \n
  • size (int):\nNumber of elements in the array.
    • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
    • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
    • \n
  • ndim (int):\nThe array's number of dimensions.
    • \n
  • shape (tuple of ints):\nShape of the array.
    • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
    • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
    • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
    • \n
\n\n
See Also
\n\n
array:  Construct an array. 
\nzeros:  Create an array, each element of which is zero. 
\nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
\ndtype:  Create a data-type. 
\nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
\n\n
Notes
\n\n
There are two modes of creating an array using __new__:
\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
    2. \n
  2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
    3. \n
\n\n
No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
\n\n
Examples
\n\n
These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
\n\n
First mode, buffer is None:
\n\n
\n
>>> 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.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
Read sfcf files from given folder structure.
\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
    • \n
  • prefix (str):\nPrefix of the sfcf files.
    • \n
  • name (str):\nName of the correlation function to read.
    • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
    • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
      • \n
    • 'bb' for boundary-boundary
      • \n
    • 'bib' for boundary-inner-boundary
      • \n
    • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
    • \n
  • wf (int):\nID of wave function
    • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
    • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
    • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
    • \n
  • ens_name (str):\nreplaces the name of the ensemble
    • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
    • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
    • \n
  • replica (list):\nlist of replica to be read, default is all
    • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
    • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
    • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
    • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
\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.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.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
Computes the singular value decomposition of a matrix of Obs.
\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
Print information about version of python, pyerrors and dependencies.
\n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
pyerrors wrapper for the errorbars method of matplotlib
\n\n
Parameters
\n\n
    \n
  • x (list):\nA list of x-values which can be Obs.
    • \n
  • y (list):\nA list of y-values which can be Obs.
    • \n
  • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
    • \n
\n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
Dump object into pickle file.
\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
    • \n
  • name (str):\nname of the file
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n\n
Returns
\n\n
    \n
  • None
    • \n
\n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
Load object from pickle file.
\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
    • \n
\n\n
Returns
\n\n
    \n
  • object (Obs):\nLoaded Object
    • \n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
Generate an Obs object with given value, dvalue and name for test purposes
\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
    • \n
  • dvalue (float):\nerror of the Obs to be generated.
    • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
    • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nGenerated Observable
    • \n
\n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
Generate observables with given covariance and autocorrelation times.
\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
    • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
    • \n
  • name (str):\nensemble name for the data to be geneated.
    • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
    • \n
  • samples (int):\nnumber of samples to be generated for each observable.
    • \n
\n\n
Returns
\n\n
    \n
  • corr_obs (list[Obs]):\nGenerated observable list
    • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
Matrix pencil method to extract k energy levels from data
\n\n
Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
    • \n
  • k (int):\nNumber of states to extract (default 1).
    • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
    • \n
\n\n
Returns
\n\n
    \n
  • energy_levels (list[Obs]):\nExtracted energy levels
    • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
Class for a general observable.
\n\n
Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
    • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
    • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
    • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
    • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
    • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
Initialize Obs object.
\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
    • \n
  • names (list):\nlist of strings labeling the individual samples
    • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
    • \n
\n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
Estimate the error and related properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
    • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
    • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
    • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
    • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
Output detailed properties of the Obs.
\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
    • \n
\n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
Reweight the obs with given rewighting factors.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
Checks whether the observable is zero within 'sigma' standard errors.
\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
    • \n
  • Works only properly when the gamma method was run.
    • \n
\n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
Checks whether the observable is zero within a given tolerance.
\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
    • \n
\n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
Plot integrated autocorrelation time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
Plot normalized autocorrelation function time for each ensemble.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
Plot replica distribution for each ensemble with more than one replicum.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
Plot derived Monte Carlo history for each ensemble
\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
    • \n
\n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
    • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
Dump the Obs to a file 'name' of chosen format.
\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
    • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
    • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
    • \n
  • path (str):\nspecifies a custom path for the file (default '.')
    • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
Export jackknife samples from the Obs
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
    • \n
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
Export bootstrap samples from the Obs
\n\n
Parameters
\n\n
    \n
  • samples (int):\nNumber of bootstrap samples to generate.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
    • \n
  • save_rng (str):\nSave the random numbers to a file if a path is specified.
    • \n
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
    • \n
\n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
Class for a complex valued observable.
\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
\n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
Executes the gamma_method for the real and the imaginary part.
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
Checks whether both real and imaginary part are zero within machine precision.
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
Vectorized version of the gamma_method applicable to lists or arrays of Obs.
\n\n
See docstring of pe.Obs.gamma_method for details.
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
Vectorized version of the gamma_method applicable to lists or arrays of Obs.
\n\n
See docstring of pe.Obs.gamma_method for details.
\n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
\n\n
Parameters
\n\n
    \n
  • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
    • \n
  • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
    • \n
  • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
    • \n
\n\n
Notes
\n\n
For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\n
new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
\n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
Reweight a list of observables.
\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
    • \n
  • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
    • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
    • \n
\n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
Correlate two observables.
\n\n
Parameters
\n\n
    \n
  • obs_a (Obs):\nFirst observable
    • \n
  • obs_b (Obs):\nSecond observable
    • \n
\n\n
Notes
\n\n
Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
\n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
Calculates the error covariance matrix of a set of observables.
\n\n
WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
\n\n
The gamma method has to be applied first to all observables.
\n\n
Parameters
\n\n
    \n
  • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
    • \n
  • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
    • \n
  • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
    • \n
  • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
    • \n
\n\n
Notes
\n\n
The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
\n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
Imports jackknife samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
\n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
Imports bootstrap samples and returns an Obs
\n\n
Parameters
\n\n
    \n
  • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
    • \n
  • name (str):\nname of the ensemble the samples are defined on.
    • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
    • \n
\n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
Combine all observables in list_of_obs into one new observable
\n\n
Parameters
\n\n
    \n
  • list_of_obs (list):\nlist of the Obs object to be combined
    • \n
\n\n
Notes
\n\n
It is not possible to combine obs which are based on the same replicum
\n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
Create an Obs based on mean(s) and a covariance matrix
\n\n
Parameters
\n\n
    \n
  • mean (list of floats or float):\nN mean value(s) of the new Obs
    • \n
  • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
    • \n
  • name (str):\nidentifier for the covariance matrix
    • \n
  • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
    • \n
\n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
Finds the root of the function func(x, d) where d is an Obs.
\n\n
Parameters
\n\n
    \n
  • d (Obs):\nObs passed to the function.
    • \n
  • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
    \n\n
    \n
    import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
    \n
    • \n
  • guess (float):\nInitial guess for the minimization.
    • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nObs valued root of the function.
    • \n
\n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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