diff --git a/docs/pyerrors/input/hadrons.html b/docs/pyerrors/input/hadrons.html index 27887597..f3d5e402 100644 --- a/docs/pyerrors/input/hadrons.html +++ b/docs/pyerrors/input/hadrons.html @@ -152,8 +152,8 @@ 55 return filtered_files, idx 56 57 - 58def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None): - 59 """Read hadrons meson hdf5 file and extract the meson labeled 'meson' + 58def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None): + 59 r'''Read hadrons meson hdf5 file and extract the meson labeled 'meson' 60 61 Parameters 62 ----------------- @@ -166,378 +166,396 @@ 69 meson : str 70 label of the meson to be extracted, standard value meson_0 which 71 corresponds to the pseudoscalar pseudoscalar two-point function. - 72 idl : range - 73 If specified only configurations in the given range are read in. - 74 """ - 75 - 76 files, idx = _get_files(path, filestem, idl) - 77 - 78 tree = meson.rsplit('_')[0] - 79 corr_data = [] - 80 infos = [] - 81 for hd5_file in files: - 82 h5file = h5py.File(path + '/' + hd5_file, "r") - 83 if not tree + '/' + meson in h5file: - 84 raise Exception("Entry '" + meson + "' not contained in the files.") - 85 raw_data = h5file[tree + '/' + meson + '/corr'] - 86 real_data = raw_data[:]["re"].astype(np.double) - 87 corr_data.append(real_data) - 88 if not infos: - 89 for k, i in h5file[tree + '/' + meson].attrs.items(): - 90 infos.append(k + ': ' + i[0].decode()) + 72 gammas : tuple of strings + 73 Instrad of a meson label one can also provide a tuple of two strings + 74 indicating the gamma matrices at source and sink. + 75 ("Gamma5", "Gamma5") corresponds to the pseudoscalar pseudoscalar + 76 two-point function. The gammas argument dominateds over meson. + 77 idl : range + 78 If specified only configurations in the given range are read in. + 79 ''' + 80 + 81 files, idx = _get_files(path, filestem, idl) + 82 + 83 tree = meson.rsplit('_')[0] + 84 if gammas is not None: + 85 h5file = h5py.File(path + '/' + files[0], "r") + 86 found_meson = None + 87 for key in h5file[tree].keys(): + 88 if gammas[0] == h5file[tree][key].attrs["gamma_snk"][0].decode() and h5file[tree][key].attrs["gamma_src"][0].decode() == gammas[1]: + 89 found_meson = key + 90 break 91 h5file.close() - 92 corr_data = np.array(corr_data) - 93 - 94 l_obs = [] - 95 for c in corr_data.T: - 96 l_obs.append(Obs([c], [ens_id], idl=[idx])) - 97 - 98 corr = Corr(l_obs) - 99 corr.tag = r", ".join(infos) -100 return corr -101 -102 -103def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None): -104 """Read hadrons DistillationContraction hdf5 files in given directory structure -105 -106 Parameters -107 ----------------- -108 path : str -109 path to the directories to read -110 ens_id : str -111 name of the ensemble, required for internal bookkeeping -112 diagrams : list -113 List of strings of the diagrams to extract, e.g. ["direct", "box", "cross"]. -114 idl : range -115 If specified only configurations in the given range are read in. -116 """ -117 -118 res_dict = {} + 92 if found_meson: + 93 meson = found_meson + 94 else: + 95 raise Exception("Source Sink combination " + str(gammas) + " not found.") + 96 + 97 corr_data = [] + 98 infos = [] + 99 for hd5_file in files: +100 h5file = h5py.File(path + '/' + hd5_file, "r") +101 if not tree + '/' + meson in h5file: +102 raise Exception("Entry '" + meson + "' not contained in the files.") +103 raw_data = h5file[tree + '/' + meson + '/corr'] +104 real_data = raw_data[:]["re"].astype(np.double) +105 corr_data.append(real_data) +106 if not infos: +107 for k, i in h5file[tree + '/' + meson].attrs.items(): +108 infos.append(k + ': ' + i[0].decode()) +109 h5file.close() +110 corr_data = np.array(corr_data) +111 +112 l_obs = [] +113 for c in corr_data.T: +114 l_obs.append(Obs([c], [ens_id], idl=[idx])) +115 +116 corr = Corr(l_obs) +117 corr.tag = r", ".join(infos) +118 return corr 119 -120 directories, idx = _get_files(path, "data", idl) -121 -122 explore_path = Path(path + "/" + directories[0]) +120 +121def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None): +122 """Read hadrons DistillationContraction hdf5 files in given directory structure 123 -124 for explore_file in explore_path.iterdir(): -125 if explore_file.is_file(): -126 stem = explore_file.with_suffix("").with_suffix("").as_posix().split("/")[-1] -127 -128 file_list = [] -129 for dir in directories: -130 tmp_path = Path(path + "/" + dir) -131 file_list.append((tmp_path / stem).as_posix() + tmp_path.suffix + ".h5") -132 -133 corr_data = {} -134 -135 for diagram in diagrams: -136 corr_data[diagram] = [] +124 Parameters +125 ----------------- +126 path : str +127 path to the directories to read +128 ens_id : str +129 name of the ensemble, required for internal bookkeeping +130 diagrams : list +131 List of strings of the diagrams to extract, e.g. ["direct", "box", "cross"]. +132 idl : range +133 If specified only configurations in the given range are read in. +134 """ +135 +136 res_dict = {} 137 -138 for n_file, (hd5_file, n_traj) in enumerate(zip(file_list, list(idx))): -139 h5file = h5py.File(hd5_file) -140 -141 if n_file == 0: -142 if h5file["DistillationContraction/Metadata"].attrs.get("TimeSources")[0].decode() != "0...": -143 raise Exception("Routine is only implemented for files containing inversions on all timeslices.") -144 -145 Nt = h5file["DistillationContraction/Metadata"].attrs.get("Nt")[0] -146 -147 identifier = [] -148 for in_file in range(4): -149 encoded_info = h5file["DistillationContraction/Metadata/DmfInputFiles"].attrs.get("DmfInputFiles_" + str(in_file)) -150 full_info = encoded_info[0].decode().split("/")[-1].replace(".h5", "").split("_") -151 my_tuple = (full_info[0], full_info[1][1:], full_info[2], full_info[3]) -152 identifier.append(my_tuple) -153 identifier = tuple(identifier) -154 # "DistillationContraction/Metadata/DmfSuffix" contains info about different quarks, irrelevant in the SU(3) case. +138 directories, idx = _get_files(path, "data", idl) +139 +140 explore_path = Path(path + "/" + directories[0]) +141 +142 for explore_file in explore_path.iterdir(): +143 if explore_file.is_file(): +144 stem = explore_file.with_suffix("").with_suffix("").as_posix().split("/")[-1] +145 +146 file_list = [] +147 for dir in directories: +148 tmp_path = Path(path + "/" + dir) +149 file_list.append((tmp_path / stem).as_posix() + tmp_path.suffix + ".h5") +150 +151 corr_data = {} +152 +153 for diagram in diagrams: +154 corr_data[diagram] = [] 155 -156 check_traj = h5file["DistillationContraction/Metadata"].attrs.get("Traj")[0] -157 -158 assert check_traj == n_traj -159 -160 for diagram in diagrams: -161 real_data = np.zeros(Nt) -162 for x0 in range(Nt): -163 raw_data = h5file["DistillationContraction/Correlators/" + diagram + "/" + str(x0)] -164 real_data += np.roll(raw_data[:]["re"].astype(np.double), -x0) -165 real_data /= Nt -166 -167 corr_data[diagram].append(real_data) -168 h5file.close() -169 -170 res_dict[str(identifier)] = {} -171 -172 for diagram in diagrams: +156 for n_file, (hd5_file, n_traj) in enumerate(zip(file_list, list(idx))): +157 h5file = h5py.File(hd5_file) +158 +159 if n_file == 0: +160 if h5file["DistillationContraction/Metadata"].attrs.get("TimeSources")[0].decode() != "0...": +161 raise Exception("Routine is only implemented for files containing inversions on all timeslices.") +162 +163 Nt = h5file["DistillationContraction/Metadata"].attrs.get("Nt")[0] +164 +165 identifier = [] +166 for in_file in range(4): +167 encoded_info = h5file["DistillationContraction/Metadata/DmfInputFiles"].attrs.get("DmfInputFiles_" + str(in_file)) +168 full_info = encoded_info[0].decode().split("/")[-1].replace(".h5", "").split("_") +169 my_tuple = (full_info[0], full_info[1][1:], full_info[2], full_info[3]) +170 identifier.append(my_tuple) +171 identifier = tuple(identifier) +172 # "DistillationContraction/Metadata/DmfSuffix" contains info about different quarks, irrelevant in the SU(3) case. 173 -174 tmp_data = np.array(corr_data[diagram]) +174 check_traj = h5file["DistillationContraction/Metadata"].attrs.get("Traj")[0] 175 -176 l_obs = [] -177 for c in tmp_data.T: -178 l_obs.append(Obs([c], [ens_id], idl=[idx])) -179 -180 corr = Corr(l_obs) -181 corr.tag = str(identifier) -182 -183 res_dict[str(identifier)][diagram] = corr +176 assert check_traj == n_traj +177 +178 for diagram in diagrams: +179 real_data = np.zeros(Nt) +180 for x0 in range(Nt): +181 raw_data = h5file["DistillationContraction/Correlators/" + diagram + "/" + str(x0)] +182 real_data += np.roll(raw_data[:]["re"].astype(np.double), -x0) +183 real_data /= Nt 184 -185 return res_dict -186 +185 corr_data[diagram].append(real_data) +186 h5file.close() 187 -188class Npr_matrix(np.ndarray): +188 res_dict[str(identifier)] = {} 189 -190 def __new__(cls, input_array, mom_in=None, mom_out=None): -191 obj = np.asarray(input_array).view(cls) -192 obj.mom_in = mom_in -193 obj.mom_out = mom_out -194 return obj -195 -196 @property -197 def g5H(self): -198 """Gamma_5 hermitean conjugate -199 -200 Uses the fact that the propagator is gamma5 hermitean, so just the -201 in and out momenta of the propagator are exchanged. -202 """ -203 return Npr_matrix(self, -204 mom_in=self.mom_out, -205 mom_out=self.mom_in) -206 -207 def _propagate_mom(self, other, name): -208 s_mom = getattr(self, name, None) -209 o_mom = getattr(other, name, None) -210 if s_mom is not None and o_mom is not None: -211 if not np.allclose(s_mom, o_mom): -212 raise Exception(name + ' does not match.') -213 return o_mom if o_mom is not None else s_mom -214 -215 def __matmul__(self, other): -216 return self.__new__(Npr_matrix, -217 super().__matmul__(other), -218 self._propagate_mom(other, 'mom_in'), -219 self._propagate_mom(other, 'mom_out')) -220 -221 def __array_finalize__(self, obj): -222 if obj is None: -223 return -224 self.mom_in = getattr(obj, 'mom_in', None) -225 self.mom_out = getattr(obj, 'mom_out', None) -226 -227 -228def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None): -229 """Read hadrons ExternalLeg hdf5 file and output an array of CObs -230 -231 Parameters -232 ---------- -233 path : str -234 path to the files to read -235 filestem : str -236 namestem of the files to read -237 ens_id : str -238 name of the ensemble, required for internal bookkeeping -239 idl : range -240 If specified only configurations in the given range are read in. -241 """ -242 -243 files, idx = _get_files(path, filestem, idl) +190 for diagram in diagrams: +191 +192 tmp_data = np.array(corr_data[diagram]) +193 +194 l_obs = [] +195 for c in tmp_data.T: +196 l_obs.append(Obs([c], [ens_id], idl=[idx])) +197 +198 corr = Corr(l_obs) +199 corr.tag = str(identifier) +200 +201 res_dict[str(identifier)][diagram] = corr +202 +203 return res_dict +204 +205 +206class Npr_matrix(np.ndarray): +207 +208 def __new__(cls, input_array, mom_in=None, mom_out=None): +209 obj = np.asarray(input_array).view(cls) +210 obj.mom_in = mom_in +211 obj.mom_out = mom_out +212 return obj +213 +214 @property +215 def g5H(self): +216 """Gamma_5 hermitean conjugate +217 +218 Uses the fact that the propagator is gamma5 hermitean, so just the +219 in and out momenta of the propagator are exchanged. +220 """ +221 return Npr_matrix(self, +222 mom_in=self.mom_out, +223 mom_out=self.mom_in) +224 +225 def _propagate_mom(self, other, name): +226 s_mom = getattr(self, name, None) +227 o_mom = getattr(other, name, None) +228 if s_mom is not None and o_mom is not None: +229 if not np.allclose(s_mom, o_mom): +230 raise Exception(name + ' does not match.') +231 return o_mom if o_mom is not None else s_mom +232 +233 def __matmul__(self, other): +234 return self.__new__(Npr_matrix, +235 super().__matmul__(other), +236 self._propagate_mom(other, 'mom_in'), +237 self._propagate_mom(other, 'mom_out')) +238 +239 def __array_finalize__(self, obj): +240 if obj is None: +241 return +242 self.mom_in = getattr(obj, 'mom_in', None) +243 self.mom_out = getattr(obj, 'mom_out', None) 244 -245 mom = None -246 -247 corr_data = [] -248 for hd5_file in files: -249 file = h5py.File(path + '/' + hd5_file, "r") -250 raw_data = file['ExternalLeg/corr'][0][0].view('complex') -251 corr_data.append(raw_data) -252 if mom is None: -253 mom = np.array(str(file['ExternalLeg/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float) -254 file.close() -255 corr_data = np.array(corr_data) -256 -257 rolled_array = np.rollaxis(corr_data, 0, 5) -258 -259 matrix = np.empty((rolled_array.shape[:-1]), dtype=object) -260 for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]): -261 real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx]) -262 imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx]) -263 matrix[si, sj, ci, cj] = CObs(real, imag) +245 +246def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None): +247 """Read hadrons ExternalLeg hdf5 file and output an array of CObs +248 +249 Parameters +250 ---------- +251 path : str +252 path to the files to read +253 filestem : str +254 namestem of the files to read +255 ens_id : str +256 name of the ensemble, required for internal bookkeeping +257 idl : range +258 If specified only configurations in the given range are read in. +259 """ +260 +261 files, idx = _get_files(path, filestem, idl) +262 +263 mom = None 264 -265 return Npr_matrix(matrix, mom_in=mom) -266 -267 -268def read_Bilinear_hd5(path, filestem, ens_id, idl=None): -269 """Read hadrons Bilinear hdf5 file and output an array of CObs -270 -271 Parameters -272 ---------- -273 path : str -274 path to the files to read -275 filestem : str -276 namestem of the files to read -277 ens_id : str -278 name of the ensemble, required for internal bookkeeping -279 idl : range -280 If specified only configurations in the given range are read in. -281 """ +265 corr_data = [] +266 for hd5_file in files: +267 file = h5py.File(path + '/' + hd5_file, "r") +268 raw_data = file['ExternalLeg/corr'][0][0].view('complex') +269 corr_data.append(raw_data) +270 if mom is None: +271 mom = np.array(str(file['ExternalLeg/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float) +272 file.close() +273 corr_data = np.array(corr_data) +274 +275 rolled_array = np.rollaxis(corr_data, 0, 5) +276 +277 matrix = np.empty((rolled_array.shape[:-1]), dtype=object) +278 for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]): +279 real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx]) +280 imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx]) +281 matrix[si, sj, ci, cj] = CObs(real, imag) 282 -283 files, idx = _get_files(path, filestem, idl) +283 return Npr_matrix(matrix, mom_in=mom) 284 -285 mom_in = None -286 mom_out = None -287 -288 corr_data = {} -289 for hd5_file in files: -290 file = h5py.File(path + '/' + hd5_file, "r") -291 for i in range(16): -292 name = file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['gamma'][0].decode('UTF-8') -293 if name not in corr_data: -294 corr_data[name] = [] -295 raw_data = file['Bilinear/Bilinear_' + str(i) + '/corr'][0][0].view('complex') -296 corr_data[name].append(raw_data) -297 if mom_in is None: -298 mom_in = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float) -299 if mom_out is None: -300 mom_out = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float) -301 -302 file.close() -303 -304 result_dict = {} +285 +286def read_Bilinear_hd5(path, filestem, ens_id, idl=None): +287 """Read hadrons Bilinear hdf5 file and output an array of CObs +288 +289 Parameters +290 ---------- +291 path : str +292 path to the files to read +293 filestem : str +294 namestem of the files to read +295 ens_id : str +296 name of the ensemble, required for internal bookkeeping +297 idl : range +298 If specified only configurations in the given range are read in. +299 """ +300 +301 files, idx = _get_files(path, filestem, idl) +302 +303 mom_in = None +304 mom_out = None 305 -306 for key, data in corr_data.items(): -307 local_data = np.array(data) -308 -309 rolled_array = np.rollaxis(local_data, 0, 5) -310 -311 matrix = np.empty((rolled_array.shape[:-1]), dtype=object) -312 for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]): -313 real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx]) -314 imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx]) -315 matrix[si, sj, ci, cj] = CObs(real, imag) -316 -317 result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out) -318 -319 return result_dict -320 +306 corr_data = {} +307 for hd5_file in files: +308 file = h5py.File(path + '/' + hd5_file, "r") +309 for i in range(16): +310 name = file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['gamma'][0].decode('UTF-8') +311 if name not in corr_data: +312 corr_data[name] = [] +313 raw_data = file['Bilinear/Bilinear_' + str(i) + '/corr'][0][0].view('complex') +314 corr_data[name].append(raw_data) +315 if mom_in is None: +316 mom_in = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float) +317 if mom_out is None: +318 mom_out = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float) +319 +320 file.close() 321 -322def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]): -323 """Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs -324 -325 Parameters -326 ---------- -327 path : str -328 path to the files to read -329 filestem : str -330 namestem of the files to read -331 ens_id : str -332 name of the ensemble, required for internal bookkeeping -333 idl : range -334 If specified only configurations in the given range are read in. -335 vertices : list -336 Vertex functions to be extracted. -337 """ +322 result_dict = {} +323 +324 for key, data in corr_data.items(): +325 local_data = np.array(data) +326 +327 rolled_array = np.rollaxis(local_data, 0, 5) +328 +329 matrix = np.empty((rolled_array.shape[:-1]), dtype=object) +330 for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]): +331 real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx]) +332 imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx]) +333 matrix[si, sj, ci, cj] = CObs(real, imag) +334 +335 result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out) +336 +337 return result_dict 338 -339 files, idx = _get_files(path, filestem, idl) -340 -341 mom_in = None -342 mom_out = None -343 -344 vertex_names = [] -345 for vertex in vertices: -346 vertex_names += _get_lorentz_names(vertex) -347 -348 corr_data = {} -349 -350 tree = 'FourQuarkFullyConnected/FourQuarkFullyConnected_' -351 -352 for hd5_file in files: -353 file = h5py.File(path + '/' + hd5_file, "r") -354 -355 for i in range(32): -356 name = (file[tree + str(i) + '/info'].attrs['gammaA'][0].decode('UTF-8'), file[tree + str(i) + '/info'].attrs['gammaB'][0].decode('UTF-8')) -357 if name in vertex_names: -358 if name not in corr_data: -359 corr_data[name] = [] -360 raw_data = file[tree + str(i) + '/corr'][0][0].view('complex') -361 corr_data[name].append(raw_data) -362 if mom_in is None: -363 mom_in = np.array(str(file[tree + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float) -364 if mom_out is None: -365 mom_out = np.array(str(file[tree + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float) -366 -367 file.close() -368 -369 intermediate_dict = {} -370 -371 for vertex in vertices: -372 lorentz_names = _get_lorentz_names(vertex) -373 for v_name in lorentz_names: -374 if v_name in [('SigmaXY', 'SigmaZT'), -375 ('SigmaXT', 'SigmaYZ'), -376 ('SigmaYZ', 'SigmaXT'), -377 ('SigmaZT', 'SigmaXY')]: -378 sign = -1 -379 else: -380 sign = 1 -381 if vertex not in intermediate_dict: -382 intermediate_dict[vertex] = sign * np.array(corr_data[v_name]) -383 else: -384 intermediate_dict[vertex] += sign * np.array(corr_data[v_name]) -385 -386 result_dict = {} -387 -388 for key, data in intermediate_dict.items(): -389 -390 rolled_array = np.moveaxis(data, 0, 8) -391 -392 matrix = np.empty((rolled_array.shape[:-1]), dtype=object) -393 for index in np.ndindex(rolled_array.shape[:-1]): -394 real = Obs([rolled_array[index].real], [ens_id], idl=[idx]) -395 imag = Obs([rolled_array[index].imag], [ens_id], idl=[idx]) -396 matrix[index] = CObs(real, imag) -397 -398 result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out) -399 -400 return result_dict -401 -402 -403def _get_lorentz_names(name): -404 lorentz_index = ['X', 'Y', 'Z', 'T'] +339 +340def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]): +341 """Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs +342 +343 Parameters +344 ---------- +345 path : str +346 path to the files to read +347 filestem : str +348 namestem of the files to read +349 ens_id : str +350 name of the ensemble, required for internal bookkeeping +351 idl : range +352 If specified only configurations in the given range are read in. +353 vertices : list +354 Vertex functions to be extracted. +355 """ +356 +357 files, idx = _get_files(path, filestem, idl) +358 +359 mom_in = None +360 mom_out = None +361 +362 vertex_names = [] +363 for vertex in vertices: +364 vertex_names += _get_lorentz_names(vertex) +365 +366 corr_data = {} +367 +368 tree = 'FourQuarkFullyConnected/FourQuarkFullyConnected_' +369 +370 for hd5_file in files: +371 file = h5py.File(path + '/' + hd5_file, "r") +372 +373 for i in range(32): +374 name = (file[tree + str(i) + '/info'].attrs['gammaA'][0].decode('UTF-8'), file[tree + str(i) + '/info'].attrs['gammaB'][0].decode('UTF-8')) +375 if name in vertex_names: +376 if name not in corr_data: +377 corr_data[name] = [] +378 raw_data = file[tree + str(i) + '/corr'][0][0].view('complex') +379 corr_data[name].append(raw_data) +380 if mom_in is None: +381 mom_in = np.array(str(file[tree + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float) +382 if mom_out is None: +383 mom_out = np.array(str(file[tree + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float) +384 +385 file.close() +386 +387 intermediate_dict = {} +388 +389 for vertex in vertices: +390 lorentz_names = _get_lorentz_names(vertex) +391 for v_name in lorentz_names: +392 if v_name in [('SigmaXY', 'SigmaZT'), +393 ('SigmaXT', 'SigmaYZ'), +394 ('SigmaYZ', 'SigmaXT'), +395 ('SigmaZT', 'SigmaXY')]: +396 sign = -1 +397 else: +398 sign = 1 +399 if vertex not in intermediate_dict: +400 intermediate_dict[vertex] = sign * np.array(corr_data[v_name]) +401 else: +402 intermediate_dict[vertex] += sign * np.array(corr_data[v_name]) +403 +404 result_dict = {} 405 -406 res = [] +406 for key, data in intermediate_dict.items(): 407 -408 if name == "TT": -409 for i in range(4): -410 for j in range(i + 1, 4): -411 res.append(("Sigma" + lorentz_index[i] + lorentz_index[j], "Sigma" + lorentz_index[i] + lorentz_index[j])) -412 return res -413 -414 if name == "TTtilde": -415 for i in range(4): -416 for j in range(i + 1, 4): -417 for k in range(4): -418 for o in range(k + 1, 4): -419 fac = epsilon_tensor_rank4(i, j, k, o) -420 if not np.isclose(fac, 0.0): -421 res.append(("Sigma" + lorentz_index[i] + lorentz_index[j], "Sigma" + lorentz_index[k] + lorentz_index[o])) -422 return res +408 rolled_array = np.moveaxis(data, 0, 8) +409 +410 matrix = np.empty((rolled_array.shape[:-1]), dtype=object) +411 for index in np.ndindex(rolled_array.shape[:-1]): +412 real = Obs([rolled_array[index].real], [ens_id], idl=[idx]) +413 imag = Obs([rolled_array[index].imag], [ens_id], idl=[idx]) +414 matrix[index] = CObs(real, imag) +415 +416 result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out) +417 +418 return result_dict +419 +420 +421def _get_lorentz_names(name): +422 lorentz_index = ['X', 'Y', 'Z', 'T'] 423 -424 assert len(name) == 2 +424 res = [] 425 -426 if 'S' in name or 'P' in name: -427 if not set(name) <= set(['S', 'P']): -428 raise Exception("'" + name + "' is not a Lorentz scalar") -429 -430 g_names = {'S': 'Identity', -431 'P': 'Gamma5'} -432 -433 res.append((g_names[name[0]], g_names[name[1]])) -434 -435 else: -436 if not set(name) <= set(['V', 'A']): -437 raise Exception("'" + name + "' is not a Lorentz scalar") -438 -439 for ind in lorentz_index: -440 res.append(('Gamma' + ind + (name[0] == 'A') * 'Gamma5', -441 'Gamma' + ind + (name[1] == 'A') * 'Gamma5')) -442 -443 return res +426 if name == "TT": +427 for i in range(4): +428 for j in range(i + 1, 4): +429 res.append(("Sigma" + lorentz_index[i] + lorentz_index[j], "Sigma" + lorentz_index[i] + lorentz_index[j])) +430 return res +431 +432 if name == "TTtilde": +433 for i in range(4): +434 for j in range(i + 1, 4): +435 for k in range(4): +436 for o in range(k + 1, 4): +437 fac = epsilon_tensor_rank4(i, j, k, o) +438 if not np.isclose(fac, 0.0): +439 res.append(("Sigma" + lorentz_index[i] + lorentz_index[j], "Sigma" + lorentz_index[k] + lorentz_index[o])) +440 return res +441 +442 assert len(name) == 2 +443 +444 if 'S' in name or 'P' in name: +445 if not set(name) <= set(['S', 'P']): +446 raise Exception("'" + name + "' is not a Lorentz scalar") +447 +448 g_names = {'S': 'Identity', +449 'P': 'Gamma5'} +450 +451 res.append((g_names[name[0]], g_names[name[1]])) +452 +453 else: +454 if not set(name) <= set(['V', 'A']): +455 raise Exception("'" + name + "' is not a Lorentz scalar") +456 +457 for ind in lorentz_index: +458 res.append(('Gamma' + ind + (name[0] == 'A') * 'Gamma5', +459 'Gamma' + ind + (name[1] == 'A') * 'Gamma5')) +460 +461 return res @@ -547,14 +565,14 @@
def - read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None) + read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)
- 
 59def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None):
- 60    """Read hadrons meson hdf5 file and extract the meson labeled 'meson'
+            
 59def read_meson_hd5(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):
+ 60    r'''Read hadrons meson hdf5 file and extract the meson labeled 'meson'
  61
  62    Parameters
  63    -----------------
@@ -567,35 +585,53 @@
  70    meson : str
  71        label of the meson to be extracted, standard value meson_0 which
  72        corresponds to the pseudoscalar pseudoscalar two-point function.
- 73    idl : range
- 74        If specified only configurations in the given range are read in.
- 75    """
- 76
- 77    files, idx = _get_files(path, filestem, idl)
- 78
- 79    tree = meson.rsplit('_')[0]
- 80    corr_data = []
- 81    infos = []
- 82    for hd5_file in files:
- 83        h5file = h5py.File(path + '/' + hd5_file, "r")
- 84        if not tree + '/' + meson in h5file:
- 85            raise Exception("Entry '" + meson + "' not contained in the files.")
- 86        raw_data = h5file[tree + '/' + meson + '/corr']
- 87        real_data = raw_data[:]["re"].astype(np.double)
- 88        corr_data.append(real_data)
- 89        if not infos:
- 90            for k, i in h5file[tree + '/' + meson].attrs.items():
- 91                infos.append(k + ': ' + i[0].decode())
+ 73    gammas : tuple of strings
+ 74        Instrad of a meson label one can also provide a tuple of two strings
+ 75        indicating the gamma matrices at source and sink.
+ 76        ("Gamma5", "Gamma5") corresponds to the pseudoscalar pseudoscalar
+ 77        two-point function. The gammas argument dominateds over meson.
+ 78    idl : range
+ 79        If specified only configurations in the given range are read in.
+ 80    '''
+ 81
+ 82    files, idx = _get_files(path, filestem, idl)
+ 83
+ 84    tree = meson.rsplit('_')[0]
+ 85    if gammas is not None:
+ 86        h5file = h5py.File(path + '/' + files[0], "r")
+ 87        found_meson = None
+ 88        for key in h5file[tree].keys():
+ 89            if gammas[0] == h5file[tree][key].attrs["gamma_snk"][0].decode() and h5file[tree][key].attrs["gamma_src"][0].decode() == gammas[1]:
+ 90                found_meson = key
+ 91                break
  92        h5file.close()
- 93    corr_data = np.array(corr_data)
- 94
- 95    l_obs = []
- 96    for c in corr_data.T:
- 97        l_obs.append(Obs([c], [ens_id], idl=[idx]))
- 98
- 99    corr = Corr(l_obs)
-100    corr.tag = r", ".join(infos)
-101    return corr
+ 93        if found_meson:
+ 94            meson = found_meson
+ 95        else:
+ 96            raise Exception("Source Sink combination " + str(gammas) + " not found.")
+ 97
+ 98    corr_data = []
+ 99    infos = []
+100    for hd5_file in files:
+101        h5file = h5py.File(path + '/' + hd5_file, "r")
+102        if not tree + '/' + meson in h5file:
+103            raise Exception("Entry '" + meson + "' not contained in the files.")
+104        raw_data = h5file[tree + '/' + meson + '/corr']
+105        real_data = raw_data[:]["re"].astype(np.double)
+106        corr_data.append(real_data)
+107        if not infos:
+108            for k, i in h5file[tree + '/' + meson].attrs.items():
+109                infos.append(k + ': ' + i[0].decode())
+110        h5file.close()
+111    corr_data = np.array(corr_data)
+112
+113    l_obs = []
+114    for c in corr_data.T:
+115        l_obs.append(Obs([c], [ens_id], idl=[idx]))
+116
+117    corr = Corr(l_obs)
+118    corr.tag = r", ".join(infos)
+119    return corr
 

 
 
@@ -613,6 +649,11 @@ name of the ensemble, required for internal bookkeeping
 
  • meson (str):
 label of the meson to be extracted, standard value meson_0 which
 corresponds to the pseudoscalar pseudoscalar two-point function.
    • 
+
  • gammas (tuple of strings):
+Instrad of a meson label one can also provide a tuple of two strings
+indicating the gamma matrices at source and sink.
+("Gamma5", "Gamma5") corresponds to the pseudoscalar pseudoscalar
+two-point function. The gammas argument dominateds over meson.
    • 
 
  • idl (range):
 If specified only configurations in the given range are read in.
    • 
 
@@ -631,89 +672,89 @@ If specified only configurations in the given range are read in.
    - 
    104def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None):
-105    """Read hadrons DistillationContraction hdf5 files in given directory structure
-106
-107    Parameters
-108    -----------------
-109    path : str
-110        path to the directories to read
-111    ens_id : str
-112        name of the ensemble, required for internal bookkeeping
-113    diagrams : list
-114        List of strings of the diagrams to extract, e.g. ["direct", "box", "cross"].
-115    idl : range
-116        If specified only configurations in the given range are read in.
-117    """
-118
-119    res_dict = {}
-120
-121    directories, idx = _get_files(path, "data", idl)
-122
-123    explore_path = Path(path + "/" + directories[0])
+            
    122def read_DistillationContraction_hd5(path, ens_id, diagrams=["direct"], idl=None):
+123    """Read hadrons DistillationContraction hdf5 files in given directory structure
 124
-125    for explore_file in explore_path.iterdir():
-126        if explore_file.is_file():
-127            stem = explore_file.with_suffix("").with_suffix("").as_posix().split("/")[-1]
-128
-129        file_list = []
-130        for dir in directories:
-131            tmp_path = Path(path + "/" + dir)
-132            file_list.append((tmp_path / stem).as_posix() + tmp_path.suffix + ".h5")
-133
-134        corr_data = {}
-135
-136        for diagram in diagrams:
-137            corr_data[diagram] = []
+125    Parameters
+126    -----------------
+127    path : str
+128        path to the directories to read
+129    ens_id : str
+130        name of the ensemble, required for internal bookkeeping
+131    diagrams : list
+132        List of strings of the diagrams to extract, e.g. ["direct", "box", "cross"].
+133    idl : range
+134        If specified only configurations in the given range are read in.
+135    """
+136
+137    res_dict = {}
 138
-139        for n_file, (hd5_file, n_traj) in enumerate(zip(file_list, list(idx))):
-140            h5file = h5py.File(hd5_file)
-141
-142            if n_file == 0:
-143                if h5file["DistillationContraction/Metadata"].attrs.get("TimeSources")[0].decode() != "0...":
-144                    raise Exception("Routine is only implemented for files containing inversions on all timeslices.")
-145
-146                Nt = h5file["DistillationContraction/Metadata"].attrs.get("Nt")[0]
-147
-148                identifier = []
-149                for in_file in range(4):
-150                    encoded_info = h5file["DistillationContraction/Metadata/DmfInputFiles"].attrs.get("DmfInputFiles_" + str(in_file))
-151                    full_info = encoded_info[0].decode().split("/")[-1].replace(".h5", "").split("_")
-152                    my_tuple = (full_info[0], full_info[1][1:], full_info[2], full_info[3])
-153                    identifier.append(my_tuple)
-154                identifier = tuple(identifier)
-155                # "DistillationContraction/Metadata/DmfSuffix" contains info about different quarks, irrelevant in the SU(3) case.
+139    directories, idx = _get_files(path, "data", idl)
+140
+141    explore_path = Path(path + "/" + directories[0])
+142
+143    for explore_file in explore_path.iterdir():
+144        if explore_file.is_file():
+145            stem = explore_file.with_suffix("").with_suffix("").as_posix().split("/")[-1]
+146
+147        file_list = []
+148        for dir in directories:
+149            tmp_path = Path(path + "/" + dir)
+150            file_list.append((tmp_path / stem).as_posix() + tmp_path.suffix + ".h5")
+151
+152        corr_data = {}
+153
+154        for diagram in diagrams:
+155            corr_data[diagram] = []
 156
-157            check_traj = h5file["DistillationContraction/Metadata"].attrs.get("Traj")[0]
-158
-159            assert check_traj == n_traj
-160
-161            for diagram in diagrams:
-162                real_data = np.zeros(Nt)
-163                for x0 in range(Nt):
-164                    raw_data = h5file["DistillationContraction/Correlators/" + diagram + "/" + str(x0)]
-165                    real_data += np.roll(raw_data[:]["re"].astype(np.double), -x0)
-166                real_data /= Nt
-167
-168                corr_data[diagram].append(real_data)
-169            h5file.close()
-170
-171        res_dict[str(identifier)] = {}
-172
-173        for diagram in diagrams:
+157        for n_file, (hd5_file, n_traj) in enumerate(zip(file_list, list(idx))):
+158            h5file = h5py.File(hd5_file)
+159
+160            if n_file == 0:
+161                if h5file["DistillationContraction/Metadata"].attrs.get("TimeSources")[0].decode() != "0...":
+162                    raise Exception("Routine is only implemented for files containing inversions on all timeslices.")
+163
+164                Nt = h5file["DistillationContraction/Metadata"].attrs.get("Nt")[0]
+165
+166                identifier = []
+167                for in_file in range(4):
+168                    encoded_info = h5file["DistillationContraction/Metadata/DmfInputFiles"].attrs.get("DmfInputFiles_" + str(in_file))
+169                    full_info = encoded_info[0].decode().split("/")[-1].replace(".h5", "").split("_")
+170                    my_tuple = (full_info[0], full_info[1][1:], full_info[2], full_info[3])
+171                    identifier.append(my_tuple)
+172                identifier = tuple(identifier)
+173                # "DistillationContraction/Metadata/DmfSuffix" contains info about different quarks, irrelevant in the SU(3) case.
 174
-175            tmp_data = np.array(corr_data[diagram])
+175            check_traj = h5file["DistillationContraction/Metadata"].attrs.get("Traj")[0]
 176
-177            l_obs = []
-178            for c in tmp_data.T:
-179                l_obs.append(Obs([c], [ens_id], idl=[idx]))
-180
-181            corr = Corr(l_obs)
-182            corr.tag = str(identifier)
-183
-184            res_dict[str(identifier)][diagram] = corr
+177            assert check_traj == n_traj
+178
+179            for diagram in diagrams:
+180                real_data = np.zeros(Nt)
+181                for x0 in range(Nt):
+182                    raw_data = h5file["DistillationContraction/Correlators/" + diagram + "/" + str(x0)]
+183                    real_data += np.roll(raw_data[:]["re"].astype(np.double), -x0)
+184                real_data /= Nt
 185
-186    return res_dict
+186                corr_data[diagram].append(real_data)
+187            h5file.close()
+188
+189        res_dict[str(identifier)] = {}
+190
+191        for diagram in diagrams:
+192
+193            tmp_data = np.array(corr_data[diagram])
+194
+195            l_obs = []
+196            for c in tmp_data.T:
+197                l_obs.append(Obs([c], [ens_id], idl=[idx]))
+198
+199            corr = Corr(l_obs)
+200            corr.tag = str(identifier)
+201
+202            res_dict[str(identifier)][diagram] = corr
+203
+204    return res_dict
 
    
 
 
@@ -746,44 +787,44 @@ If specified only configurations in the given range are read in.
    - 
    189class Npr_matrix(np.ndarray):
-190
-191    def __new__(cls, input_array, mom_in=None, mom_out=None):
-192        obj = np.asarray(input_array).view(cls)
-193        obj.mom_in = mom_in
-194        obj.mom_out = mom_out
-195        return obj
-196
-197    @property
-198    def g5H(self):
-199        """Gamma_5 hermitean conjugate
-200
-201        Uses the fact that the propagator is gamma5 hermitean, so just the
-202        in and out momenta of the propagator are exchanged.
-203        """
-204        return Npr_matrix(self,
-205                          mom_in=self.mom_out,
-206                          mom_out=self.mom_in)
-207
-208    def _propagate_mom(self, other, name):
-209        s_mom = getattr(self, name, None)
-210        o_mom = getattr(other, name, None)
-211        if s_mom is not None and o_mom is not None:
-212            if not np.allclose(s_mom, o_mom):
-213                raise Exception(name + ' does not match.')
-214        return o_mom if o_mom is not None else s_mom
-215
-216    def __matmul__(self, other):
-217        return self.__new__(Npr_matrix,
-218                            super().__matmul__(other),
-219                            self._propagate_mom(other, 'mom_in'),
-220                            self._propagate_mom(other, 'mom_out'))
-221
-222    def __array_finalize__(self, obj):
-223        if obj is None:
-224            return
-225        self.mom_in = getattr(obj, 'mom_in', None)
-226        self.mom_out = getattr(obj, 'mom_out', None)
+            
    207class Npr_matrix(np.ndarray):
+208
+209    def __new__(cls, input_array, mom_in=None, mom_out=None):
+210        obj = np.asarray(input_array).view(cls)
+211        obj.mom_in = mom_in
+212        obj.mom_out = mom_out
+213        return obj
+214
+215    @property
+216    def g5H(self):
+217        """Gamma_5 hermitean conjugate
+218
+219        Uses the fact that the propagator is gamma5 hermitean, so just the
+220        in and out momenta of the propagator are exchanged.
+221        """
+222        return Npr_matrix(self,
+223                          mom_in=self.mom_out,
+224                          mom_out=self.mom_in)
+225
+226    def _propagate_mom(self, other, name):
+227        s_mom = getattr(self, name, None)
+228        o_mom = getattr(other, name, None)
+229        if s_mom is not None and o_mom is not None:
+230            if not np.allclose(s_mom, o_mom):
+231                raise Exception(name + ' does not match.')
+232        return o_mom if o_mom is not None else s_mom
+233
+234    def __matmul__(self, other):
+235        return self.__new__(Npr_matrix,
+236                            super().__matmul__(other),
+237                            self._propagate_mom(other, 'mom_in'),
+238                            self._propagate_mom(other, 'mom_out'))
+239
+240    def __array_finalize__(self, obj):
+241        if obj is None:
+242            return
+243        self.mom_in = getattr(obj, 'mom_in', None)
+244        self.mom_out = getattr(obj, 'mom_out', None)
 
    
 
 
@@ -1034,44 +1075,44 @@ in and out momenta of the propagator are exchanged.
    - 
    229def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None):
-230    """Read hadrons ExternalLeg hdf5 file and output an array of CObs
-231
-232    Parameters
-233    ----------
-234    path : str
-235        path to the files to read
-236    filestem : str
-237        namestem of the files to read
-238    ens_id : str
-239        name of the ensemble, required for internal bookkeeping
-240    idl : range
-241        If specified only configurations in the given range are read in.
-242    """
-243
-244    files, idx = _get_files(path, filestem, idl)
-245
-246    mom = None
-247
-248    corr_data = []
-249    for hd5_file in files:
-250        file = h5py.File(path + '/' + hd5_file, "r")
-251        raw_data = file['ExternalLeg/corr'][0][0].view('complex')
-252        corr_data.append(raw_data)
-253        if mom is None:
-254            mom = np.array(str(file['ExternalLeg/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float)
-255        file.close()
-256    corr_data = np.array(corr_data)
-257
-258    rolled_array = np.rollaxis(corr_data, 0, 5)
-259
-260    matrix = np.empty((rolled_array.shape[:-1]), dtype=object)
-261    for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]):
-262        real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx])
-263        imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx])
-264        matrix[si, sj, ci, cj] = CObs(real, imag)
+            
    247def read_ExternalLeg_hd5(path, filestem, ens_id, idl=None):
+248    """Read hadrons ExternalLeg hdf5 file and output an array of CObs
+249
+250    Parameters
+251    ----------
+252    path : str
+253        path to the files to read
+254    filestem : str
+255        namestem of the files to read
+256    ens_id : str
+257        name of the ensemble, required for internal bookkeeping
+258    idl : range
+259        If specified only configurations in the given range are read in.
+260    """
+261
+262    files, idx = _get_files(path, filestem, idl)
+263
+264    mom = None
 265
-266    return Npr_matrix(matrix, mom_in=mom)
+266    corr_data = []
+267    for hd5_file in files:
+268        file = h5py.File(path + '/' + hd5_file, "r")
+269        raw_data = file['ExternalLeg/corr'][0][0].view('complex')
+270        corr_data.append(raw_data)
+271        if mom is None:
+272            mom = np.array(str(file['ExternalLeg/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float)
+273        file.close()
+274    corr_data = np.array(corr_data)
+275
+276    rolled_array = np.rollaxis(corr_data, 0, 5)
+277
+278    matrix = np.empty((rolled_array.shape[:-1]), dtype=object)
+279    for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]):
+280        real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx])
+281        imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx])
+282        matrix[si, sj, ci, cj] = CObs(real, imag)
+283
+284    return Npr_matrix(matrix, mom_in=mom)
 
    
 
 
@@ -1104,58 +1145,58 @@ If specified only configurations in the given range are read in.
    - 
    269def read_Bilinear_hd5(path, filestem, ens_id, idl=None):
-270    """Read hadrons Bilinear hdf5 file and output an array of CObs
-271
-272    Parameters
-273    ----------
-274    path : str
-275        path to the files to read
-276    filestem : str
-277        namestem of the files to read
-278    ens_id : str
-279        name of the ensemble, required for internal bookkeeping
-280    idl : range
-281        If specified only configurations in the given range are read in.
-282    """
-283
-284    files, idx = _get_files(path, filestem, idl)
-285
-286    mom_in = None
-287    mom_out = None
-288
-289    corr_data = {}
-290    for hd5_file in files:
-291        file = h5py.File(path + '/' + hd5_file, "r")
-292        for i in range(16):
-293            name = file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['gamma'][0].decode('UTF-8')
-294            if name not in corr_data:
-295                corr_data[name] = []
-296            raw_data = file['Bilinear/Bilinear_' + str(i) + '/corr'][0][0].view('complex')
-297            corr_data[name].append(raw_data)
-298            if mom_in is None:
-299                mom_in = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float)
-300            if mom_out is None:
-301                mom_out = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float)
-302
-303        file.close()
-304
-305    result_dict = {}
+            
    287def read_Bilinear_hd5(path, filestem, ens_id, idl=None):
+288    """Read hadrons Bilinear hdf5 file and output an array of CObs
+289
+290    Parameters
+291    ----------
+292    path : str
+293        path to the files to read
+294    filestem : str
+295        namestem of the files to read
+296    ens_id : str
+297        name of the ensemble, required for internal bookkeeping
+298    idl : range
+299        If specified only configurations in the given range are read in.
+300    """
+301
+302    files, idx = _get_files(path, filestem, idl)
+303
+304    mom_in = None
+305    mom_out = None
 306
-307    for key, data in corr_data.items():
-308        local_data = np.array(data)
-309
-310        rolled_array = np.rollaxis(local_data, 0, 5)
-311
-312        matrix = np.empty((rolled_array.shape[:-1]), dtype=object)
-313        for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]):
-314            real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx])
-315            imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx])
-316            matrix[si, sj, ci, cj] = CObs(real, imag)
-317
-318        result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out)
-319
-320    return result_dict
+307    corr_data = {}
+308    for hd5_file in files:
+309        file = h5py.File(path + '/' + hd5_file, "r")
+310        for i in range(16):
+311            name = file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['gamma'][0].decode('UTF-8')
+312            if name not in corr_data:
+313                corr_data[name] = []
+314            raw_data = file['Bilinear/Bilinear_' + str(i) + '/corr'][0][0].view('complex')
+315            corr_data[name].append(raw_data)
+316            if mom_in is None:
+317                mom_in = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float)
+318            if mom_out is None:
+319                mom_out = np.array(str(file['Bilinear/Bilinear_' + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float)
+320
+321        file.close()
+322
+323    result_dict = {}
+324
+325    for key, data in corr_data.items():
+326        local_data = np.array(data)
+327
+328        rolled_array = np.rollaxis(local_data, 0, 5)
+329
+330        matrix = np.empty((rolled_array.shape[:-1]), dtype=object)
+331        for si, sj, ci, cj in np.ndindex(rolled_array.shape[:-1]):
+332            real = Obs([rolled_array[si, sj, ci, cj].real], [ens_id], idl=[idx])
+333            imag = Obs([rolled_array[si, sj, ci, cj].imag], [ens_id], idl=[idx])
+334            matrix[si, sj, ci, cj] = CObs(real, imag)
+335
+336        result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out)
+337
+338    return result_dict
 
    
 
 
@@ -1188,85 +1229,85 @@ If specified only configurations in the given range are read in.
    - 
    323def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]):
-324    """Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
-325
-326    Parameters
-327    ----------
-328    path : str
-329        path to the files to read
-330    filestem : str
-331        namestem of the files to read
-332    ens_id : str
-333        name of the ensemble, required for internal bookkeeping
-334    idl : range
-335        If specified only configurations in the given range are read in.
-336    vertices : list
-337        Vertex functions to be extracted.
-338    """
-339
-340    files, idx = _get_files(path, filestem, idl)
-341
-342    mom_in = None
-343    mom_out = None
-344
-345    vertex_names = []
-346    for vertex in vertices:
-347        vertex_names += _get_lorentz_names(vertex)
-348
-349    corr_data = {}
-350
-351    tree = 'FourQuarkFullyConnected/FourQuarkFullyConnected_'
-352
-353    for hd5_file in files:
-354        file = h5py.File(path + '/' + hd5_file, "r")
-355
-356        for i in range(32):
-357            name = (file[tree + str(i) + '/info'].attrs['gammaA'][0].decode('UTF-8'), file[tree + str(i) + '/info'].attrs['gammaB'][0].decode('UTF-8'))
-358            if name in vertex_names:
-359                if name not in corr_data:
-360                    corr_data[name] = []
-361                raw_data = file[tree + str(i) + '/corr'][0][0].view('complex')
-362                corr_data[name].append(raw_data)
-363                if mom_in is None:
-364                    mom_in = np.array(str(file[tree + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float)
-365                if mom_out is None:
-366                    mom_out = np.array(str(file[tree + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float)
-367
-368        file.close()
-369
-370    intermediate_dict = {}
-371
-372    for vertex in vertices:
-373        lorentz_names = _get_lorentz_names(vertex)
-374        for v_name in lorentz_names:
-375            if v_name in [('SigmaXY', 'SigmaZT'),
-376                          ('SigmaXT', 'SigmaYZ'),
-377                          ('SigmaYZ', 'SigmaXT'),
-378                          ('SigmaZT', 'SigmaXY')]:
-379                sign = -1
-380            else:
-381                sign = 1
-382            if vertex not in intermediate_dict:
-383                intermediate_dict[vertex] = sign * np.array(corr_data[v_name])
-384            else:
-385                intermediate_dict[vertex] += sign * np.array(corr_data[v_name])
-386
-387    result_dict = {}
-388
-389    for key, data in intermediate_dict.items():
-390
-391        rolled_array = np.moveaxis(data, 0, 8)
-392
-393        matrix = np.empty((rolled_array.shape[:-1]), dtype=object)
-394        for index in np.ndindex(rolled_array.shape[:-1]):
-395            real = Obs([rolled_array[index].real], [ens_id], idl=[idx])
-396            imag = Obs([rolled_array[index].imag], [ens_id], idl=[idx])
-397            matrix[index] = CObs(real, imag)
-398
-399        result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out)
-400
-401    return result_dict
+            
    341def read_Fourquark_hd5(path, filestem, ens_id, idl=None, vertices=["VA", "AV"]):
+342    """Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
+343
+344    Parameters
+345    ----------
+346    path : str
+347        path to the files to read
+348    filestem : str
+349        namestem of the files to read
+350    ens_id : str
+351        name of the ensemble, required for internal bookkeeping
+352    idl : range
+353        If specified only configurations in the given range are read in.
+354    vertices : list
+355        Vertex functions to be extracted.
+356    """
+357
+358    files, idx = _get_files(path, filestem, idl)
+359
+360    mom_in = None
+361    mom_out = None
+362
+363    vertex_names = []
+364    for vertex in vertices:
+365        vertex_names += _get_lorentz_names(vertex)
+366
+367    corr_data = {}
+368
+369    tree = 'FourQuarkFullyConnected/FourQuarkFullyConnected_'
+370
+371    for hd5_file in files:
+372        file = h5py.File(path + '/' + hd5_file, "r")
+373
+374        for i in range(32):
+375            name = (file[tree + str(i) + '/info'].attrs['gammaA'][0].decode('UTF-8'), file[tree + str(i) + '/info'].attrs['gammaB'][0].decode('UTF-8'))
+376            if name in vertex_names:
+377                if name not in corr_data:
+378                    corr_data[name] = []
+379                raw_data = file[tree + str(i) + '/corr'][0][0].view('complex')
+380                corr_data[name].append(raw_data)
+381                if mom_in is None:
+382                    mom_in = np.array(str(file[tree + str(i) + '/info'].attrs['pIn'])[3:-2].strip().split(), dtype=float)
+383                if mom_out is None:
+384                    mom_out = np.array(str(file[tree + str(i) + '/info'].attrs['pOut'])[3:-2].strip().split(), dtype=float)
+385
+386        file.close()
+387
+388    intermediate_dict = {}
+389
+390    for vertex in vertices:
+391        lorentz_names = _get_lorentz_names(vertex)
+392        for v_name in lorentz_names:
+393            if v_name in [('SigmaXY', 'SigmaZT'),
+394                          ('SigmaXT', 'SigmaYZ'),
+395                          ('SigmaYZ', 'SigmaXT'),
+396                          ('SigmaZT', 'SigmaXY')]:
+397                sign = -1
+398            else:
+399                sign = 1
+400            if vertex not in intermediate_dict:
+401                intermediate_dict[vertex] = sign * np.array(corr_data[v_name])
+402            else:
+403                intermediate_dict[vertex] += sign * np.array(corr_data[v_name])
+404
+405    result_dict = {}
+406
+407    for key, data in intermediate_dict.items():
+408
+409        rolled_array = np.moveaxis(data, 0, 8)
+410
+411        matrix = np.empty((rolled_array.shape[:-1]), dtype=object)
+412        for index in np.ndindex(rolled_array.shape[:-1]):
+413            real = Obs([rolled_array[index].real], [ens_id], idl=[idx])
+414            imag = Obs([rolled_array[index].imag], [ens_id], idl=[idx])
+415            matrix[index] = CObs(real, imag)
+416
+417        result_dict[key] = Npr_matrix(matrix, mom_in=mom_in, mom_out=mom_out)
+418
+419    return result_dict
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index a506dcee..f90bb554 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact liner error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    print(my_corr[3])\n> 0.3227(33)\n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    o.covobs[k].grad\n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n\n
    Citing
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.\nand
      • \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.\nwhere applicable.
      • \n
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "
    Solve the 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
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\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", "type": "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", "type": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n   'fit' fits a constant to the plateau region\n   'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8]
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized
      • \n
    • ylabel (str):\nLabel for the y-axis
      • \n
    • save (str):\npath to file in which the figure should be saved
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    \n", "signature": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
    \n", "signature": "(self, range=[0, None])", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags={}\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags={},\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "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", "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", "type": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n\n
    Second mode:
    \n\n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
    \n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
    \n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
    \n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
    \n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
    \n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation 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", "type": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
    \n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 7922}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 108}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 94}, "pyerrors.correlators.Corr.reweighted": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.gamma_method": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 13}, "pyerrors.correlators.Corr.projected": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "type": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact liner error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    print(my_corr[3])\n> 0.3227(33)\n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    o.covobs[k].grad\n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n\n
    Citing
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.\nand
      • \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.\nwhere applicable.
      • \n
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "
    Solve the 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
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\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", "type": "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", "type": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n   'fit' fits a constant to the plateau region\n   'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8]
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized
      • \n
    • ylabel (str):\nLabel for the y-axis
      • \n
    • save (str):\npath to file in which the figure should be saved
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    \n", "signature": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
    \n", "signature": "(self, range=[0, None])", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags={}\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags={},\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\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", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "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", "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", "type": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n\n
    Second mode:
    \n\n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
    \n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
    \n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
    \n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
    \n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
    \n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation 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", "type": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
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