diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index 2feb79c5..09d150da 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -251,1099 +251,1099 @@ 8from .misc import dump_object, _assert_equal_properties 9from .fits import least_squares 10from .roots import find_root - 11 + 11from . import linalg 12 - 13class Corr: - 14 r"""The class for a correlator (time dependent sequence of pe.Obs). - 15 - 16 Everything, this class does, can be achieved using lists or arrays of Obs. - 17 But it is simply more convenient to have a dedicated object for correlators. - 18 One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient - 19 to iterate over all timeslices for every operation. This is especially true, when dealing with matrices. - 20 - 21 The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice. - 22 Other dependency (eg. spatial) are not supported. - 23 - 24 The Corr class can also deal with missing measurements or paddings for fixed boundary conditions. - 25 The missing entries are represented via the `None` object. - 26 - 27 Initialization - 28 -------------- - 29 A simple correlator can be initialized with a list or a one-dimensional array of `Obs` or `Cobs` - 30 ```python - 31 corr11 = pe.Corr([obs1, obs2]) - 32 corr11 = pe.Corr(np.array([obs1, obs2])) - 33 ``` - 34 A matrix-valued correlator can either be initialized via a two-dimensional array of `Corr` objects - 35 ```python - 36 matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]])) - 37 ``` - 38 or alternatively via a three-dimensional array of `Obs` or `CObs` of shape (T, N, N) where T is - 39 the temporal extent of the correlator and N is the dimension of the matrix. - 40 """ - 41 - 42 __slots__ = ["content", "N", "T", "tag", "prange"] - 43 - 44 def __init__(self, data_input, padding=[0, 0], prange=None): - 45 """ Initialize a Corr object. - 46 - 47 Parameters - 48 ---------- - 49 data_input : list or array - 50 list of Obs or list of arrays of Obs or array of Corrs (see class docstring for details). - 51 padding : list, optional - 52 List with two entries where the first labels the padding - 53 at the front of the correlator and the second the padding - 54 at the back. - 55 prange : list, optional - 56 List containing the first and last timeslice of the plateau - 57 region identified for this correlator. - 58 """ - 59 - 60 if isinstance(data_input, np.ndarray): - 61 if data_input.ndim == 1: - 62 data_input = list(data_input) - 63 elif data_input.ndim == 2: - 64 if not data_input.shape[0] == data_input.shape[1]: - 65 raise ValueError("Array needs to be square.") - 66 if not all([isinstance(item, Corr) for item in data_input.flatten()]): - 67 raise ValueError("If the input is an array, its elements must be of type pe.Corr.") - 68 if not all([item.N == 1 for item in data_input.flatten()]): - 69 raise ValueError("Can only construct matrix correlator from single valued correlators.") - 70 if not len(set([item.T for item in data_input.flatten()])) == 1: - 71 raise ValueError("All input Correlators must be defined over the same timeslices.") - 72 - 73 T = data_input[0, 0].T - 74 N = data_input.shape[0] - 75 input_as_list = [] - 76 for t in range(T): - 77 if any([(item.content[t] is None) for item in data_input.flatten()]): - 78 if not all([(item.content[t] is None) for item in data_input.flatten()]): - 79 warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss.!", RuntimeWarning) - 80 input_as_list.append(None) - 81 else: - 82 array_at_timeslace = np.empty([N, N], dtype="object") - 83 for i in range(N): - 84 for j in range(N): - 85 array_at_timeslace[i, j] = data_input[i, j][t] - 86 input_as_list.append(array_at_timeslace) - 87 data_input = input_as_list - 88 elif data_input.ndim == 3: - 89 if not data_input.shape[1] == data_input.shape[2]: - 90 raise ValueError("Array needs to be square.") - 91 data_input = list(data_input) - 92 else: - 93 raise ValueError("Arrays with ndim>3 not supported.") - 94 - 95 if isinstance(data_input, list): - 96 - 97 if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]): - 98 _assert_equal_properties([o for o in data_input if o is not None]) - 99 self.content = [np.asarray([item]) if item is not None else None for item in data_input] - 100 self.N = 1 - 101 elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]): - 102 self.content = data_input - 103 noNull = [a for a in self.content if not (a is None)] # To check if the matrices are correct for all undefined elements - 104 self.N = noNull[0].shape[0] - 105 if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]: - 106 raise ValueError("Smearing matrices are not NxN.") - 107 if (not all([item.shape == noNull[0].shape for item in noNull])): - 108 raise ValueError("Items in data_input are not of identical shape." + str(noNull)) - 109 else: - 110 raise TypeError("'data_input' contains item of wrong type.") - 111 else: - 112 raise TypeError("Data input was not given as list or correct array.") - 113 - 114 self.tag = None - 115 - 116 # An undefined timeslice is represented by the None object - 117 self.content = [None] * padding[0] + self.content + [None] * padding[1] - 118 self.T = len(self.content) - 119 self.prange = prange - 120 - 121 def __getitem__(self, idx): - 122 """Return the content of timeslice idx""" - 123 if self.content[idx] is None: - 124 return None - 125 elif len(self.content[idx]) == 1: - 126 return self.content[idx][0] - 127 else: - 128 return self.content[idx] - 129 - 130 @property - 131 def reweighted(self): - 132 bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]]) - 133 if np.all(bool_array == 1): - 134 return True - 135 elif np.all(bool_array == 0): - 136 return False - 137 else: - 138 raise Exception("Reweighting status of correlator corrupted.") - 139 - 140 def gamma_method(self, **kwargs): - 141 """Apply the gamma method to the content of the Corr.""" - 142 for item in self.content: - 143 if not (item is None): - 144 if self.N == 1: - 145 item[0].gamma_method(**kwargs) - 146 else: - 147 for i in range(self.N): - 148 for j in range(self.N): - 149 item[i, j].gamma_method(**kwargs) - 150 - 151 gm = gamma_method - 152 - 153 def projected(self, vector_l=None, vector_r=None, normalize=False): - 154 """We need to project the Correlator with a Vector to get a single value at each timeslice. - 155 - 156 The method can use one or two vectors. - 157 If two are specified it returns v1@G@v2 (the order might be very important.) - 158 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to - 159 """ - 160 if self.N == 1: - 161 raise Exception("Trying to project a Corr, that already has N=1.") - 162 - 163 if vector_l is None: - 164 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) - 165 elif (vector_r is None): - 166 vector_r = vector_l - 167 if isinstance(vector_l, list) and not isinstance(vector_r, list): - 168 if len(vector_l) != self.T: - 169 raise Exception("Length of vector list must be equal to T") - 170 vector_r = [vector_r] * self.T - 171 if isinstance(vector_r, list) and not isinstance(vector_l, list): - 172 if len(vector_r) != self.T: - 173 raise Exception("Length of vector list must be equal to T") - 174 vector_l = [vector_l] * self.T - 175 - 176 if not isinstance(vector_l, list): - 177 if not vector_l.shape == vector_r.shape == (self.N,): - 178 raise Exception("Vectors are of wrong shape!") - 179 if normalize: - 180 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) - 181 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] - 182 - 183 else: - 184 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. - 185 if normalize: - 186 for t in range(self.T): - 187 vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t]) - 188 - 189 newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)] - 190 return Corr(newcontent) - 191 - 192 def item(self, i, j): - 193 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. - 194 - 195 Parameters - 196 ---------- - 197 i : int - 198 First index to be picked. - 199 j : int - 200 Second index to be picked. - 201 """ - 202 if self.N == 1: - 203 raise Exception("Trying to pick item from projected Corr") - 204 newcontent = [None if (item is None) else item[i, j] for item in self.content] - 205 return Corr(newcontent) - 206 - 207 def plottable(self): - 208 """Outputs the correlator in a plotable format. - 209 - 210 Outputs three lists containing the timeslice index, the value on each - 211 timeslice and the error on each timeslice. - 212 """ - 213 if self.N != 1: - 214 raise Exception("Can only make Corr[N=1] plottable") - 215 x_list = [x for x in range(self.T) if not self.content[x] is None] - 216 y_list = [y[0].value for y in self.content if y is not None] - 217 y_err_list = [y[0].dvalue for y in self.content if y is not None] - 218 - 219 return x_list, y_list, y_err_list - 220 - 221 def symmetric(self): - 222 """ Symmetrize the correlator around x0=0.""" - 223 if self.N != 1: - 224 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') - 225 if self.T % 2 != 0: - 226 raise Exception("Can not symmetrize odd T") - 227 - 228 if self.content[0] is not None: - 229 if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0: - 230 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) - 231 - 232 newcontent = [self.content[0]] - 233 for t in range(1, self.T): - 234 if (self.content[t] is None) or (self.content[self.T - t] is None): - 235 newcontent.append(None) - 236 else: - 237 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) - 238 if (all([x is None for x in newcontent])): - 239 raise Exception("Corr could not be symmetrized: No redundant values") - 240 return Corr(newcontent, prange=self.prange) - 241 - 242 def anti_symmetric(self): - 243 """Anti-symmetrize the correlator around x0=0.""" - 244 if self.N != 1: - 245 raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.') - 246 if self.T % 2 != 0: - 247 raise Exception("Can not symmetrize odd T") - 248 - 249 test = 1 * self - 250 test.gamma_method() - 251 if not all([o.is_zero_within_error(3) for o in test.content[0]]): - 252 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) - 253 - 254 newcontent = [self.content[0]] - 255 for t in range(1, self.T): - 256 if (self.content[t] is None) or (self.content[self.T - t] is None): - 257 newcontent.append(None) - 258 else: - 259 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) - 260 if (all([x is None for x in newcontent])): - 261 raise Exception("Corr could not be symmetrized: No redundant values") - 262 return Corr(newcontent, prange=self.prange) - 263 - 264 def is_matrix_symmetric(self): - 265 """Checks whether a correlator matrices is symmetric on every timeslice.""" - 266 if self.N == 1: - 267 raise TypeError("Only works for correlator matrices.") - 268 for t in range(self.T): - 269 if self[t] is None: - 270 continue - 271 for i in range(self.N): - 272 for j in range(i + 1, self.N): - 273 if self[t][i, j] is self[t][j, i]: - 274 continue - 275 if hash(self[t][i, j]) != hash(self[t][j, i]): - 276 return False - 277 return True - 278 - 279 def trace(self): - 280 """Calculates the per-timeslice trace of a correlator matrix.""" - 281 if self.N == 1: - 282 raise ValueError("Only works for correlator matrices.") - 283 newcontent = [] - 284 for t in range(self.T): - 285 if _check_for_none(self, self.content[t]): - 286 newcontent.append(None) - 287 else: - 288 newcontent.append(np.trace(self.content[t])) - 289 return Corr(newcontent) - 290 - 291 def matrix_symmetric(self): - 292 """Symmetrizes the correlator matrices on every timeslice.""" - 293 if self.N == 1: - 294 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 295 if self.is_matrix_symmetric(): - 296 return 1.0 * self - 297 else: - 298 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 299 return 0.5 * (Corr(transposed) + self) - 300 - 301 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 302 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 303 - 304 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 305 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 306 ```python - 307 C.GEVP(t0=2)[0] # Ground state vector(s) - 308 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 309 ``` - 310 - 311 Parameters - 312 ---------- - 313 t0 : int - 314 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 315 ts : int - 316 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 317 If sort="Eigenvector" it gives a reference point for the sorting method. - 318 sort : string - 319 If 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. - 320 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 321 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 322 The reference state is identified by its eigenvalue at $t=t_s$. - 323 - 324 Other Parameters - 325 ---------------- - 326 state : int - 327 Returns only the vector(s) for a specified state. The lowest state is zero. - 328 ''' - 329 - 330 if self.N == 1: - 331 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 332 if ts is not None: - 333 if (ts <= t0): - 334 raise Exception("ts has to be larger than t0.") - 335 - 336 if "sorted_list" in kwargs: - 337 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 338 sort = kwargs.get("sorted_list") - 339 - 340 if self.is_matrix_symmetric(): - 341 symmetric_corr = self - 342 else: - 343 symmetric_corr = self.matrix_symmetric() - 344 - 345 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) - 346 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. + 13 + 14class Corr: + 15 r"""The class for a correlator (time dependent sequence of pe.Obs). + 16 + 17 Everything, this class does, can be achieved using lists or arrays of Obs. + 18 But it is simply more convenient to have a dedicated object for correlators. + 19 One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient + 20 to iterate over all timeslices for every operation. This is especially true, when dealing with matrices. + 21 + 22 The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice. + 23 Other dependency (eg. spatial) are not supported. + 24 + 25 The Corr class can also deal with missing measurements or paddings for fixed boundary conditions. + 26 The missing entries are represented via the `None` object. + 27 + 28 Initialization + 29 -------------- + 30 A simple correlator can be initialized with a list or a one-dimensional array of `Obs` or `Cobs` + 31 ```python + 32 corr11 = pe.Corr([obs1, obs2]) + 33 corr11 = pe.Corr(np.array([obs1, obs2])) + 34 ``` + 35 A matrix-valued correlator can either be initialized via a two-dimensional array of `Corr` objects + 36 ```python + 37 matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]])) + 38 ``` + 39 or alternatively via a three-dimensional array of `Obs` or `CObs` of shape (T, N, N) where T is + 40 the temporal extent of the correlator and N is the dimension of the matrix. + 41 """ + 42 + 43 __slots__ = ["content", "N", "T", "tag", "prange"] + 44 + 45 def __init__(self, data_input, padding=[0, 0], prange=None): + 46 """ Initialize a Corr object. + 47 + 48 Parameters + 49 ---------- + 50 data_input : list or array + 51 list of Obs or list of arrays of Obs or array of Corrs (see class docstring for details). + 52 padding : list, optional + 53 List with two entries where the first labels the padding + 54 at the front of the correlator and the second the padding + 55 at the back. + 56 prange : list, optional + 57 List containing the first and last timeslice of the plateau + 58 region identified for this correlator. + 59 """ + 60 + 61 if isinstance(data_input, np.ndarray): + 62 if data_input.ndim == 1: + 63 data_input = list(data_input) + 64 elif data_input.ndim == 2: + 65 if not data_input.shape[0] == data_input.shape[1]: + 66 raise ValueError("Array needs to be square.") + 67 if not all([isinstance(item, Corr) for item in data_input.flatten()]): + 68 raise ValueError("If the input is an array, its elements must be of type pe.Corr.") + 69 if not all([item.N == 1 for item in data_input.flatten()]): + 70 raise ValueError("Can only construct matrix correlator from single valued correlators.") + 71 if not len(set([item.T for item in data_input.flatten()])) == 1: + 72 raise ValueError("All input Correlators must be defined over the same timeslices.") + 73 + 74 T = data_input[0, 0].T + 75 N = data_input.shape[0] + 76 input_as_list = [] + 77 for t in range(T): + 78 if any([(item.content[t] is None) for item in data_input.flatten()]): + 79 if not all([(item.content[t] is None) for item in data_input.flatten()]): + 80 warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss.!", RuntimeWarning) + 81 input_as_list.append(None) + 82 else: + 83 array_at_timeslace = np.empty([N, N], dtype="object") + 84 for i in range(N): + 85 for j in range(N): + 86 array_at_timeslace[i, j] = data_input[i, j][t] + 87 input_as_list.append(array_at_timeslace) + 88 data_input = input_as_list + 89 elif data_input.ndim == 3: + 90 if not data_input.shape[1] == data_input.shape[2]: + 91 raise ValueError("Array needs to be square.") + 92 data_input = list(data_input) + 93 else: + 94 raise ValueError("Arrays with ndim>3 not supported.") + 95 + 96 if isinstance(data_input, list): + 97 + 98 if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]): + 99 _assert_equal_properties([o for o in data_input if o is not None]) + 100 self.content = [np.asarray([item]) if item is not None else None for item in data_input] + 101 self.N = 1 + 102 elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]): + 103 self.content = data_input + 104 noNull = [a for a in self.content if not (a is None)] # To check if the matrices are correct for all undefined elements + 105 self.N = noNull[0].shape[0] + 106 if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]: + 107 raise ValueError("Smearing matrices are not NxN.") + 108 if (not all([item.shape == noNull[0].shape for item in noNull])): + 109 raise ValueError("Items in data_input are not of identical shape." + str(noNull)) + 110 else: + 111 raise TypeError("'data_input' contains item of wrong type.") + 112 else: + 113 raise TypeError("Data input was not given as list or correct array.") + 114 + 115 self.tag = None + 116 + 117 # An undefined timeslice is represented by the None object + 118 self.content = [None] * padding[0] + self.content + [None] * padding[1] + 119 self.T = len(self.content) + 120 self.prange = prange + 121 + 122 def __getitem__(self, idx): + 123 """Return the content of timeslice idx""" + 124 if self.content[idx] is None: + 125 return None + 126 elif len(self.content[idx]) == 1: + 127 return self.content[idx][0] + 128 else: + 129 return self.content[idx] + 130 + 131 @property + 132 def reweighted(self): + 133 bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]]) + 134 if np.all(bool_array == 1): + 135 return True + 136 elif np.all(bool_array == 0): + 137 return False + 138 else: + 139 raise Exception("Reweighting status of correlator corrupted.") + 140 + 141 def gamma_method(self, **kwargs): + 142 """Apply the gamma method to the content of the Corr.""" + 143 for item in self.content: + 144 if not (item is None): + 145 if self.N == 1: + 146 item[0].gamma_method(**kwargs) + 147 else: + 148 for i in range(self.N): + 149 for j in range(self.N): + 150 item[i, j].gamma_method(**kwargs) + 151 + 152 gm = gamma_method + 153 + 154 def projected(self, vector_l=None, vector_r=None, normalize=False): + 155 """We need to project the Correlator with a Vector to get a single value at each timeslice. + 156 + 157 The method can use one or two vectors. + 158 If two are specified it returns v1@G@v2 (the order might be very important.) + 159 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to + 160 """ + 161 if self.N == 1: + 162 raise Exception("Trying to project a Corr, that already has N=1.") + 163 + 164 if vector_l is None: + 165 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) + 166 elif (vector_r is None): + 167 vector_r = vector_l + 168 if isinstance(vector_l, list) and not isinstance(vector_r, list): + 169 if len(vector_l) != self.T: + 170 raise Exception("Length of vector list must be equal to T") + 171 vector_r = [vector_r] * self.T + 172 if isinstance(vector_r, list) and not isinstance(vector_l, list): + 173 if len(vector_r) != self.T: + 174 raise Exception("Length of vector list must be equal to T") + 175 vector_l = [vector_l] * self.T + 176 + 177 if not isinstance(vector_l, list): + 178 if not vector_l.shape == vector_r.shape == (self.N,): + 179 raise Exception("Vectors are of wrong shape!") + 180 if normalize: + 181 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) + 182 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] + 183 + 184 else: + 185 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. + 186 if normalize: + 187 for t in range(self.T): + 188 vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t]) + 189 + 190 newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)] + 191 return Corr(newcontent) + 192 + 193 def item(self, i, j): + 194 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. + 195 + 196 Parameters + 197 ---------- + 198 i : int + 199 First index to be picked. + 200 j : int + 201 Second index to be picked. + 202 """ + 203 if self.N == 1: + 204 raise Exception("Trying to pick item from projected Corr") + 205 newcontent = [None if (item is None) else item[i, j] for item in self.content] + 206 return Corr(newcontent) + 207 + 208 def plottable(self): + 209 """Outputs the correlator in a plotable format. + 210 + 211 Outputs three lists containing the timeslice index, the value on each + 212 timeslice and the error on each timeslice. + 213 """ + 214 if self.N != 1: + 215 raise Exception("Can only make Corr[N=1] plottable") + 216 x_list = [x for x in range(self.T) if not self.content[x] is None] + 217 y_list = [y[0].value for y in self.content if y is not None] + 218 y_err_list = [y[0].dvalue for y in self.content if y is not None] + 219 + 220 return x_list, y_list, y_err_list + 221 + 222 def symmetric(self): + 223 """ Symmetrize the correlator around x0=0.""" + 224 if self.N != 1: + 225 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') + 226 if self.T % 2 != 0: + 227 raise Exception("Can not symmetrize odd T") + 228 + 229 if self.content[0] is not None: + 230 if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0: + 231 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) + 232 + 233 newcontent = [self.content[0]] + 234 for t in range(1, self.T): + 235 if (self.content[t] is None) or (self.content[self.T - t] is None): + 236 newcontent.append(None) + 237 else: + 238 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) + 239 if (all([x is None for x in newcontent])): + 240 raise Exception("Corr could not be symmetrized: No redundant values") + 241 return Corr(newcontent, prange=self.prange) + 242 + 243 def anti_symmetric(self): + 244 """Anti-symmetrize the correlator around x0=0.""" + 245 if self.N != 1: + 246 raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.') + 247 if self.T % 2 != 0: + 248 raise Exception("Can not symmetrize odd T") + 249 + 250 test = 1 * self + 251 test.gamma_method() + 252 if not all([o.is_zero_within_error(3) for o in test.content[0]]): + 253 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) + 254 + 255 newcontent = [self.content[0]] + 256 for t in range(1, self.T): + 257 if (self.content[t] is None) or (self.content[self.T - t] is None): + 258 newcontent.append(None) + 259 else: + 260 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) + 261 if (all([x is None for x in newcontent])): + 262 raise Exception("Corr could not be symmetrized: No redundant values") + 263 return Corr(newcontent, prange=self.prange) + 264 + 265 def is_matrix_symmetric(self): + 266 """Checks whether a correlator matrices is symmetric on every timeslice.""" + 267 if self.N == 1: + 268 raise TypeError("Only works for correlator matrices.") + 269 for t in range(self.T): + 270 if self[t] is None: + 271 continue + 272 for i in range(self.N): + 273 for j in range(i + 1, self.N): + 274 if self[t][i, j] is self[t][j, i]: + 275 continue + 276 if hash(self[t][i, j]) != hash(self[t][j, i]): + 277 return False + 278 return True + 279 + 280 def trace(self): + 281 """Calculates the per-timeslice trace of a correlator matrix.""" + 282 if self.N == 1: + 283 raise ValueError("Only works for correlator matrices.") + 284 newcontent = [] + 285 for t in range(self.T): + 286 if _check_for_none(self, self.content[t]): + 287 newcontent.append(None) + 288 else: + 289 newcontent.append(np.trace(self.content[t])) + 290 return Corr(newcontent) + 291 + 292 def matrix_symmetric(self): + 293 """Symmetrizes the correlator matrices on every timeslice.""" + 294 if self.N == 1: + 295 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") + 296 if self.is_matrix_symmetric(): + 297 return 1.0 * self + 298 else: + 299 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] + 300 return 0.5 * (Corr(transposed) + self) + 301 + 302 def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs): + 303 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. + 304 + 305 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the + 306 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing + 307 ```python + 308 C.GEVP(t0=2)[0] # Ground state vector(s) + 309 C.GEVP(t0=2)[:3] # Vectors for the lowest three states + 310 ``` + 311 + 312 Parameters + 313 ---------- + 314 t0 : int + 315 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ + 316 ts : int + 317 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. + 318 If sort="Eigenvector" it gives a reference point for the sorting method. + 319 sort : string + 320 If 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. + 321 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default) + 322 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. + 323 The reference state is identified by its eigenvalue at $t=t_s$. + 324 - None: The GEVP is solved only at ts, no sorting is necessary + 325 vector_obs : bool + 326 If True, uncertainties are propagated in the eigenvector computation (default False). + 327 + 328 Other Parameters + 329 ---------------- + 330 state : int + 331 Returns only the vector(s) for a specified state. The lowest state is zero. + 332 method : str + 333 Method used to solve the GEVP. + 334 - "eigh": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False) + 335 - "cholesky": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True. + 336 ''' + 337 + 338 if self.N == 1: + 339 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") + 340 if ts is not None: + 341 if (ts <= t0): + 342 raise Exception("ts has to be larger than t0.") + 343 + 344 if "sorted_list" in kwargs: + 345 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) + 346 sort = kwargs.get("sorted_list") 347 - 348 if sort is None: - 349 if (ts is None): - 350 raise Exception("ts is required if sort=None.") - 351 if (self.content[t0] is None) or (self.content[ts] is None): - 352 raise Exception("Corr not defined at t0/ts.") - 353 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) - 354 reordered_vecs = _GEVP_solver(Gt, G0) - 355 - 356 elif sort in ["Eigenvalue", "Eigenvector"]: - 357 if sort == "Eigenvalue" and ts is not None: - 358 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) - 359 all_vecs = [None] * (t0 + 1) - 360 for t in range(t0 + 1, self.T): - 361 try: - 362 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) - 363 all_vecs.append(_GEVP_solver(Gt, G0)) - 364 except Exception: - 365 all_vecs.append(None) - 366 if sort == "Eigenvector": - 367 if ts is None: - 368 raise Exception("ts is required for the Eigenvector sorting method.") - 369 all_vecs = _sort_vectors(all_vecs, ts) - 370 - 371 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 372 else: - 373 raise Exception("Unkown value for 'sort'.") - 374 - 375 if "state" in kwargs: - 376 return reordered_vecs[kwargs.get("state")] - 377 else: - 378 return reordered_vecs - 379 - 380 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 381 """Determines the eigenvalue of the GEVP by solving and projecting the correlator - 382 - 383 Parameters - 384 ---------- - 385 state : int - 386 The state one is interested in ordered by energy. The lowest state is zero. - 387 - 388 All other parameters are identical to the ones of Corr.GEVP. - 389 """ - 390 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 391 return self.projected(vec) - 392 - 393 def Hankel(self, N, periodic=False): - 394 """Constructs an NxN Hankel matrix - 395 - 396 C(t) c(t+1) ... c(t+n-1) - 397 C(t+1) c(t+2) ... c(t+n) - 398 ................. - 399 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) - 400 - 401 Parameters - 402 ---------- - 403 N : int - 404 Dimension of the Hankel matrix - 405 periodic : bool, optional - 406 determines whether the matrix is extended periodically - 407 """ - 408 - 409 if self.N != 1: - 410 raise Exception("Multi-operator Prony not implemented!") - 411 - 412 array = np.empty([N, N], dtype="object") - 413 new_content = [] - 414 for t in range(self.T): - 415 new_content.append(array.copy()) - 416 - 417 def wrap(i): - 418 while i >= self.T: - 419 i -= self.T - 420 return i - 421 - 422 for t in range(self.T): - 423 for i in range(N): - 424 for j in range(N): - 425 if periodic: - 426 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 427 elif (t + i + j) >= self.T: - 428 new_content[t] = None - 429 else: - 430 new_content[t][i, j] = self.content[t + i + j][0] - 431 - 432 return Corr(new_content) - 433 - 434 def roll(self, dt): - 435 """Periodically shift the correlator by dt timeslices + 348 if self.is_matrix_symmetric(): + 349 symmetric_corr = self + 350 else: + 351 symmetric_corr = self.matrix_symmetric() + 352 + 353 def _get_mat_at_t(t, vector_obs=vector_obs): + 354 if vector_obs: + 355 return symmetric_corr[t] + 356 else: + 357 return np.vectorize(lambda x: x.value)(symmetric_corr[t]) + 358 G0 = _get_mat_at_t(t0) + 359 + 360 method = kwargs.get('method', 'eigh') + 361 if vector_obs: + 362 chol = linalg.cholesky(G0) + 363 chol_inv = linalg.inv(chol) + 364 method = 'cholesky' + 365 else: + 366 chol = np.linalg.cholesky(_get_mat_at_t(t0, vector_obs=False)) # Check if matrix G0 is positive-semidefinite. + 367 if method == 'cholesky': + 368 chol_inv = np.linalg.inv(chol) + 369 else: + 370 chol_inv = None + 371 + 372 if sort is None: + 373 if (ts is None): + 374 raise Exception("ts is required if sort=None.") + 375 if (self.content[t0] is None) or (self.content[ts] is None): + 376 raise Exception("Corr not defined at t0/ts.") + 377 Gt = _get_mat_at_t(ts) + 378 reordered_vecs = _GEVP_solver(Gt, G0, method=method, chol_inv=chol_inv) + 379 if kwargs.get('auto_gamma', False) and vector_obs: + 380 [[o.gm() for o in ev if isinstance(o, Obs)] for ev in reordered_vecs] + 381 + 382 elif sort in ["Eigenvalue", "Eigenvector"]: + 383 if sort == "Eigenvalue" and ts is not None: + 384 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) + 385 all_vecs = [None] * (t0 + 1) + 386 for t in range(t0 + 1, self.T): + 387 try: + 388 Gt = _get_mat_at_t(t) + 389 all_vecs.append(_GEVP_solver(Gt, G0, method=method, chol_inv=chol_inv)) + 390 except Exception: + 391 all_vecs.append(None) + 392 if sort == "Eigenvector": + 393 if ts is None: + 394 raise Exception("ts is required for the Eigenvector sorting method.") + 395 all_vecs = _sort_vectors(all_vecs, ts) + 396 + 397 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] + 398 if kwargs.get('auto_gamma', False) and vector_obs: + 399 [[[o.gm() for o in evn] for evn in ev if evn is not None] for ev in reordered_vecs] + 400 else: + 401 raise Exception("Unknown value for 'sort'. Choose 'Eigenvalue', 'Eigenvector' or None.") + 402 + 403 if "state" in kwargs: + 404 return reordered_vecs[kwargs.get("state")] + 405 else: + 406 return reordered_vecs + 407 + 408 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs): + 409 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 410 + 411 Parameters + 412 ---------- + 413 state : int + 414 The state one is interested in ordered by energy. The lowest state is zero. + 415 + 416 All other parameters are identical to the ones of Corr.GEVP. + 417 """ + 418 vec = self.GEVP(t0, ts=ts, sort=sort, **kwargs)[state] + 419 return self.projected(vec) + 420 + 421 def Hankel(self, N, periodic=False): + 422 """Constructs an NxN Hankel matrix + 423 + 424 C(t) c(t+1) ... c(t+n-1) + 425 C(t+1) c(t+2) ... c(t+n) + 426 ................. + 427 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) + 428 + 429 Parameters + 430 ---------- + 431 N : int + 432 Dimension of the Hankel matrix + 433 periodic : bool, optional + 434 determines whether the matrix is extended periodically + 435 """ 436 - 437 Parameters - 438 ---------- - 439 dt : int - 440 number of timeslices - 441 """ - 442 return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0))) - 443 - 444 def reverse(self): - 445 """Reverse the time ordering of the Corr""" - 446 return Corr(self.content[:: -1]) - 447 - 448 def thin(self, spacing=2, offset=0): - 449 """Thin out a correlator to suppress correlations - 450 - 451 Parameters - 452 ---------- - 453 spacing : int - 454 Keep only every 'spacing'th entry of the correlator - 455 offset : int - 456 Offset the equal spacing - 457 """ - 458 new_content = [] - 459 for t in range(self.T): - 460 if (offset + t) % spacing != 0: - 461 new_content.append(None) - 462 else: - 463 new_content.append(self.content[t]) - 464 return Corr(new_content) - 465 - 466 def correlate(self, partner): - 467 """Correlate the correlator with another correlator or Obs - 468 - 469 Parameters - 470 ---------- - 471 partner : Obs or Corr - 472 partner to correlate the correlator with. - 473 Can either be an Obs which is correlated with all entries of the - 474 correlator or a Corr of same length. - 475 """ - 476 if self.N != 1: - 477 raise Exception("Only one-dimensional correlators can be safely correlated.") - 478 new_content = [] - 479 for x0, t_slice in enumerate(self.content): - 480 if _check_for_none(self, t_slice): - 481 new_content.append(None) - 482 else: - 483 if isinstance(partner, Corr): - 484 if _check_for_none(partner, partner.content[x0]): - 485 new_content.append(None) - 486 else: - 487 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 488 elif isinstance(partner, Obs): # Should this include CObs? - 489 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 490 else: - 491 raise Exception("Can only correlate with an Obs or a Corr.") - 492 - 493 return Corr(new_content) - 494 - 495 def reweight(self, weight, **kwargs): - 496 """Reweight the correlator. - 497 - 498 Parameters - 499 ---------- - 500 weight : Obs - 501 Reweighting factor. An Observable that has to be defined on a superset of the - 502 configurations in obs[i].idl for all i. - 503 all_configs : bool - 504 if True, the reweighted observables are normalized by the average of - 505 the reweighting factor on all configurations in weight.idl and not - 506 on the configurations in obs[i].idl. - 507 """ - 508 if self.N != 1: - 509 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 510 new_content = [] - 511 for t_slice in self.content: - 512 if _check_for_none(self, t_slice): - 513 new_content.append(None) - 514 else: - 515 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 516 return Corr(new_content) - 517 - 518 def T_symmetry(self, partner, parity=+1): - 519 """Return the time symmetry average of the correlator and its partner + 437 if self.N != 1: + 438 raise Exception("Multi-operator Prony not implemented!") + 439 + 440 array = np.empty([N, N], dtype="object") + 441 new_content = [] + 442 for t in range(self.T): + 443 new_content.append(array.copy()) + 444 + 445 def wrap(i): + 446 while i >= self.T: + 447 i -= self.T + 448 return i + 449 + 450 for t in range(self.T): + 451 for i in range(N): + 452 for j in range(N): + 453 if periodic: + 454 new_content[t][i, j] = self.content[wrap(t + i + j)][0] + 455 elif (t + i + j) >= self.T: + 456 new_content[t] = None + 457 else: + 458 new_content[t][i, j] = self.content[t + i + j][0] + 459 + 460 return Corr(new_content) + 461 + 462 def roll(self, dt): + 463 """Periodically shift the correlator by dt timeslices + 464 + 465 Parameters + 466 ---------- + 467 dt : int + 468 number of timeslices + 469 """ + 470 return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0))) + 471 + 472 def reverse(self): + 473 """Reverse the time ordering of the Corr""" + 474 return Corr(self.content[:: -1]) + 475 + 476 def thin(self, spacing=2, offset=0): + 477 """Thin out a correlator to suppress correlations + 478 + 479 Parameters + 480 ---------- + 481 spacing : int + 482 Keep only every 'spacing'th entry of the correlator + 483 offset : int + 484 Offset the equal spacing + 485 """ + 486 new_content = [] + 487 for t in range(self.T): + 488 if (offset + t) % spacing != 0: + 489 new_content.append(None) + 490 else: + 491 new_content.append(self.content[t]) + 492 return Corr(new_content) + 493 + 494 def correlate(self, partner): + 495 """Correlate the correlator with another correlator or Obs + 496 + 497 Parameters + 498 ---------- + 499 partner : Obs or Corr + 500 partner to correlate the correlator with. + 501 Can either be an Obs which is correlated with all entries of the + 502 correlator or a Corr of same length. + 503 """ + 504 if self.N != 1: + 505 raise Exception("Only one-dimensional correlators can be safely correlated.") + 506 new_content = [] + 507 for x0, t_slice in enumerate(self.content): + 508 if _check_for_none(self, t_slice): + 509 new_content.append(None) + 510 else: + 511 if isinstance(partner, Corr): + 512 if _check_for_none(partner, partner.content[x0]): + 513 new_content.append(None) + 514 else: + 515 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) + 516 elif isinstance(partner, Obs): # Should this include CObs? + 517 new_content.append(np.array([correlate(o, partner) for o in t_slice])) + 518 else: + 519 raise Exception("Can only correlate with an Obs or a Corr.") 520 - 521 Parameters - 522 ---------- - 523 partner : Corr - 524 Time symmetry partner of the Corr - 525 parity : int - 526 Parity quantum number of the correlator, can be +1 or -1 - 527 """ - 528 if self.N != 1: - 529 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 530 if not isinstance(partner, Corr): - 531 raise Exception("T partner has to be a Corr object.") - 532 if parity not in [+1, -1]: - 533 raise Exception("Parity has to be +1 or -1.") - 534 T_partner = parity * partner.reverse() - 535 - 536 t_slices = [] - 537 test = (self - T_partner) - 538 test.gamma_method() - 539 for x0, t_slice in enumerate(test.content): - 540 if t_slice is not None: - 541 if not t_slice[0].is_zero_within_error(5): - 542 t_slices.append(x0) - 543 if t_slices: - 544 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) + 521 return Corr(new_content) + 522 + 523 def reweight(self, weight, **kwargs): + 524 """Reweight the correlator. + 525 + 526 Parameters + 527 ---------- + 528 weight : Obs + 529 Reweighting factor. An Observable that has to be defined on a superset of the + 530 configurations in obs[i].idl for all i. + 531 all_configs : bool + 532 if True, the reweighted observables are normalized by the average of + 533 the reweighting factor on all configurations in weight.idl and not + 534 on the configurations in obs[i].idl. + 535 """ + 536 if self.N != 1: + 537 raise Exception("Reweighting only implemented for one-dimensional correlators.") + 538 new_content = [] + 539 for t_slice in self.content: + 540 if _check_for_none(self, t_slice): + 541 new_content.append(None) + 542 else: + 543 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) + 544 return Corr(new_content) 545 - 546 return (self + T_partner) / 2 - 547 - 548 def deriv(self, variant="symmetric"): - 549 """Return the first derivative of the correlator with respect to x0. - 550 - 551 Parameters - 552 ---------- - 553 variant : str - 554 decides which definition of the finite differences derivative is used. - 555 Available choice: symmetric, forward, backward, improved, log, default: symmetric - 556 """ - 557 if self.N != 1: - 558 raise Exception("deriv only implemented for one-dimensional correlators.") - 559 if variant == "symmetric": - 560 newcontent = [] - 561 for t in range(1, self.T - 1): - 562 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 563 newcontent.append(None) - 564 else: - 565 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 566 if (all([x is None for x in newcontent])): - 567 raise Exception('Derivative is undefined at all timeslices') - 568 return Corr(newcontent, padding=[1, 1]) - 569 elif variant == "forward": - 570 newcontent = [] - 571 for t in range(self.T - 1): - 572 if (self.content[t] is None) or (self.content[t + 1] is None): - 573 newcontent.append(None) - 574 else: - 575 newcontent.append(self.content[t + 1] - self.content[t]) - 576 if (all([x is None for x in newcontent])): - 577 raise Exception("Derivative is undefined at all timeslices") - 578 return Corr(newcontent, padding=[0, 1]) - 579 elif variant == "backward": - 580 newcontent = [] - 581 for t in range(1, self.T): - 582 if (self.content[t - 1] is None) or (self.content[t] is None): - 583 newcontent.append(None) - 584 else: - 585 newcontent.append(self.content[t] - self.content[t - 1]) - 586 if (all([x is None for x in newcontent])): - 587 raise Exception("Derivative is undefined at all timeslices") - 588 return Corr(newcontent, padding=[1, 0]) - 589 elif variant == "improved": - 590 newcontent = [] - 591 for t in range(2, self.T - 2): - 592 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): - 593 newcontent.append(None) - 594 else: - 595 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 596 if (all([x is None for x in newcontent])): - 597 raise Exception('Derivative is undefined at all timeslices') - 598 return Corr(newcontent, padding=[2, 2]) - 599 elif variant == 'log': - 600 newcontent = [] - 601 for t in range(self.T): - 602 if (self.content[t] is None) or (self.content[t] <= 0): - 603 newcontent.append(None) - 604 else: - 605 newcontent.append(np.log(self.content[t])) - 606 if (all([x is None for x in newcontent])): - 607 raise Exception("Log is undefined at all timeslices") - 608 logcorr = Corr(newcontent) - 609 return self * logcorr.deriv('symmetric') - 610 else: - 611 raise Exception("Unknown variant.") - 612 - 613 def second_deriv(self, variant="symmetric"): - 614 r"""Return the second derivative of the correlator with respect to x0. - 615 - 616 Parameters - 617 ---------- - 618 variant : str - 619 decides which definition of the finite differences derivative is used. - 620 Available choice: - 621 - symmetric (default) - 622 $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$ - 623 - big_symmetric - 624 $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$ - 625 - improved - 626 $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$ - 627 - log - 628 $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$ - 629 """ - 630 if self.N != 1: - 631 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 632 if variant == "symmetric": - 633 newcontent = [] - 634 for t in range(1, self.T - 1): - 635 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 636 newcontent.append(None) - 637 else: - 638 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 639 if (all([x is None for x in newcontent])): - 640 raise Exception("Derivative is undefined at all timeslices") - 641 return Corr(newcontent, padding=[1, 1]) - 642 elif variant == "big_symmetric": - 643 newcontent = [] - 644 for t in range(2, self.T - 2): - 645 if (self.content[t - 2] is None) or (self.content[t + 2] is None): - 646 newcontent.append(None) - 647 else: - 648 newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4) - 649 if (all([x is None for x in newcontent])): - 650 raise Exception("Derivative is undefined at all timeslices") - 651 return Corr(newcontent, padding=[2, 2]) - 652 elif variant == "improved": - 653 newcontent = [] - 654 for t in range(2, self.T - 2): - 655 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): - 656 newcontent.append(None) - 657 else: - 658 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) - 659 if (all([x is None for x in newcontent])): - 660 raise Exception("Derivative is undefined at all timeslices") - 661 return Corr(newcontent, padding=[2, 2]) - 662 elif variant == 'log': - 663 newcontent = [] - 664 for t in range(self.T): - 665 if (self.content[t] is None) or (self.content[t] <= 0): - 666 newcontent.append(None) - 667 else: - 668 newcontent.append(np.log(self.content[t])) - 669 if (all([x is None for x in newcontent])): - 670 raise Exception("Log is undefined at all timeslices") - 671 logcorr = Corr(newcontent) - 672 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) - 673 else: - 674 raise Exception("Unknown variant.") - 675 - 676 def m_eff(self, variant='log', guess=1.0): - 677 """Returns the effective mass of the correlator as correlator object - 678 - 679 Parameters - 680 ---------- - 681 variant : str - 682 log : uses the standard effective mass log(C(t) / C(t+1)) - 683 cosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. - 684 sinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m. - 685 See, e.g., arXiv:1205.5380 - 686 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 687 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 - 688 guess : float - 689 guess for the root finder, only relevant for the root variant - 690 """ - 691 if self.N != 1: - 692 raise Exception('Correlator must be projected before getting m_eff') - 693 if variant == 'log': - 694 newcontent = [] - 695 for t in range(self.T - 1): - 696 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 697 newcontent.append(None) - 698 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 699 newcontent.append(None) - 700 else: - 701 newcontent.append(self.content[t] / self.content[t + 1]) - 702 if (all([x is None for x in newcontent])): - 703 raise Exception('m_eff is undefined at all timeslices') - 704 - 705 return np.log(Corr(newcontent, padding=[0, 1])) + 546 def T_symmetry(self, partner, parity=+1): + 547 """Return the time symmetry average of the correlator and its partner + 548 + 549 Parameters + 550 ---------- + 551 partner : Corr + 552 Time symmetry partner of the Corr + 553 parity : int + 554 Parity quantum number of the correlator, can be +1 or -1 + 555 """ + 556 if self.N != 1: + 557 raise Exception("T_symmetry only implemented for one-dimensional correlators.") + 558 if not isinstance(partner, Corr): + 559 raise Exception("T partner has to be a Corr object.") + 560 if parity not in [+1, -1]: + 561 raise Exception("Parity has to be +1 or -1.") + 562 T_partner = parity * partner.reverse() + 563 + 564 t_slices = [] + 565 test = (self - T_partner) + 566 test.gamma_method() + 567 for x0, t_slice in enumerate(test.content): + 568 if t_slice is not None: + 569 if not t_slice[0].is_zero_within_error(5): + 570 t_slices.append(x0) + 571 if t_slices: + 572 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) + 573 + 574 return (self + T_partner) / 2 + 575 + 576 def deriv(self, variant="symmetric"): + 577 """Return the first derivative of the correlator with respect to x0. + 578 + 579 Parameters + 580 ---------- + 581 variant : str + 582 decides which definition of the finite differences derivative is used. + 583 Available choice: symmetric, forward, backward, improved, log, default: symmetric + 584 """ + 585 if self.N != 1: + 586 raise Exception("deriv only implemented for one-dimensional correlators.") + 587 if variant == "symmetric": + 588 newcontent = [] + 589 for t in range(1, self.T - 1): + 590 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 591 newcontent.append(None) + 592 else: + 593 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) + 594 if (all([x is None for x in newcontent])): + 595 raise Exception('Derivative is undefined at all timeslices') + 596 return Corr(newcontent, padding=[1, 1]) + 597 elif variant == "forward": + 598 newcontent = [] + 599 for t in range(self.T - 1): + 600 if (self.content[t] is None) or (self.content[t + 1] is None): + 601 newcontent.append(None) + 602 else: + 603 newcontent.append(self.content[t + 1] - self.content[t]) + 604 if (all([x is None for x in newcontent])): + 605 raise Exception("Derivative is undefined at all timeslices") + 606 return Corr(newcontent, padding=[0, 1]) + 607 elif variant == "backward": + 608 newcontent = [] + 609 for t in range(1, self.T): + 610 if (self.content[t - 1] is None) or (self.content[t] is None): + 611 newcontent.append(None) + 612 else: + 613 newcontent.append(self.content[t] - self.content[t - 1]) + 614 if (all([x is None for x in newcontent])): + 615 raise Exception("Derivative is undefined at all timeslices") + 616 return Corr(newcontent, padding=[1, 0]) + 617 elif variant == "improved": + 618 newcontent = [] + 619 for t in range(2, self.T - 2): + 620 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 621 newcontent.append(None) + 622 else: + 623 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) + 624 if (all([x is None for x in newcontent])): + 625 raise Exception('Derivative is undefined at all timeslices') + 626 return Corr(newcontent, padding=[2, 2]) + 627 elif variant == 'log': + 628 newcontent = [] + 629 for t in range(self.T): + 630 if (self.content[t] is None) or (self.content[t] <= 0): + 631 newcontent.append(None) + 632 else: + 633 newcontent.append(np.log(self.content[t])) + 634 if (all([x is None for x in newcontent])): + 635 raise Exception("Log is undefined at all timeslices") + 636 logcorr = Corr(newcontent) + 637 return self * logcorr.deriv('symmetric') + 638 else: + 639 raise Exception("Unknown variant.") + 640 + 641 def second_deriv(self, variant="symmetric"): + 642 r"""Return the second derivative of the correlator with respect to x0. + 643 + 644 Parameters + 645 ---------- + 646 variant : str + 647 decides which definition of the finite differences derivative is used. + 648 Available choice: + 649 - symmetric (default) + 650 $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$ + 651 - big_symmetric + 652 $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$ + 653 - improved + 654 $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$ + 655 - log + 656 $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$ + 657 """ + 658 if self.N != 1: + 659 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 660 if variant == "symmetric": + 661 newcontent = [] + 662 for t in range(1, self.T - 1): + 663 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 664 newcontent.append(None) + 665 else: + 666 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 667 if (all([x is None for x in newcontent])): + 668 raise Exception("Derivative is undefined at all timeslices") + 669 return Corr(newcontent, padding=[1, 1]) + 670 elif variant == "big_symmetric": + 671 newcontent = [] + 672 for t in range(2, self.T - 2): + 673 if (self.content[t - 2] is None) or (self.content[t + 2] is None): + 674 newcontent.append(None) + 675 else: + 676 newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4) + 677 if (all([x is None for x in newcontent])): + 678 raise Exception("Derivative is undefined at all timeslices") + 679 return Corr(newcontent, padding=[2, 2]) + 680 elif variant == "improved": + 681 newcontent = [] + 682 for t in range(2, self.T - 2): + 683 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 684 newcontent.append(None) + 685 else: + 686 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) + 687 if (all([x is None for x in newcontent])): + 688 raise Exception("Derivative is undefined at all timeslices") + 689 return Corr(newcontent, padding=[2, 2]) + 690 elif variant == 'log': + 691 newcontent = [] + 692 for t in range(self.T): + 693 if (self.content[t] is None) or (self.content[t] <= 0): + 694 newcontent.append(None) + 695 else: + 696 newcontent.append(np.log(self.content[t])) + 697 if (all([x is None for x in newcontent])): + 698 raise Exception("Log is undefined at all timeslices") + 699 logcorr = Corr(newcontent) + 700 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) + 701 else: + 702 raise Exception("Unknown variant.") + 703 + 704 def m_eff(self, variant='log', guess=1.0): + 705 """Returns the effective mass of the correlator as correlator object 706 - 707 elif variant == 'logsym': - 708 newcontent = [] - 709 for t in range(1, self.T - 1): - 710 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 711 newcontent.append(None) - 712 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: - 713 newcontent.append(None) - 714 else: - 715 newcontent.append(self.content[t - 1] / self.content[t + 1]) - 716 if (all([x is None for x in newcontent])): - 717 raise Exception('m_eff is undefined at all timeslices') - 718 - 719 return np.log(Corr(newcontent, padding=[1, 1])) / 2 - 720 - 721 elif variant in ['periodic', 'cosh', 'sinh']: - 722 if variant in ['periodic', 'cosh']: - 723 func = anp.cosh - 724 else: - 725 func = anp.sinh - 726 - 727 def root_function(x, d): - 728 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 729 - 730 newcontent = [] - 731 for t in range(self.T - 1): - 732 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 733 newcontent.append(None) - 734 # Fill the two timeslices in the middle of the lattice with their predecessors - 735 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 736 newcontent.append(newcontent[-1]) - 737 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 738 newcontent.append(None) - 739 else: - 740 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 741 if (all([x is None for x in newcontent])): - 742 raise Exception('m_eff is undefined at all timeslices') - 743 - 744 return Corr(newcontent, padding=[0, 1]) - 745 - 746 elif variant == 'arccosh': - 747 newcontent = [] - 748 for t in range(1, self.T - 1): - 749 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): - 750 newcontent.append(None) - 751 else: - 752 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) - 753 if (all([x is None for x in newcontent])): - 754 raise Exception("m_eff is undefined at all timeslices") - 755 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 756 - 757 else: - 758 raise Exception('Unknown variant.') - 759 - 760 def fit(self, function, fitrange=None, silent=False, **kwargs): - 761 r'''Fits function to the data - 762 - 763 Parameters - 764 ---------- - 765 function : obj - 766 function to fit to the data. See fits.least_squares for details. - 767 fitrange : list - 768 Two element list containing the timeslices on which the fit is supposed to start and stop. - 769 Caution: This range is inclusive as opposed to standard python indexing. - 770 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 771 If not specified, self.prange or all timeslices are used. - 772 silent : bool - 773 Decides whether output is printed to the standard output. - 774 ''' - 775 if self.N != 1: - 776 raise Exception("Correlator must be projected before fitting") - 777 - 778 if fitrange is None: - 779 if self.prange: - 780 fitrange = self.prange - 781 else: - 782 fitrange = [0, self.T - 1] - 783 else: - 784 if not isinstance(fitrange, list): - 785 raise Exception("fitrange has to be a list with two elements") - 786 if len(fitrange) != 2: - 787 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 788 - 789 xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 790 ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 791 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 792 return result - 793 - 794 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 795 """ Extract a plateau value from a Corr object - 796 - 797 Parameters - 798 ---------- - 799 plateau_range : list - 800 list with two entries, indicating the first and the last timeslice - 801 of the plateau region. - 802 method : str - 803 method to extract the plateau. - 804 'fit' fits a constant to the plateau region - 805 'avg', 'average' or 'mean' just average over the given timeslices. - 806 auto_gamma : bool - 807 apply gamma_method with default parameters to the Corr. Defaults to None - 808 """ - 809 if not plateau_range: - 810 if self.prange: - 811 plateau_range = self.prange - 812 else: - 813 raise Exception("no plateau range provided") - 814 if self.N != 1: - 815 raise Exception("Correlator must be projected before getting a plateau.") - 816 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 817 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 818 if auto_gamma: - 819 self.gamma_method() - 820 if method == "fit": - 821 def const_func(a, t): - 822 return a[0] - 823 return self.fit(const_func, plateau_range)[0] - 824 elif method in ["avg", "average", "mean"]: - 825 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 826 return returnvalue - 827 - 828 else: - 829 raise Exception("Unsupported plateau method: " + method) - 830 - 831 def set_prange(self, prange): - 832 """Sets the attribute prange of the Corr object.""" - 833 if not len(prange) == 2: - 834 raise Exception("prange must be a list or array with two values") - 835 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 836 raise Exception("Start and end point must be integers") - 837 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 838 raise Exception("Start and end point must define a range in the interval 0,T") - 839 - 840 self.prange = prange - 841 return - 842 - 843 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): - 844 """Plots the correlator using the tag of the correlator as label if available. - 845 - 846 Parameters - 847 ---------- - 848 x_range : list - 849 list of two values, determining the range of the x-axis e.g. [4, 8]. - 850 comp : Corr or list of Corr - 851 Correlator or list of correlators which are plotted for comparison. - 852 The tags of these correlators are used as labels if available. - 853 logscale : bool - 854 Sets y-axis to logscale. - 855 plateau : Obs - 856 Plateau value to be visualized in the figure. - 857 fit_res : Fit_result - 858 Fit_result object to be visualized. - 859 fit_key : str - 860 Key for the fit function in Fit_result.fit_function (for combined fits). - 861 ylabel : str - 862 Label for the y-axis. - 863 save : str - 864 path to file in which the figure should be saved. - 865 auto_gamma : bool - 866 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 867 hide_sigma : float - 868 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 869 references : list - 870 List of floating point values that are displayed as horizontal lines for reference. - 871 title : string - 872 Optional title of the figure. - 873 """ - 874 if self.N != 1: - 875 raise Exception("Correlator must be projected before plotting") - 876 - 877 if auto_gamma: - 878 self.gamma_method() - 879 - 880 if x_range is None: - 881 x_range = [0, self.T - 1] - 882 - 883 fig = plt.figure() - 884 ax1 = fig.add_subplot(111) - 885 - 886 x, y, y_err = self.plottable() - 887 if hide_sigma: - 888 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 889 else: - 890 hide_from = None - 891 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 892 if logscale: - 893 ax1.set_yscale('log') - 894 else: - 895 if y_range is None: - 896 try: - 897 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) - 898 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) - 899 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 900 except Exception: - 901 pass - 902 else: - 903 ax1.set_ylim(y_range) - 904 if comp: - 905 if isinstance(comp, (Corr, list)): - 906 for corr in comp if isinstance(comp, list) else [comp]: - 907 if auto_gamma: - 908 corr.gamma_method() - 909 x, y, y_err = corr.plottable() - 910 if hide_sigma: - 911 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 912 else: - 913 hide_from = None - 914 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 915 else: - 916 raise Exception("'comp' must be a correlator or a list of correlators.") - 917 - 918 if plateau: - 919 if isinstance(plateau, Obs): - 920 if auto_gamma: - 921 plateau.gamma_method() - 922 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 923 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 924 else: - 925 raise Exception("'plateau' must be an Obs") - 926 - 927 if references: - 928 if isinstance(references, list): - 929 for ref in references: - 930 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 931 else: - 932 raise Exception("'references' must be a list of floating pint values.") - 933 - 934 if self.prange: - 935 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0) - 936 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0) - 937 - 938 if fit_res: - 939 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 940 if isinstance(fit_res.fit_function, dict): - 941 if fit_key: - 942 ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) - 943 else: - 944 raise ValueError("Please provide a 'fit_key' for visualizing combined fits.") - 945 else: - 946 ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) - 947 - 948 ax1.set_xlabel(r'$x_0 / a$') - 949 if ylabel: - 950 ax1.set_ylabel(ylabel) - 951 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 952 - 953 handles, labels = ax1.get_legend_handles_labels() - 954 if labels: - 955 ax1.legend() - 956 - 957 if title: - 958 plt.title(title) - 959 - 960 plt.draw() + 707 Parameters + 708 ---------- + 709 variant : str + 710 log : uses the standard effective mass log(C(t) / C(t+1)) + 711 cosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. + 712 sinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m. + 713 See, e.g., arXiv:1205.5380 + 714 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 715 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 + 716 guess : float + 717 guess for the root finder, only relevant for the root variant + 718 """ + 719 if self.N != 1: + 720 raise Exception('Correlator must be projected before getting m_eff') + 721 if variant == 'log': + 722 newcontent = [] + 723 for t in range(self.T - 1): + 724 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 725 newcontent.append(None) + 726 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 727 newcontent.append(None) + 728 else: + 729 newcontent.append(self.content[t] / self.content[t + 1]) + 730 if (all([x is None for x in newcontent])): + 731 raise Exception('m_eff is undefined at all timeslices') + 732 + 733 return np.log(Corr(newcontent, padding=[0, 1])) + 734 + 735 elif variant == 'logsym': + 736 newcontent = [] + 737 for t in range(1, self.T - 1): + 738 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 739 newcontent.append(None) + 740 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: + 741 newcontent.append(None) + 742 else: + 743 newcontent.append(self.content[t - 1] / self.content[t + 1]) + 744 if (all([x is None for x in newcontent])): + 745 raise Exception('m_eff is undefined at all timeslices') + 746 + 747 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 748 + 749 elif variant in ['periodic', 'cosh', 'sinh']: + 750 if variant in ['periodic', 'cosh']: + 751 func = anp.cosh + 752 else: + 753 func = anp.sinh + 754 + 755 def root_function(x, d): + 756 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 757 + 758 newcontent = [] + 759 for t in range(self.T - 1): + 760 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 761 newcontent.append(None) + 762 # Fill the two timeslices in the middle of the lattice with their predecessors + 763 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 764 newcontent.append(newcontent[-1]) + 765 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 766 newcontent.append(None) + 767 else: + 768 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) + 769 if (all([x is None for x in newcontent])): + 770 raise Exception('m_eff is undefined at all timeslices') + 771 + 772 return Corr(newcontent, padding=[0, 1]) + 773 + 774 elif variant == 'arccosh': + 775 newcontent = [] + 776 for t in range(1, self.T - 1): + 777 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): + 778 newcontent.append(None) + 779 else: + 780 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 781 if (all([x is None for x in newcontent])): + 782 raise Exception("m_eff is undefined at all timeslices") + 783 return np.arccosh(Corr(newcontent, padding=[1, 1])) + 784 + 785 else: + 786 raise Exception('Unknown variant.') + 787 + 788 def fit(self, function, fitrange=None, silent=False, **kwargs): + 789 r'''Fits function to the data + 790 + 791 Parameters + 792 ---------- + 793 function : obj + 794 function to fit to the data. See fits.least_squares for details. + 795 fitrange : list + 796 Two element list containing the timeslices on which the fit is supposed to start and stop. + 797 Caution: This range is inclusive as opposed to standard python indexing. + 798 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 799 If not specified, self.prange or all timeslices are used. + 800 silent : bool + 801 Decides whether output is printed to the standard output. + 802 ''' + 803 if self.N != 1: + 804 raise Exception("Correlator must be projected before fitting") + 805 + 806 if fitrange is None: + 807 if self.prange: + 808 fitrange = self.prange + 809 else: + 810 fitrange = [0, self.T - 1] + 811 else: + 812 if not isinstance(fitrange, list): + 813 raise Exception("fitrange has to be a list with two elements") + 814 if len(fitrange) != 2: + 815 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 816 + 817 xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) + 818 ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) + 819 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 820 return result + 821 + 822 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 823 """ Extract a plateau value from a Corr object + 824 + 825 Parameters + 826 ---------- + 827 plateau_range : list + 828 list with two entries, indicating the first and the last timeslice + 829 of the plateau region. + 830 method : str + 831 method to extract the plateau. + 832 'fit' fits a constant to the plateau region + 833 'avg', 'average' or 'mean' just average over the given timeslices. + 834 auto_gamma : bool + 835 apply gamma_method with default parameters to the Corr. Defaults to None + 836 """ + 837 if not plateau_range: + 838 if self.prange: + 839 plateau_range = self.prange + 840 else: + 841 raise Exception("no plateau range provided") + 842 if self.N != 1: + 843 raise Exception("Correlator must be projected before getting a plateau.") + 844 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 845 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 846 if auto_gamma: + 847 self.gamma_method() + 848 if method == "fit": + 849 def const_func(a, t): + 850 return a[0] + 851 return self.fit(const_func, plateau_range)[0] + 852 elif method in ["avg", "average", "mean"]: + 853 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 854 return returnvalue + 855 + 856 else: + 857 raise Exception("Unsupported plateau method: " + method) + 858 + 859 def set_prange(self, prange): + 860 """Sets the attribute prange of the Corr object.""" + 861 if not len(prange) == 2: + 862 raise Exception("prange must be a list or array with two values") + 863 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 864 raise Exception("Start and end point must be integers") + 865 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 866 raise Exception("Start and end point must define a range in the interval 0,T") + 867 + 868 self.prange = prange + 869 return + 870 + 871 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): + 872 """Plots the correlator using the tag of the correlator as label if available. + 873 + 874 Parameters + 875 ---------- + 876 x_range : list + 877 list of two values, determining the range of the x-axis e.g. [4, 8]. + 878 comp : Corr or list of Corr + 879 Correlator or list of correlators which are plotted for comparison. + 880 The tags of these correlators are used as labels if available. + 881 logscale : bool + 882 Sets y-axis to logscale. + 883 plateau : Obs + 884 Plateau value to be visualized in the figure. + 885 fit_res : Fit_result + 886 Fit_result object to be visualized. + 887 fit_key : str + 888 Key for the fit function in Fit_result.fit_function (for combined fits). + 889 ylabel : str + 890 Label for the y-axis. + 891 save : str + 892 path to file in which the figure should be saved. + 893 auto_gamma : bool + 894 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 895 hide_sigma : float + 896 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 897 references : list + 898 List of floating point values that are displayed as horizontal lines for reference. + 899 title : string + 900 Optional title of the figure. + 901 """ + 902 if self.N != 1: + 903 raise Exception("Correlator must be projected before plotting") + 904 + 905 if auto_gamma: + 906 self.gamma_method() + 907 + 908 if x_range is None: + 909 x_range = [0, self.T - 1] + 910 + 911 fig = plt.figure() + 912 ax1 = fig.add_subplot(111) + 913 + 914 x, y, y_err = self.plottable() + 915 if hide_sigma: + 916 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 917 else: + 918 hide_from = None + 919 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 920 if logscale: + 921 ax1.set_yscale('log') + 922 else: + 923 if y_range is None: + 924 try: + 925 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 926 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 927 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 928 except Exception: + 929 pass + 930 else: + 931 ax1.set_ylim(y_range) + 932 if comp: + 933 if isinstance(comp, (Corr, list)): + 934 for corr in comp if isinstance(comp, list) else [comp]: + 935 if auto_gamma: + 936 corr.gamma_method() + 937 x, y, y_err = corr.plottable() + 938 if hide_sigma: + 939 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 940 else: + 941 hide_from = None + 942 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 943 else: + 944 raise Exception("'comp' must be a correlator or a list of correlators.") + 945 + 946 if plateau: + 947 if isinstance(plateau, Obs): + 948 if auto_gamma: + 949 plateau.gamma_method() + 950 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 951 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 952 else: + 953 raise Exception("'plateau' must be an Obs") + 954 + 955 if references: + 956 if isinstance(references, list): + 957 for ref in references: + 958 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 959 else: + 960 raise Exception("'references' must be a list of floating pint values.") 961 - 962 if save: - 963 if isinstance(save, str): - 964 fig.savefig(save, bbox_inches='tight') - 965 else: - 966 raise Exception("'save' has to be a string.") - 967 - 968 def spaghetti_plot(self, logscale=True): - 969 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 970 - 971 Parameters - 972 ---------- - 973 logscale : bool - 974 Determines whether the scale of the y-axis is logarithmic or standard. - 975 """ - 976 if self.N != 1: - 977 raise Exception("Correlator needs to be projected first.") - 978 - 979 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) - 980 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 981 - 982 for name in mc_names: - 983 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 962 if self.prange: + 963 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0) + 964 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0) + 965 + 966 if fit_res: + 967 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 968 if isinstance(fit_res.fit_function, dict): + 969 if fit_key: + 970 ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) + 971 else: + 972 raise ValueError("Please provide a 'fit_key' for visualizing combined fits.") + 973 else: + 974 ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) + 975 + 976 ax1.set_xlabel(r'$x_0 / a$') + 977 if ylabel: + 978 ax1.set_ylabel(ylabel) + 979 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 980 + 981 handles, labels = ax1.get_legend_handles_labels() + 982 if labels: + 983 ax1.legend() 984 - 985 fig = plt.figure() - 986 ax = fig.add_subplot(111) - 987 for dat in data: - 988 ax.plot(x0_vals, dat, ls='-', marker='') + 985 if title: + 986 plt.title(title) + 987 + 988 plt.draw() 989 - 990 if logscale is True: - 991 ax.set_yscale('log') - 992 - 993 ax.set_xlabel(r'$x_0 / a$') - 994 plt.title(name) - 995 plt.draw() - 996 - 997 def dump(self, filename, datatype="json.gz", **kwargs): - 998 """Dumps the Corr into a file of chosen type + 990 if save: + 991 if isinstance(save, str): + 992 fig.savefig(save, bbox_inches='tight') + 993 else: + 994 raise Exception("'save' has to be a string.") + 995 + 996 def spaghetti_plot(self, logscale=True): + 997 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 998 999 Parameters 1000 ---------- -1001 filename : str -1002 Name of the file to be saved. -1003 datatype : str -1004 Format of the exported file. Supported formats include -1005 "json.gz" and "pickle" -1006 path : str -1007 specifies a custom path for the file (default '.') -1008 """ -1009 if datatype == "json.gz": -1010 from .input.json import dump_to_json -1011 if 'path' in kwargs: -1012 file_name = kwargs.get('path') + '/' + filename -1013 else: -1014 file_name = filename -1015 dump_to_json(self, file_name) -1016 elif datatype == "pickle": -1017 dump_object(self, filename, **kwargs) -1018 else: -1019 raise Exception("Unknown datatype " + str(datatype)) +1001 logscale : bool +1002 Determines whether the scale of the y-axis is logarithmic or standard. +1003 """ +1004 if self.N != 1: +1005 raise Exception("Correlator needs to be projected first.") +1006 +1007 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) +1008 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] +1009 +1010 for name in mc_names: +1011 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T +1012 +1013 fig = plt.figure() +1014 ax = fig.add_subplot(111) +1015 for dat in data: +1016 ax.plot(x0_vals, dat, ls='-', marker='') +1017 +1018 if logscale is True: +1019 ax.set_yscale('log') 1020 -1021 def print(self, print_range=None): -1022 print(self.__repr__(print_range)) -1023 -1024 def __repr__(self, print_range=None): -1025 if print_range is None: -1026 print_range = [0, None] -1027 -1028 content_string = "" -1029 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here -1030 -1031 if self.tag is not None: -1032 content_string += "Description: " + self.tag + "\n" -1033 if self.N != 1: -1034 return content_string -1035 -1036 if print_range[1]: -1037 print_range[1] += 1 -1038 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' -1039 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): -1040 if sub_corr is None: -1041 content_string += str(i + print_range[0]) + '\n' -1042 else: -1043 content_string += str(i + print_range[0]) -1044 for element in sub_corr: -1045 content_string += f"\t{element:+2}" -1046 content_string += '\n' -1047 return content_string +1021 ax.set_xlabel(r'$x_0 / a$') +1022 plt.title(name) +1023 plt.draw() +1024 +1025 def dump(self, filename, datatype="json.gz", **kwargs): +1026 """Dumps the Corr into a file of chosen type +1027 Parameters +1028 ---------- +1029 filename : str +1030 Name of the file to be saved. +1031 datatype : str +1032 Format of the exported file. Supported formats include +1033 "json.gz" and "pickle" +1034 path : str +1035 specifies a custom path for the file (default '.') +1036 """ +1037 if datatype == "json.gz": +1038 from .input.json import dump_to_json +1039 if 'path' in kwargs: +1040 file_name = kwargs.get('path') + '/' + filename +1041 else: +1042 file_name = filename +1043 dump_to_json(self, file_name) +1044 elif datatype == "pickle": +1045 dump_object(self, filename, **kwargs) +1046 else: +1047 raise Exception("Unknown datatype " + str(datatype)) 1048 -1049 def __str__(self): -1050 return self.__repr__() +1049 def print(self, print_range=None): +1050 print(self.__repr__(print_range)) 1051 -1052 # We define the basic operations, that can be performed with correlators. -1053 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. -1054 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. -1055 # One could try and tell Obs to check if the y in __mul__ is a Corr and -1056 -1057 __array_priority__ = 10000 +1052 def __repr__(self, print_range=None): +1053 if print_range is None: +1054 print_range = [0, None] +1055 +1056 content_string = "" +1057 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here 1058 -1059 def __eq__(self, y): -1060 if isinstance(y, Corr): -1061 comp = np.asarray(y.content, dtype=object) -1062 else: -1063 comp = np.asarray(y) -1064 return np.asarray(self.content, dtype=object) == comp -1065 -1066 def __add__(self, y): -1067 if isinstance(y, Corr): -1068 if ((self.N != y.N) or (self.T != y.T)): -1069 raise Exception("Addition of Corrs with different shape") -1070 newcontent = [] -1071 for t in range(self.T): -1072 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1073 newcontent.append(None) -1074 else: -1075 newcontent.append(self.content[t] + y.content[t]) -1076 return Corr(newcontent) -1077 -1078 elif isinstance(y, (Obs, int, float, CObs, complex)): -1079 newcontent = [] -1080 for t in range(self.T): -1081 if _check_for_none(self, self.content[t]): -1082 newcontent.append(None) -1083 else: -1084 newcontent.append(self.content[t] + y) -1085 return Corr(newcontent, prange=self.prange) -1086 elif isinstance(y, np.ndarray): -1087 if y.shape == (self.T,): -1088 return Corr(list((np.array(self.content).T + y).T)) -1089 else: -1090 raise ValueError("operands could not be broadcast together") -1091 else: -1092 raise TypeError("Corr + wrong type") +1059 if self.tag is not None: +1060 content_string += "Description: " + self.tag + "\n" +1061 if self.N != 1: +1062 return content_string +1063 +1064 if print_range[1]: +1065 print_range[1] += 1 +1066 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' +1067 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): +1068 if sub_corr is None: +1069 content_string += str(i + print_range[0]) + '\n' +1070 else: +1071 content_string += str(i + print_range[0]) +1072 for element in sub_corr: +1073 content_string += f"\t{element:+2}" +1074 content_string += '\n' +1075 return content_string +1076 +1077 def __str__(self): +1078 return self.__repr__() +1079 +1080 # We define the basic operations, that can be performed with correlators. +1081 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. +1082 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. +1083 # One could try and tell Obs to check if the y in __mul__ is a Corr and +1084 +1085 __array_priority__ = 10000 +1086 +1087 def __eq__(self, y): +1088 if isinstance(y, Corr): +1089 comp = np.asarray(y.content, dtype=object) +1090 else: +1091 comp = np.asarray(y) +1092 return np.asarray(self.content, dtype=object) == comp 1093 -1094 def __mul__(self, y): +1094 def __add__(self, y): 1095 if isinstance(y, Corr): -1096 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1097 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1096 if ((self.N != y.N) or (self.T != y.T)): +1097 raise Exception("Addition of Corrs with different shape") 1098 newcontent = [] 1099 for t in range(self.T): 1100 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): 1101 newcontent.append(None) 1102 else: -1103 newcontent.append(self.content[t] * y.content[t]) +1103 newcontent.append(self.content[t] + y.content[t]) 1104 return Corr(newcontent) 1105 1106 elif isinstance(y, (Obs, int, float, CObs, complex)): @@ -1352,322 +1352,408 @@ 1109 if _check_for_none(self, self.content[t]): 1110 newcontent.append(None) 1111 else: -1112 newcontent.append(self.content[t] * y) +1112 newcontent.append(self.content[t] + y) 1113 return Corr(newcontent, prange=self.prange) 1114 elif isinstance(y, np.ndarray): 1115 if y.shape == (self.T,): -1116 return Corr(list((np.array(self.content).T * y).T)) +1116 return Corr(list((np.array(self.content).T + y).T)) 1117 else: 1118 raise ValueError("operands could not be broadcast together") 1119 else: -1120 raise TypeError("Corr * wrong type") +1120 raise TypeError("Corr + wrong type") 1121 -1122 def __matmul__(self, y): -1123 if isinstance(y, np.ndarray): -1124 if y.ndim != 2 or y.shape[0] != y.shape[1]: -1125 raise ValueError("Can only multiply correlators by square matrices.") -1126 if not self.N == y.shape[0]: -1127 raise ValueError("matmul: mismatch of matrix dimensions") -1128 newcontent = [] -1129 for t in range(self.T): -1130 if _check_for_none(self, self.content[t]): -1131 newcontent.append(None) -1132 else: -1133 newcontent.append(self.content[t] @ y) -1134 return Corr(newcontent) -1135 elif isinstance(y, Corr): -1136 if not self.N == y.N: -1137 raise ValueError("matmul: mismatch of matrix dimensions") -1138 newcontent = [] -1139 for t in range(self.T): -1140 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1141 newcontent.append(None) -1142 else: -1143 newcontent.append(self.content[t] @ y.content[t]) -1144 return Corr(newcontent) -1145 -1146 else: -1147 return NotImplemented -1148 -1149 def __rmatmul__(self, y): -1150 if isinstance(y, np.ndarray): -1151 if y.ndim != 2 or y.shape[0] != y.shape[1]: -1152 raise ValueError("Can only multiply correlators by square matrices.") -1153 if not self.N == y.shape[0]: -1154 raise ValueError("matmul: mismatch of matrix dimensions") -1155 newcontent = [] -1156 for t in range(self.T): -1157 if _check_for_none(self, self.content[t]): -1158 newcontent.append(None) -1159 else: -1160 newcontent.append(y @ self.content[t]) -1161 return Corr(newcontent) -1162 else: -1163 return NotImplemented -1164 -1165 def __truediv__(self, y): -1166 if isinstance(y, Corr): -1167 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1168 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1169 newcontent = [] -1170 for t in range(self.T): -1171 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1172 newcontent.append(None) -1173 else: -1174 newcontent.append(self.content[t] / y.content[t]) -1175 for t in range(self.T): -1176 if _check_for_none(self, newcontent[t]): -1177 continue -1178 if np.isnan(np.sum(newcontent[t]).value): -1179 newcontent[t] = None -1180 -1181 if all([item is None for item in newcontent]): -1182 raise Exception("Division returns completely undefined correlator") -1183 return Corr(newcontent) -1184 -1185 elif isinstance(y, (Obs, CObs)): -1186 if isinstance(y, Obs): -1187 if y.value == 0: -1188 raise Exception('Division by zero will return undefined correlator') -1189 if isinstance(y, CObs): -1190 if y.is_zero(): -1191 raise Exception('Division by zero will return undefined correlator') +1122 def __mul__(self, y): +1123 if isinstance(y, Corr): +1124 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1125 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1126 newcontent = [] +1127 for t in range(self.T): +1128 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1129 newcontent.append(None) +1130 else: +1131 newcontent.append(self.content[t] * y.content[t]) +1132 return Corr(newcontent) +1133 +1134 elif isinstance(y, (Obs, int, float, CObs, complex)): +1135 newcontent = [] +1136 for t in range(self.T): +1137 if _check_for_none(self, self.content[t]): +1138 newcontent.append(None) +1139 else: +1140 newcontent.append(self.content[t] * y) +1141 return Corr(newcontent, prange=self.prange) +1142 elif isinstance(y, np.ndarray): +1143 if y.shape == (self.T,): +1144 return Corr(list((np.array(self.content).T * y).T)) +1145 else: +1146 raise ValueError("operands could not be broadcast together") +1147 else: +1148 raise TypeError("Corr * wrong type") +1149 +1150 def __matmul__(self, y): +1151 if isinstance(y, np.ndarray): +1152 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1153 raise ValueError("Can only multiply correlators by square matrices.") +1154 if not self.N == y.shape[0]: +1155 raise ValueError("matmul: mismatch of matrix dimensions") +1156 newcontent = [] +1157 for t in range(self.T): +1158 if _check_for_none(self, self.content[t]): +1159 newcontent.append(None) +1160 else: +1161 newcontent.append(self.content[t] @ y) +1162 return Corr(newcontent) +1163 elif isinstance(y, Corr): +1164 if not self.N == y.N: +1165 raise ValueError("matmul: mismatch of matrix dimensions") +1166 newcontent = [] +1167 for t in range(self.T): +1168 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1169 newcontent.append(None) +1170 else: +1171 newcontent.append(self.content[t] @ y.content[t]) +1172 return Corr(newcontent) +1173 +1174 else: +1175 return NotImplemented +1176 +1177 def __rmatmul__(self, y): +1178 if isinstance(y, np.ndarray): +1179 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1180 raise ValueError("Can only multiply correlators by square matrices.") +1181 if not self.N == y.shape[0]: +1182 raise ValueError("matmul: mismatch of matrix dimensions") +1183 newcontent = [] +1184 for t in range(self.T): +1185 if _check_for_none(self, self.content[t]): +1186 newcontent.append(None) +1187 else: +1188 newcontent.append(y @ self.content[t]) +1189 return Corr(newcontent) +1190 else: +1191 return NotImplemented 1192 -1193 newcontent = [] -1194 for t in range(self.T): -1195 if _check_for_none(self, self.content[t]): -1196 newcontent.append(None) -1197 else: -1198 newcontent.append(self.content[t] / y) -1199 return Corr(newcontent, prange=self.prange) -1200 -1201 elif isinstance(y, (int, float)): -1202 if y == 0: -1203 raise Exception('Division by zero will return undefined correlator') -1204 newcontent = [] -1205 for t in range(self.T): -1206 if _check_for_none(self, self.content[t]): -1207 newcontent.append(None) -1208 else: -1209 newcontent.append(self.content[t] / y) -1210 return Corr(newcontent, prange=self.prange) -1211 elif isinstance(y, np.ndarray): -1212 if y.shape == (self.T,): -1213 return Corr(list((np.array(self.content).T / y).T)) -1214 else: -1215 raise ValueError("operands could not be broadcast together") -1216 else: -1217 raise TypeError('Corr / wrong type') -1218 -1219 def __neg__(self): -1220 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1221 return Corr(newcontent, prange=self.prange) -1222 -1223 def __sub__(self, y): -1224 return self + (-y) -1225 -1226 def __pow__(self, y): -1227 if isinstance(y, (Obs, int, float, CObs)): -1228 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1229 return Corr(newcontent, prange=self.prange) -1230 else: -1231 raise TypeError('Type of exponent not supported') -1232 -1233 def __abs__(self): -1234 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1235 return Corr(newcontent, prange=self.prange) -1236 -1237 # The numpy functions: -1238 def sqrt(self): -1239 return self ** 0.5 -1240 -1241 def log(self): -1242 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1243 return Corr(newcontent, prange=self.prange) -1244 -1245 def exp(self): -1246 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1247 return Corr(newcontent, prange=self.prange) -1248 -1249 def _apply_func_to_corr(self, func): -1250 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1251 for t in range(self.T): -1252 if _check_for_none(self, newcontent[t]): -1253 continue -1254 tmp_sum = np.sum(newcontent[t]) -1255 if hasattr(tmp_sum, "value"): -1256 if np.isnan(tmp_sum.value): -1257 newcontent[t] = None -1258 if all([item is None for item in newcontent]): -1259 raise Exception('Operation returns undefined correlator') -1260 return Corr(newcontent) -1261 -1262 def sin(self): -1263 return self._apply_func_to_corr(np.sin) +1193 def __truediv__(self, y): +1194 if isinstance(y, Corr): +1195 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1196 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1197 newcontent = [] +1198 for t in range(self.T): +1199 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1200 newcontent.append(None) +1201 else: +1202 newcontent.append(self.content[t] / y.content[t]) +1203 for t in range(self.T): +1204 if _check_for_none(self, newcontent[t]): +1205 continue +1206 if np.isnan(np.sum(newcontent[t]).value): +1207 newcontent[t] = None +1208 +1209 if all([item is None for item in newcontent]): +1210 raise Exception("Division returns completely undefined correlator") +1211 return Corr(newcontent) +1212 +1213 elif isinstance(y, (Obs, CObs)): +1214 if isinstance(y, Obs): +1215 if y.value == 0: +1216 raise Exception('Division by zero will return undefined correlator') +1217 if isinstance(y, CObs): +1218 if y.is_zero(): +1219 raise Exception('Division by zero will return undefined correlator') +1220 +1221 newcontent = [] +1222 for t in range(self.T): +1223 if _check_for_none(self, self.content[t]): +1224 newcontent.append(None) +1225 else: +1226 newcontent.append(self.content[t] / y) +1227 return Corr(newcontent, prange=self.prange) +1228 +1229 elif isinstance(y, (int, float)): +1230 if y == 0: +1231 raise Exception('Division by zero will return undefined correlator') +1232 newcontent = [] +1233 for t in range(self.T): +1234 if _check_for_none(self, self.content[t]): +1235 newcontent.append(None) +1236 else: +1237 newcontent.append(self.content[t] / y) +1238 return Corr(newcontent, prange=self.prange) +1239 elif isinstance(y, np.ndarray): +1240 if y.shape == (self.T,): +1241 return Corr(list((np.array(self.content).T / y).T)) +1242 else: +1243 raise ValueError("operands could not be broadcast together") +1244 else: +1245 raise TypeError('Corr / wrong type') +1246 +1247 def __neg__(self): +1248 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1249 return Corr(newcontent, prange=self.prange) +1250 +1251 def __sub__(self, y): +1252 return self + (-y) +1253 +1254 def __pow__(self, y): +1255 if isinstance(y, (Obs, int, float, CObs)): +1256 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1257 return Corr(newcontent, prange=self.prange) +1258 else: +1259 raise TypeError('Type of exponent not supported') +1260 +1261 def __abs__(self): +1262 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1263 return Corr(newcontent, prange=self.prange) 1264 -1265 def cos(self): -1266 return self._apply_func_to_corr(np.cos) -1267 -1268 def tan(self): -1269 return self._apply_func_to_corr(np.tan) -1270 -1271 def sinh(self): -1272 return self._apply_func_to_corr(np.sinh) -1273 -1274 def cosh(self): -1275 return self._apply_func_to_corr(np.cosh) +1265 # The numpy functions: +1266 def sqrt(self): +1267 return self ** 0.5 +1268 +1269 def log(self): +1270 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1271 return Corr(newcontent, prange=self.prange) +1272 +1273 def exp(self): +1274 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1275 return Corr(newcontent, prange=self.prange) 1276 -1277 def tanh(self): -1278 return self._apply_func_to_corr(np.tanh) -1279 -1280 def arcsin(self): -1281 return self._apply_func_to_corr(np.arcsin) -1282 -1283 def arccos(self): -1284 return self._apply_func_to_corr(np.arccos) -1285 -1286 def arctan(self): -1287 return self._apply_func_to_corr(np.arctan) -1288 -1289 def arcsinh(self): -1290 return self._apply_func_to_corr(np.arcsinh) -1291 -1292 def arccosh(self): -1293 return self._apply_func_to_corr(np.arccosh) -1294 -1295 def arctanh(self): -1296 return self._apply_func_to_corr(np.arctanh) -1297 -1298 # Right hand side operations (require tweak in main module to work) -1299 def __radd__(self, y): -1300 return self + y +1277 def _apply_func_to_corr(self, func): +1278 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1279 for t in range(self.T): +1280 if _check_for_none(self, newcontent[t]): +1281 continue +1282 tmp_sum = np.sum(newcontent[t]) +1283 if hasattr(tmp_sum, "value"): +1284 if np.isnan(tmp_sum.value): +1285 newcontent[t] = None +1286 if all([item is None for item in newcontent]): +1287 raise Exception('Operation returns undefined correlator') +1288 return Corr(newcontent) +1289 +1290 def sin(self): +1291 return self._apply_func_to_corr(np.sin) +1292 +1293 def cos(self): +1294 return self._apply_func_to_corr(np.cos) +1295 +1296 def tan(self): +1297 return self._apply_func_to_corr(np.tan) +1298 +1299 def sinh(self): +1300 return self._apply_func_to_corr(np.sinh) 1301 -1302 def __rsub__(self, y): -1303 return -self + y +1302 def cosh(self): +1303 return self._apply_func_to_corr(np.cosh) 1304 -1305 def __rmul__(self, y): -1306 return self * y +1305 def tanh(self): +1306 return self._apply_func_to_corr(np.tanh) 1307 -1308 def __rtruediv__(self, y): -1309 return (self / y) ** (-1) +1308 def arcsin(self): +1309 return self._apply_func_to_corr(np.arcsin) 1310 -1311 @property -1312 def real(self): -1313 def return_real(obs_OR_cobs): -1314 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1315 return np.vectorize(lambda x: x.real)(obs_OR_cobs) -1316 else: -1317 return obs_OR_cobs -1318 -1319 return self._apply_func_to_corr(return_real) -1320 -1321 @property -1322 def imag(self): -1323 def return_imag(obs_OR_cobs): -1324 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1325 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) -1326 else: -1327 return obs_OR_cobs * 0 # So it stays the right type -1328 -1329 return self._apply_func_to_corr(return_imag) -1330 -1331 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1332 r''' Project large correlation matrix to lowest states -1333 -1334 This method can be used to reduce the size of an (N x N) correlation matrix -1335 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1336 is still small. -1337 -1338 Parameters -1339 ---------- -1340 Ntrunc: int -1341 Rank of the target matrix. -1342 tproj: int -1343 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1344 The default value is 3. -1345 t0proj: int -1346 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1347 discouraged for O(a) improved theories, since the correctness of the procedure -1348 cannot be granted in this case. The default value is 2. -1349 basematrix : Corr -1350 Correlation matrix that is used to determine the eigenvectors of the -1351 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1352 is is not specified. -1353 -1354 Notes -1355 ----- -1356 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1357 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1358 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1359 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1360 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1361 correlation matrix and to remove some noise that is added by irrelevant operators. -1362 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1363 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1364 ''' +1311 def arccos(self): +1312 return self._apply_func_to_corr(np.arccos) +1313 +1314 def arctan(self): +1315 return self._apply_func_to_corr(np.arctan) +1316 +1317 def arcsinh(self): +1318 return self._apply_func_to_corr(np.arcsinh) +1319 +1320 def arccosh(self): +1321 return self._apply_func_to_corr(np.arccosh) +1322 +1323 def arctanh(self): +1324 return self._apply_func_to_corr(np.arctanh) +1325 +1326 # Right hand side operations (require tweak in main module to work) +1327 def __radd__(self, y): +1328 return self + y +1329 +1330 def __rsub__(self, y): +1331 return -self + y +1332 +1333 def __rmul__(self, y): +1334 return self * y +1335 +1336 def __rtruediv__(self, y): +1337 return (self / y) ** (-1) +1338 +1339 @property +1340 def real(self): +1341 def return_real(obs_OR_cobs): +1342 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1343 return np.vectorize(lambda x: x.real)(obs_OR_cobs) +1344 else: +1345 return obs_OR_cobs +1346 +1347 return self._apply_func_to_corr(return_real) +1348 +1349 @property +1350 def imag(self): +1351 def return_imag(obs_OR_cobs): +1352 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1353 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) +1354 else: +1355 return obs_OR_cobs * 0 # So it stays the right type +1356 +1357 return self._apply_func_to_corr(return_imag) +1358 +1359 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1360 r''' Project large correlation matrix to lowest states +1361 +1362 This method can be used to reduce the size of an (N x N) correlation matrix +1363 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1364 is still small. 1365 -1366 if self.N == 1: -1367 raise Exception('Method cannot be applied to one-dimensional correlators.') -1368 if basematrix is None: -1369 basematrix = self -1370 if Ntrunc >= basematrix.N: -1371 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1372 if basematrix.N != self.N: -1373 raise Exception('basematrix and targetmatrix have to be of the same size.') -1374 -1375 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1376 -1377 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1378 rmat = [] -1379 for t in range(basematrix.T): -1380 for i in range(Ntrunc): -1381 for j in range(Ntrunc): -1382 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1383 rmat.append(np.copy(tmpmat)) -1384 -1385 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1386 return Corr(newcontent) -1387 -1388 -1389def _sort_vectors(vec_set, ts): -1390 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" -1391 reference_sorting = np.array(vec_set[ts]) -1392 N = reference_sorting.shape[0] -1393 sorted_vec_set = [] -1394 for t in range(len(vec_set)): -1395 if vec_set[t] is None: -1396 sorted_vec_set.append(None) -1397 elif not t == ts: -1398 perms = [list(o) for o in permutations([i for i in range(N)], N)] -1399 best_score = 0 -1400 for perm in perms: -1401 current_score = 1 -1402 for k in range(N): -1403 new_sorting = reference_sorting.copy() -1404 new_sorting[perm[k], :] = vec_set[t][k] -1405 current_score *= abs(np.linalg.det(new_sorting)) -1406 if current_score > best_score: -1407 best_score = current_score -1408 best_perm = perm -1409 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) -1410 else: -1411 sorted_vec_set.append(vec_set[t]) +1366 Parameters +1367 ---------- +1368 Ntrunc: int +1369 Rank of the target matrix. +1370 tproj: int +1371 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1372 The default value is 3. +1373 t0proj: int +1374 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1375 discouraged for O(a) improved theories, since the correctness of the procedure +1376 cannot be granted in this case. The default value is 2. +1377 basematrix : Corr +1378 Correlation matrix that is used to determine the eigenvectors of the +1379 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1380 is is not specified. +1381 +1382 Notes +1383 ----- +1384 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1385 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1386 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1387 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1388 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1389 correlation matrix and to remove some noise that is added by irrelevant operators. +1390 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1391 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1392 ''' +1393 +1394 if self.N == 1: +1395 raise Exception('Method cannot be applied to one-dimensional correlators.') +1396 if basematrix is None: +1397 basematrix = self +1398 if Ntrunc >= basematrix.N: +1399 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1400 if basematrix.N != self.N: +1401 raise Exception('basematrix and targetmatrix have to be of the same size.') +1402 +1403 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1404 +1405 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1406 rmat = [] +1407 for t in range(basematrix.T): +1408 for i in range(Ntrunc): +1409 for j in range(Ntrunc): +1410 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1411 rmat.append(np.copy(tmpmat)) 1412 -1413 return sorted_vec_set -1414 +1413 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1414 return Corr(newcontent) 1415 -1416def _check_for_none(corr, entry): -1417 """Checks if entry for correlator corr is None""" -1418 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1416 +1417def _sort_vectors(vec_set_in, ts): +1418 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" 1419 -1420 -1421def _GEVP_solver(Gt, G0): -1422 """Helper function for solving the GEVP and sorting the eigenvectors. -1423 -1424 The helper function assumes that both provided matrices are symmetric and -1425 only processes the lower triangular part of both matrices. In case the matrices -1426 are not symmetric the upper triangular parts are effectively discarded.""" -1427 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] +1420 if isinstance(vec_set_in[ts][0][0], Obs): +1421 vec_set = [anp.vectorize(lambda x: float(x))(vi) if vi is not None else vi for vi in vec_set_in] +1422 else: +1423 vec_set = vec_set_in +1424 reference_sorting = np.array(vec_set[ts]) +1425 N = reference_sorting.shape[0] +1426 sorted_vec_set = [] +1427 for t in range(len(vec_set)): +1428 if vec_set[t] is None: +1429 sorted_vec_set.append(None) +1430 elif not t == ts: +1431 perms = [list(o) for o in permutations([i for i in range(N)], N)] +1432 best_score = 0 +1433 for perm in perms: +1434 current_score = 1 +1435 for k in range(N): +1436 new_sorting = reference_sorting.copy() +1437 new_sorting[perm[k], :] = vec_set[t][k] +1438 current_score *= abs(np.linalg.det(new_sorting)) +1439 if current_score > best_score: +1440 best_score = current_score +1441 best_perm = perm +1442 sorted_vec_set.append([vec_set_in[t][k] for k in best_perm]) +1443 else: +1444 sorted_vec_set.append(vec_set_in[t]) +1445 +1446 return sorted_vec_set +1447 +1448 +1449def _check_for_none(corr, entry): +1450 """Checks if entry for correlator corr is None""" +1451 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1452 +1453 +1454def _GEVP_solver(Gt, G0, method='eigh', chol_inv=None): +1455 r"""Helper function for solving the GEVP and sorting the eigenvectors. +1456 +1457 Solves $G(t)v_i=\lambda_i G(t_0)v_i$ and returns the eigenvectors v_i +1458 +1459 The helper function assumes that both provided matrices are symmetric and +1460 only processes the lower triangular part of both matrices. In case the matrices +1461 are not symmetric the upper triangular parts are effectively discarded. +1462 +1463 Parameters +1464 ---------- +1465 Gt : array +1466 The correlator at time t for the left hand side of the GEVP +1467 G0 : array +1468 The correlator at time t0 for the right hand side of the GEVP +1469 Method used to solve the GEVP. +1470 - "eigh": Use scipy.linalg.eigh to solve the GEVP. +1471 - "cholesky": Use manually implemented solution via the Cholesky decomposition. +1472 chol_inv : array, optional +1473 Inverse of the Cholesky decomposition of G0. May be provided to +1474 speed up the computation in the case of method=='cholesky' +1475 +1476 """ +1477 if isinstance(G0[0][0], Obs): +1478 vector_obs = True +1479 else: +1480 vector_obs = False +1481 +1482 if method == 'cholesky': +1483 if vector_obs: +1484 cholesky = linalg.cholesky +1485 inv = linalg.inv +1486 eigv = linalg.eigv +1487 matmul = linalg.matmul +1488 else: +1489 cholesky = np.linalg.cholesky +1490 inv = np.linalg.inv +1491 +1492 def eigv(x, **kwargs): +1493 return np.linalg.eigh(x)[1] +1494 +1495 def matmul(*operands): +1496 return np.linalg.multi_dot(operands) +1497 N = Gt.shape[0] +1498 output = [[] for j in range(N)] +1499 if chol_inv is None: +1500 chol = cholesky(G0) # This will automatically report if the matrix is not pos-def +1501 chol_inv = inv(chol) +1502 +1503 try: +1504 new_matrix = matmul(chol_inv, Gt, chol_inv.T) +1505 ev = eigv(new_matrix) +1506 ev = matmul(chol_inv.T, ev) +1507 output = np.flip(ev, axis=1).T +1508 except (np.linalg.LinAlgError, TypeError, ValueError): # The above code can fail because of linalg-errors or because the entry of the corr is None +1509 for s in range(N): +1510 output[s] = None +1511 return output +1512 elif method == 'eigh': +1513 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] @@ -1683,1097 +1769,1096 @@ - 
  14class Corr:
-  15    r"""The class for a correlator (time dependent sequence of pe.Obs).
-  16
-  17    Everything, this class does, can be achieved using lists or arrays of Obs.
-  18    But it is simply more convenient to have a dedicated object for correlators.
-  19    One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient
-  20    to iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
-  21
-  22    The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.
-  23    Other dependency (eg. spatial) are not supported.
-  24
-  25    The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.
-  26    The missing entries are represented via the `None` object.
-  27
-  28    Initialization
-  29    --------------
-  30    A simple correlator can be initialized with a list or a one-dimensional array of `Obs` or `Cobs`
-  31    ```python
-  32    corr11 = pe.Corr([obs1, obs2])
-  33    corr11 = pe.Corr(np.array([obs1, obs2]))
-  34    ```
-  35    A matrix-valued correlator can either be initialized via a two-dimensional array of `Corr` objects
-  36    ```python
-  37    matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))
-  38    ```
-  39    or alternatively via a three-dimensional array of `Obs` or `CObs` of shape (T, N, N) where T is
-  40    the temporal extent of the correlator and N is the dimension of the matrix.
-  41    """
-  42
-  43    __slots__ = ["content", "N", "T", "tag", "prange"]
-  44
-  45    def __init__(self, data_input, padding=[0, 0], prange=None):
-  46        """ Initialize a Corr object.
-  47
-  48        Parameters
-  49        ----------
-  50        data_input : list or array
-  51            list of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
-  52        padding : list, optional
-  53            List with two entries where the first labels the padding
-  54            at the front of the correlator and the second the padding
-  55            at the back.
-  56        prange : list, optional
-  57            List containing the first and last timeslice of the plateau
-  58            region identified for this correlator.
-  59        """
-  60
-  61        if isinstance(data_input, np.ndarray):
-  62            if data_input.ndim == 1:
-  63                data_input = list(data_input)
-  64            elif data_input.ndim == 2:
-  65                if not data_input.shape[0] == data_input.shape[1]:
-  66                    raise ValueError("Array needs to be square.")
-  67                if not all([isinstance(item, Corr) for item in data_input.flatten()]):
-  68                    raise ValueError("If the input is an array, its elements must be of type pe.Corr.")
-  69                if not all([item.N == 1 for item in data_input.flatten()]):
-  70                    raise ValueError("Can only construct matrix correlator from single valued correlators.")
-  71                if not len(set([item.T for item in data_input.flatten()])) == 1:
-  72                    raise ValueError("All input Correlators must be defined over the same timeslices.")
-  73
-  74                T = data_input[0, 0].T
-  75                N = data_input.shape[0]
-  76                input_as_list = []
-  77                for t in range(T):
-  78                    if any([(item.content[t] is None) for item in data_input.flatten()]):
-  79                        if not all([(item.content[t] is None) for item in data_input.flatten()]):
-  80                            warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss.!", RuntimeWarning)
-  81                        input_as_list.append(None)
-  82                    else:
-  83                        array_at_timeslace = np.empty([N, N], dtype="object")
-  84                        for i in range(N):
-  85                            for j in range(N):
-  86                                array_at_timeslace[i, j] = data_input[i, j][t]
-  87                        input_as_list.append(array_at_timeslace)
-  88                data_input = input_as_list
-  89            elif data_input.ndim == 3:
-  90                if not data_input.shape[1] == data_input.shape[2]:
-  91                    raise ValueError("Array needs to be square.")
-  92                data_input = list(data_input)
-  93            else:
-  94                raise ValueError("Arrays with ndim>3 not supported.")
-  95
-  96        if isinstance(data_input, list):
-  97
-  98            if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
-  99                _assert_equal_properties([o for o in data_input if o is not None])
- 100                self.content = [np.asarray([item]) if item is not None else None for item in data_input]
- 101                self.N = 1
- 102            elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]):
- 103                self.content = data_input
- 104                noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
- 105                self.N = noNull[0].shape[0]
- 106                if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
- 107                    raise ValueError("Smearing matrices are not NxN.")
- 108                if (not all([item.shape == noNull[0].shape for item in noNull])):
- 109                    raise ValueError("Items in data_input are not of identical shape." + str(noNull))
- 110            else:
- 111                raise TypeError("'data_input' contains item of wrong type.")
- 112        else:
- 113            raise TypeError("Data input was not given as list or correct array.")
- 114
- 115        self.tag = None
- 116
- 117        # An undefined timeslice is represented by the None object
- 118        self.content = [None] * padding[0] + self.content + [None] * padding[1]
- 119        self.T = len(self.content)
- 120        self.prange = prange
- 121
- 122    def __getitem__(self, idx):
- 123        """Return the content of timeslice idx"""
- 124        if self.content[idx] is None:
- 125            return None
- 126        elif len(self.content[idx]) == 1:
- 127            return self.content[idx][0]
- 128        else:
- 129            return self.content[idx]
- 130
- 131    @property
- 132    def reweighted(self):
- 133        bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]])
- 134        if np.all(bool_array == 1):
- 135            return True
- 136        elif np.all(bool_array == 0):
- 137            return False
- 138        else:
- 139            raise Exception("Reweighting status of correlator corrupted.")
- 140
- 141    def gamma_method(self, **kwargs):
- 142        """Apply the gamma method to the content of the Corr."""
- 143        for item in self.content:
- 144            if not (item is None):
- 145                if self.N == 1:
- 146                    item[0].gamma_method(**kwargs)
- 147                else:
- 148                    for i in range(self.N):
- 149                        for j in range(self.N):
- 150                            item[i, j].gamma_method(**kwargs)
- 151
- 152    gm = gamma_method
- 153
- 154    def projected(self, vector_l=None, vector_r=None, normalize=False):
- 155        """We need to project the Correlator with a Vector to get a single value at each timeslice.
- 156
- 157        The method can use one or two vectors.
- 158        If two are specified it returns v1@G@v2 (the order might be very important.)
- 159        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
- 160        """
- 161        if self.N == 1:
- 162            raise Exception("Trying to project a Corr, that already has N=1.")
- 163
- 164        if vector_l is None:
- 165            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
- 166        elif (vector_r is None):
- 167            vector_r = vector_l
- 168        if isinstance(vector_l, list) and not isinstance(vector_r, list):
- 169            if len(vector_l) != self.T:
- 170                raise Exception("Length of vector list must be equal to T")
- 171            vector_r = [vector_r] * self.T
- 172        if isinstance(vector_r, list) and not isinstance(vector_l, list):
- 173            if len(vector_r) != self.T:
- 174                raise Exception("Length of vector list must be equal to T")
- 175            vector_l = [vector_l] * self.T
- 176
- 177        if not isinstance(vector_l, list):
- 178            if not vector_l.shape == vector_r.shape == (self.N,):
- 179                raise Exception("Vectors are of wrong shape!")
- 180            if normalize:
- 181                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
- 182            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
- 183
- 184        else:
- 185            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
- 186            if normalize:
- 187                for t in range(self.T):
- 188                    vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t])
- 189
- 190            newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
- 191        return Corr(newcontent)
- 192
- 193    def item(self, i, j):
- 194        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
- 195
- 196        Parameters
- 197        ----------
- 198        i : int
- 199            First index to be picked.
- 200        j : int
- 201            Second index to be picked.
- 202        """
- 203        if self.N == 1:
- 204            raise Exception("Trying to pick item from projected Corr")
- 205        newcontent = [None if (item is None) else item[i, j] for item in self.content]
- 206        return Corr(newcontent)
- 207
- 208    def plottable(self):
- 209        """Outputs the correlator in a plotable format.
- 210
- 211        Outputs three lists containing the timeslice index, the value on each
- 212        timeslice and the error on each timeslice.
- 213        """
- 214        if self.N != 1:
- 215            raise Exception("Can only make Corr[N=1] plottable")
- 216        x_list = [x for x in range(self.T) if not self.content[x] is None]
- 217        y_list = [y[0].value for y in self.content if y is not None]
- 218        y_err_list = [y[0].dvalue for y in self.content if y is not None]
- 219
- 220        return x_list, y_list, y_err_list
- 221
- 222    def symmetric(self):
- 223        """ Symmetrize the correlator around x0=0."""
- 224        if self.N != 1:
- 225            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
- 226        if self.T % 2 != 0:
- 227            raise Exception("Can not symmetrize odd T")
- 228
- 229        if self.content[0] is not None:
- 230            if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0:
- 231                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
- 232
- 233        newcontent = [self.content[0]]
- 234        for t in range(1, self.T):
- 235            if (self.content[t] is None) or (self.content[self.T - t] is None):
- 236                newcontent.append(None)
- 237            else:
- 238                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
- 239        if (all([x is None for x in newcontent])):
- 240            raise Exception("Corr could not be symmetrized: No redundant values")
- 241        return Corr(newcontent, prange=self.prange)
- 242
- 243    def anti_symmetric(self):
- 244        """Anti-symmetrize the correlator around x0=0."""
- 245        if self.N != 1:
- 246            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
- 247        if self.T % 2 != 0:
- 248            raise Exception("Can not symmetrize odd T")
- 249
- 250        test = 1 * self
- 251        test.gamma_method()
- 252        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
- 253            warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)
- 254
- 255        newcontent = [self.content[0]]
- 256        for t in range(1, self.T):
- 257            if (self.content[t] is None) or (self.content[self.T - t] is None):
- 258                newcontent.append(None)
- 259            else:
- 260                newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
- 261        if (all([x is None for x in newcontent])):
- 262            raise Exception("Corr could not be symmetrized: No redundant values")
- 263        return Corr(newcontent, prange=self.prange)
- 264
- 265    def is_matrix_symmetric(self):
- 266        """Checks whether a correlator matrices is symmetric on every timeslice."""
- 267        if self.N == 1:
- 268            raise TypeError("Only works for correlator matrices.")
- 269        for t in range(self.T):
- 270            if self[t] is None:
- 271                continue
- 272            for i in range(self.N):
- 273                for j in range(i + 1, self.N):
- 274                    if self[t][i, j] is self[t][j, i]:
- 275                        continue
- 276                    if hash(self[t][i, j]) != hash(self[t][j, i]):
- 277                        return False
- 278        return True
- 279
- 280    def trace(self):
- 281        """Calculates the per-timeslice trace of a correlator matrix."""
- 282        if self.N == 1:
- 283            raise ValueError("Only works for correlator matrices.")
- 284        newcontent = []
- 285        for t in range(self.T):
- 286            if _check_for_none(self, self.content[t]):
- 287                newcontent.append(None)
- 288            else:
- 289                newcontent.append(np.trace(self.content[t]))
- 290        return Corr(newcontent)
- 291
- 292    def matrix_symmetric(self):
- 293        """Symmetrizes the correlator matrices on every timeslice."""
- 294        if self.N == 1:
- 295            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
- 296        if self.is_matrix_symmetric():
- 297            return 1.0 * self
- 298        else:
- 299            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
- 300            return 0.5 * (Corr(transposed) + self)
- 301
- 302    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
- 303        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
- 304
- 305        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
- 306        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
- 307        ```python
- 308        C.GEVP(t0=2)[0]  # Ground state vector(s)
- 309        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
- 310        ```
- 311
- 312        Parameters
- 313        ----------
- 314        t0 : int
- 315            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
- 316        ts : int
- 317            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
- 318            If sort="Eigenvector" it gives a reference point for the sorting method.
- 319        sort : string
- 320            If 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.
- 321            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
- 322            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
- 323              The reference state is identified by its eigenvalue at $t=t_s$.
- 324
- 325        Other Parameters
- 326        ----------------
- 327        state : int
- 328           Returns only the vector(s) for a specified state. The lowest state is zero.
- 329        '''
- 330
- 331        if self.N == 1:
- 332            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
- 333        if ts is not None:
- 334            if (ts <= t0):
- 335                raise Exception("ts has to be larger than t0.")
- 336
- 337        if "sorted_list" in kwargs:
- 338            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
- 339            sort = kwargs.get("sorted_list")
- 340
- 341        if self.is_matrix_symmetric():
- 342            symmetric_corr = self
- 343        else:
- 344            symmetric_corr = self.matrix_symmetric()
- 345
- 346        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
- 347        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
+            
  15class Corr:
+  16    r"""The class for a correlator (time dependent sequence of pe.Obs).
+  17
+  18    Everything, this class does, can be achieved using lists or arrays of Obs.
+  19    But it is simply more convenient to have a dedicated object for correlators.
+  20    One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient
+  21    to iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
+  22
+  23    The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.
+  24    Other dependency (eg. spatial) are not supported.
+  25
+  26    The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.
+  27    The missing entries are represented via the `None` object.
+  28
+  29    Initialization
+  30    --------------
+  31    A simple correlator can be initialized with a list or a one-dimensional array of `Obs` or `Cobs`
+  32    ```python
+  33    corr11 = pe.Corr([obs1, obs2])
+  34    corr11 = pe.Corr(np.array([obs1, obs2]))
+  35    ```
+  36    A matrix-valued correlator can either be initialized via a two-dimensional array of `Corr` objects
+  37    ```python
+  38    matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))
+  39    ```
+  40    or alternatively via a three-dimensional array of `Obs` or `CObs` of shape (T, N, N) where T is
+  41    the temporal extent of the correlator and N is the dimension of the matrix.
+  42    """
+  43
+  44    __slots__ = ["content", "N", "T", "tag", "prange"]
+  45
+  46    def __init__(self, data_input, padding=[0, 0], prange=None):
+  47        """ Initialize a Corr object.
+  48
+  49        Parameters
+  50        ----------
+  51        data_input : list or array
+  52            list of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
+  53        padding : list, optional
+  54            List with two entries where the first labels the padding
+  55            at the front of the correlator and the second the padding
+  56            at the back.
+  57        prange : list, optional
+  58            List containing the first and last timeslice of the plateau
+  59            region identified for this correlator.
+  60        """
+  61
+  62        if isinstance(data_input, np.ndarray):
+  63            if data_input.ndim == 1:
+  64                data_input = list(data_input)
+  65            elif data_input.ndim == 2:
+  66                if not data_input.shape[0] == data_input.shape[1]:
+  67                    raise ValueError("Array needs to be square.")
+  68                if not all([isinstance(item, Corr) for item in data_input.flatten()]):
+  69                    raise ValueError("If the input is an array, its elements must be of type pe.Corr.")
+  70                if not all([item.N == 1 for item in data_input.flatten()]):
+  71                    raise ValueError("Can only construct matrix correlator from single valued correlators.")
+  72                if not len(set([item.T for item in data_input.flatten()])) == 1:
+  73                    raise ValueError("All input Correlators must be defined over the same timeslices.")
+  74
+  75                T = data_input[0, 0].T
+  76                N = data_input.shape[0]
+  77                input_as_list = []
+  78                for t in range(T):
+  79                    if any([(item.content[t] is None) for item in data_input.flatten()]):
+  80                        if not all([(item.content[t] is None) for item in data_input.flatten()]):
+  81                            warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss.!", RuntimeWarning)
+  82                        input_as_list.append(None)
+  83                    else:
+  84                        array_at_timeslace = np.empty([N, N], dtype="object")
+  85                        for i in range(N):
+  86                            for j in range(N):
+  87                                array_at_timeslace[i, j] = data_input[i, j][t]
+  88                        input_as_list.append(array_at_timeslace)
+  89                data_input = input_as_list
+  90            elif data_input.ndim == 3:
+  91                if not data_input.shape[1] == data_input.shape[2]:
+  92                    raise ValueError("Array needs to be square.")
+  93                data_input = list(data_input)
+  94            else:
+  95                raise ValueError("Arrays with ndim>3 not supported.")
+  96
+  97        if isinstance(data_input, list):
+  98
+  99            if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
+ 100                _assert_equal_properties([o for o in data_input if o is not None])
+ 101                self.content = [np.asarray([item]) if item is not None else None for item in data_input]
+ 102                self.N = 1
+ 103            elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]):
+ 104                self.content = data_input
+ 105                noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
+ 106                self.N = noNull[0].shape[0]
+ 107                if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
+ 108                    raise ValueError("Smearing matrices are not NxN.")
+ 109                if (not all([item.shape == noNull[0].shape for item in noNull])):
+ 110                    raise ValueError("Items in data_input are not of identical shape." + str(noNull))
+ 111            else:
+ 112                raise TypeError("'data_input' contains item of wrong type.")
+ 113        else:
+ 114            raise TypeError("Data input was not given as list or correct array.")
+ 115
+ 116        self.tag = None
+ 117
+ 118        # An undefined timeslice is represented by the None object
+ 119        self.content = [None] * padding[0] + self.content + [None] * padding[1]
+ 120        self.T = len(self.content)
+ 121        self.prange = prange
+ 122
+ 123    def __getitem__(self, idx):
+ 124        """Return the content of timeslice idx"""
+ 125        if self.content[idx] is None:
+ 126            return None
+ 127        elif len(self.content[idx]) == 1:
+ 128            return self.content[idx][0]
+ 129        else:
+ 130            return self.content[idx]
+ 131
+ 132    @property
+ 133    def reweighted(self):
+ 134        bool_array = np.array([list(map(lambda x: x.reweighted, o)) for o in [x for x in self.content if x is not None]])
+ 135        if np.all(bool_array == 1):
+ 136            return True
+ 137        elif np.all(bool_array == 0):
+ 138            return False
+ 139        else:
+ 140            raise Exception("Reweighting status of correlator corrupted.")
+ 141
+ 142    def gamma_method(self, **kwargs):
+ 143        """Apply the gamma method to the content of the Corr."""
+ 144        for item in self.content:
+ 145            if not (item is None):
+ 146                if self.N == 1:
+ 147                    item[0].gamma_method(**kwargs)
+ 148                else:
+ 149                    for i in range(self.N):
+ 150                        for j in range(self.N):
+ 151                            item[i, j].gamma_method(**kwargs)
+ 152
+ 153    gm = gamma_method
+ 154
+ 155    def projected(self, vector_l=None, vector_r=None, normalize=False):
+ 156        """We need to project the Correlator with a Vector to get a single value at each timeslice.
+ 157
+ 158        The method can use one or two vectors.
+ 159        If two are specified it returns v1@G@v2 (the order might be very important.)
+ 160        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
+ 161        """
+ 162        if self.N == 1:
+ 163            raise Exception("Trying to project a Corr, that already has N=1.")
+ 164
+ 165        if vector_l is None:
+ 166            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
+ 167        elif (vector_r is None):
+ 168            vector_r = vector_l
+ 169        if isinstance(vector_l, list) and not isinstance(vector_r, list):
+ 170            if len(vector_l) != self.T:
+ 171                raise Exception("Length of vector list must be equal to T")
+ 172            vector_r = [vector_r] * self.T
+ 173        if isinstance(vector_r, list) and not isinstance(vector_l, list):
+ 174            if len(vector_r) != self.T:
+ 175                raise Exception("Length of vector list must be equal to T")
+ 176            vector_l = [vector_l] * self.T
+ 177
+ 178        if not isinstance(vector_l, list):
+ 179            if not vector_l.shape == vector_r.shape == (self.N,):
+ 180                raise Exception("Vectors are of wrong shape!")
+ 181            if normalize:
+ 182                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
+ 183            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
+ 184
+ 185        else:
+ 186            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
+ 187            if normalize:
+ 188                for t in range(self.T):
+ 189                    vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t])
+ 190
+ 191            newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
+ 192        return Corr(newcontent)
+ 193
+ 194    def item(self, i, j):
+ 195        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
+ 196
+ 197        Parameters
+ 198        ----------
+ 199        i : int
+ 200            First index to be picked.
+ 201        j : int
+ 202            Second index to be picked.
+ 203        """
+ 204        if self.N == 1:
+ 205            raise Exception("Trying to pick item from projected Corr")
+ 206        newcontent = [None if (item is None) else item[i, j] for item in self.content]
+ 207        return Corr(newcontent)
+ 208
+ 209    def plottable(self):
+ 210        """Outputs the correlator in a plotable format.
+ 211
+ 212        Outputs three lists containing the timeslice index, the value on each
+ 213        timeslice and the error on each timeslice.
+ 214        """
+ 215        if self.N != 1:
+ 216            raise Exception("Can only make Corr[N=1] plottable")
+ 217        x_list = [x for x in range(self.T) if not self.content[x] is None]
+ 218        y_list = [y[0].value for y in self.content if y is not None]
+ 219        y_err_list = [y[0].dvalue for y in self.content if y is not None]
+ 220
+ 221        return x_list, y_list, y_err_list
+ 222
+ 223    def symmetric(self):
+ 224        """ Symmetrize the correlator around x0=0."""
+ 225        if self.N != 1:
+ 226            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
+ 227        if self.T % 2 != 0:
+ 228            raise Exception("Can not symmetrize odd T")
+ 229
+ 230        if self.content[0] is not None:
+ 231            if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0:
+ 232                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
+ 233
+ 234        newcontent = [self.content[0]]
+ 235        for t in range(1, self.T):
+ 236            if (self.content[t] is None) or (self.content[self.T - t] is None):
+ 237                newcontent.append(None)
+ 238            else:
+ 239                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
+ 240        if (all([x is None for x in newcontent])):
+ 241            raise Exception("Corr could not be symmetrized: No redundant values")
+ 242        return Corr(newcontent, prange=self.prange)
+ 243
+ 244    def anti_symmetric(self):
+ 245        """Anti-symmetrize the correlator around x0=0."""
+ 246        if self.N != 1:
+ 247            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
+ 248        if self.T % 2 != 0:
+ 249            raise Exception("Can not symmetrize odd T")
+ 250
+ 251        test = 1 * self
+ 252        test.gamma_method()
+ 253        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
+ 254            warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)
+ 255
+ 256        newcontent = [self.content[0]]
+ 257        for t in range(1, self.T):
+ 258            if (self.content[t] is None) or (self.content[self.T - t] is None):
+ 259                newcontent.append(None)
+ 260            else:
+ 261                newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
+ 262        if (all([x is None for x in newcontent])):
+ 263            raise Exception("Corr could not be symmetrized: No redundant values")
+ 264        return Corr(newcontent, prange=self.prange)
+ 265
+ 266    def is_matrix_symmetric(self):
+ 267        """Checks whether a correlator matrices is symmetric on every timeslice."""
+ 268        if self.N == 1:
+ 269            raise TypeError("Only works for correlator matrices.")
+ 270        for t in range(self.T):
+ 271            if self[t] is None:
+ 272                continue
+ 273            for i in range(self.N):
+ 274                for j in range(i + 1, self.N):
+ 275                    if self[t][i, j] is self[t][j, i]:
+ 276                        continue
+ 277                    if hash(self[t][i, j]) != hash(self[t][j, i]):
+ 278                        return False
+ 279        return True
+ 280
+ 281    def trace(self):
+ 282        """Calculates the per-timeslice trace of a correlator matrix."""
+ 283        if self.N == 1:
+ 284            raise ValueError("Only works for correlator matrices.")
+ 285        newcontent = []
+ 286        for t in range(self.T):
+ 287            if _check_for_none(self, self.content[t]):
+ 288                newcontent.append(None)
+ 289            else:
+ 290                newcontent.append(np.trace(self.content[t]))
+ 291        return Corr(newcontent)
+ 292
+ 293    def matrix_symmetric(self):
+ 294        """Symmetrizes the correlator matrices on every timeslice."""
+ 295        if self.N == 1:
+ 296            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
+ 297        if self.is_matrix_symmetric():
+ 298            return 1.0 * self
+ 299        else:
+ 300            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
+ 301            return 0.5 * (Corr(transposed) + self)
+ 302
+ 303    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
+ 304        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
+ 305
+ 306        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
+ 307        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
+ 308        ```python
+ 309        C.GEVP(t0=2)[0]  # Ground state vector(s)
+ 310        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
+ 311        ```
+ 312
+ 313        Parameters
+ 314        ----------
+ 315        t0 : int
+ 316            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
+ 317        ts : int
+ 318            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
+ 319            If sort="Eigenvector" it gives a reference point for the sorting method.
+ 320        sort : string
+ 321            If 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.
+ 322            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
+ 323            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
+ 324              The reference state is identified by its eigenvalue at $t=t_s$.
+ 325            - None: The GEVP is solved only at ts, no sorting is necessary
+ 326        vector_obs : bool
+ 327            If True, uncertainties are propagated in the eigenvector computation (default False).
+ 328
+ 329        Other Parameters
+ 330        ----------------
+ 331        state : int
+ 332           Returns only the vector(s) for a specified state. The lowest state is zero.
+ 333        method : str
+ 334           Method used to solve the GEVP.
+ 335           - "eigh": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
+ 336           - "cholesky": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
+ 337        '''
+ 338
+ 339        if self.N == 1:
+ 340            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
+ 341        if ts is not None:
+ 342            if (ts <= t0):
+ 343                raise Exception("ts has to be larger than t0.")
+ 344
+ 345        if "sorted_list" in kwargs:
+ 346            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
+ 347            sort = kwargs.get("sorted_list")
  348
- 349        if sort is None:
- 350            if (ts is None):
- 351                raise Exception("ts is required if sort=None.")
- 352            if (self.content[t0] is None) or (self.content[ts] is None):
- 353                raise Exception("Corr not defined at t0/ts.")
- 354            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
- 355            reordered_vecs = _GEVP_solver(Gt, G0)
- 356
- 357        elif sort in ["Eigenvalue", "Eigenvector"]:
- 358            if sort == "Eigenvalue" and ts is not None:
- 359                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
- 360            all_vecs = [None] * (t0 + 1)
- 361            for t in range(t0 + 1, self.T):
- 362                try:
- 363                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
- 364                    all_vecs.append(_GEVP_solver(Gt, G0))
- 365                except Exception:
- 366                    all_vecs.append(None)
- 367            if sort == "Eigenvector":
- 368                if ts is None:
- 369                    raise Exception("ts is required for the Eigenvector sorting method.")
- 370                all_vecs = _sort_vectors(all_vecs, ts)
- 371
- 372            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
- 373        else:
- 374            raise Exception("Unkown value for 'sort'.")
- 375
- 376        if "state" in kwargs:
- 377            return reordered_vecs[kwargs.get("state")]
- 378        else:
- 379            return reordered_vecs
- 380
- 381    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
- 382        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
- 383
- 384        Parameters
- 385        ----------
- 386        state : int
- 387            The state one is interested in ordered by energy. The lowest state is zero.
- 388
- 389        All other parameters are identical to the ones of Corr.GEVP.
- 390        """
- 391        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
- 392        return self.projected(vec)
- 393
- 394    def Hankel(self, N, periodic=False):
- 395        """Constructs an NxN Hankel matrix
- 396
- 397        C(t) c(t+1) ... c(t+n-1)
- 398        C(t+1) c(t+2) ... c(t+n)
- 399        .................
- 400        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
- 401
- 402        Parameters
- 403        ----------
- 404        N : int
- 405            Dimension of the Hankel matrix
- 406        periodic : bool, optional
- 407            determines whether the matrix is extended periodically
- 408        """
- 409
- 410        if self.N != 1:
- 411            raise Exception("Multi-operator Prony not implemented!")
- 412
- 413        array = np.empty([N, N], dtype="object")
- 414        new_content = []
- 415        for t in range(self.T):
- 416            new_content.append(array.copy())
- 417
- 418        def wrap(i):
- 419            while i >= self.T:
- 420                i -= self.T
- 421            return i
- 422
- 423        for t in range(self.T):
- 424            for i in range(N):
- 425                for j in range(N):
- 426                    if periodic:
- 427                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
- 428                    elif (t + i + j) >= self.T:
- 429                        new_content[t] = None
- 430                    else:
- 431                        new_content[t][i, j] = self.content[t + i + j][0]
- 432
- 433        return Corr(new_content)
- 434
- 435    def roll(self, dt):
- 436        """Periodically shift the correlator by dt timeslices
+ 349        if self.is_matrix_symmetric():
+ 350            symmetric_corr = self
+ 351        else:
+ 352            symmetric_corr = self.matrix_symmetric()
+ 353
+ 354        def _get_mat_at_t(t, vector_obs=vector_obs):
+ 355            if vector_obs:
+ 356                return symmetric_corr[t]
+ 357            else:
+ 358                return np.vectorize(lambda x: x.value)(symmetric_corr[t])
+ 359        G0 = _get_mat_at_t(t0)
+ 360
+ 361        method = kwargs.get('method', 'eigh')
+ 362        if vector_obs:
+ 363            chol = linalg.cholesky(G0)
+ 364            chol_inv = linalg.inv(chol)
+ 365            method = 'cholesky'
+ 366        else:
+ 367            chol = np.linalg.cholesky(_get_mat_at_t(t0, vector_obs=False))  # Check if matrix G0 is positive-semidefinite.
+ 368            if method == 'cholesky':
+ 369                chol_inv = np.linalg.inv(chol)
+ 370            else:
+ 371                chol_inv = None
+ 372
+ 373        if sort is None:
+ 374            if (ts is None):
+ 375                raise Exception("ts is required if sort=None.")
+ 376            if (self.content[t0] is None) or (self.content[ts] is None):
+ 377                raise Exception("Corr not defined at t0/ts.")
+ 378            Gt = _get_mat_at_t(ts)
+ 379            reordered_vecs = _GEVP_solver(Gt, G0, method=method, chol_inv=chol_inv)
+ 380            if kwargs.get('auto_gamma', False) and vector_obs:
+ 381                [[o.gm() for o in ev if isinstance(o, Obs)] for ev in reordered_vecs]
+ 382
+ 383        elif sort in ["Eigenvalue", "Eigenvector"]:
+ 384            if sort == "Eigenvalue" and ts is not None:
+ 385                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
+ 386            all_vecs = [None] * (t0 + 1)
+ 387            for t in range(t0 + 1, self.T):
+ 388                try:
+ 389                    Gt = _get_mat_at_t(t)
+ 390                    all_vecs.append(_GEVP_solver(Gt, G0, method=method, chol_inv=chol_inv))
+ 391                except Exception:
+ 392                    all_vecs.append(None)
+ 393            if sort == "Eigenvector":
+ 394                if ts is None:
+ 395                    raise Exception("ts is required for the Eigenvector sorting method.")
+ 396                all_vecs = _sort_vectors(all_vecs, ts)
+ 397
+ 398            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
+ 399            if kwargs.get('auto_gamma', False) and vector_obs:
+ 400                [[[o.gm() for o in evn] for evn in ev if evn is not None] for ev in reordered_vecs]
+ 401        else:
+ 402            raise Exception("Unknown value for 'sort'. Choose 'Eigenvalue', 'Eigenvector' or None.")
+ 403
+ 404        if "state" in kwargs:
+ 405            return reordered_vecs[kwargs.get("state")]
+ 406        else:
+ 407            return reordered_vecs
+ 408
+ 409    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
+ 410        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
+ 411
+ 412        Parameters
+ 413        ----------
+ 414        state : int
+ 415            The state one is interested in ordered by energy. The lowest state is zero.
+ 416
+ 417        All other parameters are identical to the ones of Corr.GEVP.
+ 418        """
+ 419        vec = self.GEVP(t0, ts=ts, sort=sort, **kwargs)[state]
+ 420        return self.projected(vec)
+ 421
+ 422    def Hankel(self, N, periodic=False):
+ 423        """Constructs an NxN Hankel matrix
+ 424
+ 425        C(t) c(t+1) ... c(t+n-1)
+ 426        C(t+1) c(t+2) ... c(t+n)
+ 427        .................
+ 428        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
+ 429
+ 430        Parameters
+ 431        ----------
+ 432        N : int
+ 433            Dimension of the Hankel matrix
+ 434        periodic : bool, optional
+ 435            determines whether the matrix is extended periodically
+ 436        """
  437
- 438        Parameters
- 439        ----------
- 440        dt : int
- 441            number of timeslices
- 442        """
- 443        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
- 444
- 445    def reverse(self):
- 446        """Reverse the time ordering of the Corr"""
- 447        return Corr(self.content[:: -1])
- 448
- 449    def thin(self, spacing=2, offset=0):
- 450        """Thin out a correlator to suppress correlations
- 451
- 452        Parameters
- 453        ----------
- 454        spacing : int
- 455            Keep only every 'spacing'th entry of the correlator
- 456        offset : int
- 457            Offset the equal spacing
- 458        """
- 459        new_content = []
- 460        for t in range(self.T):
- 461            if (offset + t) % spacing != 0:
- 462                new_content.append(None)
- 463            else:
- 464                new_content.append(self.content[t])
- 465        return Corr(new_content)
- 466
- 467    def correlate(self, partner):
- 468        """Correlate the correlator with another correlator or Obs
- 469
- 470        Parameters
- 471        ----------
- 472        partner : Obs or Corr
- 473            partner to correlate the correlator with.
- 474            Can either be an Obs which is correlated with all entries of the
- 475            correlator or a Corr of same length.
- 476        """
- 477        if self.N != 1:
- 478            raise Exception("Only one-dimensional correlators can be safely correlated.")
- 479        new_content = []
- 480        for x0, t_slice in enumerate(self.content):
- 481            if _check_for_none(self, t_slice):
- 482                new_content.append(None)
- 483            else:
- 484                if isinstance(partner, Corr):
- 485                    if _check_for_none(partner, partner.content[x0]):
- 486                        new_content.append(None)
- 487                    else:
- 488                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
- 489                elif isinstance(partner, Obs):  # Should this include CObs?
- 490                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
- 491                else:
- 492                    raise Exception("Can only correlate with an Obs or a Corr.")
- 493
- 494        return Corr(new_content)
- 495
- 496    def reweight(self, weight, **kwargs):
- 497        """Reweight the correlator.
- 498
- 499        Parameters
- 500        ----------
- 501        weight : Obs
- 502            Reweighting factor. An Observable that has to be defined on a superset of the
- 503            configurations in obs[i].idl for all i.
- 504        all_configs : bool
- 505            if True, the reweighted observables are normalized by the average of
- 506            the reweighting factor on all configurations in weight.idl and not
- 507            on the configurations in obs[i].idl.
- 508        """
- 509        if self.N != 1:
- 510            raise Exception("Reweighting only implemented for one-dimensional correlators.")
- 511        new_content = []
- 512        for t_slice in self.content:
- 513            if _check_for_none(self, t_slice):
- 514                new_content.append(None)
- 515            else:
- 516                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
- 517        return Corr(new_content)
- 518
- 519    def T_symmetry(self, partner, parity=+1):
- 520        """Return the time symmetry average of the correlator and its partner
+ 438        if self.N != 1:
+ 439            raise Exception("Multi-operator Prony not implemented!")
+ 440
+ 441        array = np.empty([N, N], dtype="object")
+ 442        new_content = []
+ 443        for t in range(self.T):
+ 444            new_content.append(array.copy())
+ 445
+ 446        def wrap(i):
+ 447            while i >= self.T:
+ 448                i -= self.T
+ 449            return i
+ 450
+ 451        for t in range(self.T):
+ 452            for i in range(N):
+ 453                for j in range(N):
+ 454                    if periodic:
+ 455                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
+ 456                    elif (t + i + j) >= self.T:
+ 457                        new_content[t] = None
+ 458                    else:
+ 459                        new_content[t][i, j] = self.content[t + i + j][0]
+ 460
+ 461        return Corr(new_content)
+ 462
+ 463    def roll(self, dt):
+ 464        """Periodically shift the correlator by dt timeslices
+ 465
+ 466        Parameters
+ 467        ----------
+ 468        dt : int
+ 469            number of timeslices
+ 470        """
+ 471        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
+ 472
+ 473    def reverse(self):
+ 474        """Reverse the time ordering of the Corr"""
+ 475        return Corr(self.content[:: -1])
+ 476
+ 477    def thin(self, spacing=2, offset=0):
+ 478        """Thin out a correlator to suppress correlations
+ 479
+ 480        Parameters
+ 481        ----------
+ 482        spacing : int
+ 483            Keep only every 'spacing'th entry of the correlator
+ 484        offset : int
+ 485            Offset the equal spacing
+ 486        """
+ 487        new_content = []
+ 488        for t in range(self.T):
+ 489            if (offset + t) % spacing != 0:
+ 490                new_content.append(None)
+ 491            else:
+ 492                new_content.append(self.content[t])
+ 493        return Corr(new_content)
+ 494
+ 495    def correlate(self, partner):
+ 496        """Correlate the correlator with another correlator or Obs
+ 497
+ 498        Parameters
+ 499        ----------
+ 500        partner : Obs or Corr
+ 501            partner to correlate the correlator with.
+ 502            Can either be an Obs which is correlated with all entries of the
+ 503            correlator or a Corr of same length.
+ 504        """
+ 505        if self.N != 1:
+ 506            raise Exception("Only one-dimensional correlators can be safely correlated.")
+ 507        new_content = []
+ 508        for x0, t_slice in enumerate(self.content):
+ 509            if _check_for_none(self, t_slice):
+ 510                new_content.append(None)
+ 511            else:
+ 512                if isinstance(partner, Corr):
+ 513                    if _check_for_none(partner, partner.content[x0]):
+ 514                        new_content.append(None)
+ 515                    else:
+ 516                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
+ 517                elif isinstance(partner, Obs):  # Should this include CObs?
+ 518                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
+ 519                else:
+ 520                    raise Exception("Can only correlate with an Obs or a Corr.")
  521
- 522        Parameters
- 523        ----------
- 524        partner : Corr
- 525            Time symmetry partner of the Corr
- 526        parity : int
- 527            Parity quantum number of the correlator, can be +1 or -1
- 528        """
- 529        if self.N != 1:
- 530            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
- 531        if not isinstance(partner, Corr):
- 532            raise Exception("T partner has to be a Corr object.")
- 533        if parity not in [+1, -1]:
- 534            raise Exception("Parity has to be +1 or -1.")
- 535        T_partner = parity * partner.reverse()
- 536
- 537        t_slices = []
- 538        test = (self - T_partner)
- 539        test.gamma_method()
- 540        for x0, t_slice in enumerate(test.content):
- 541            if t_slice is not None:
- 542                if not t_slice[0].is_zero_within_error(5):
- 543                    t_slices.append(x0)
- 544        if t_slices:
- 545            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
+ 522        return Corr(new_content)
+ 523
+ 524    def reweight(self, weight, **kwargs):
+ 525        """Reweight the correlator.
+ 526
+ 527        Parameters
+ 528        ----------
+ 529        weight : Obs
+ 530            Reweighting factor. An Observable that has to be defined on a superset of the
+ 531            configurations in obs[i].idl for all i.
+ 532        all_configs : bool
+ 533            if True, the reweighted observables are normalized by the average of
+ 534            the reweighting factor on all configurations in weight.idl and not
+ 535            on the configurations in obs[i].idl.
+ 536        """
+ 537        if self.N != 1:
+ 538            raise Exception("Reweighting only implemented for one-dimensional correlators.")
+ 539        new_content = []
+ 540        for t_slice in self.content:
+ 541            if _check_for_none(self, t_slice):
+ 542                new_content.append(None)
+ 543            else:
+ 544                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
+ 545        return Corr(new_content)
  546
- 547        return (self + T_partner) / 2
- 548
- 549    def deriv(self, variant="symmetric"):
- 550        """Return the first derivative of the correlator with respect to x0.
- 551
- 552        Parameters
- 553        ----------
- 554        variant : str
- 555            decides which definition of the finite differences derivative is used.
- 556            Available choice: symmetric, forward, backward, improved, log, default: symmetric
- 557        """
- 558        if self.N != 1:
- 559            raise Exception("deriv only implemented for one-dimensional correlators.")
- 560        if variant == "symmetric":
- 561            newcontent = []
- 562            for t in range(1, self.T - 1):
- 563                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
- 564                    newcontent.append(None)
- 565                else:
- 566                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
- 567            if (all([x is None for x in newcontent])):
- 568                raise Exception('Derivative is undefined at all timeslices')
- 569            return Corr(newcontent, padding=[1, 1])
- 570        elif variant == "forward":
- 571            newcontent = []
- 572            for t in range(self.T - 1):
- 573                if (self.content[t] is None) or (self.content[t + 1] is None):
- 574                    newcontent.append(None)
- 575                else:
- 576                    newcontent.append(self.content[t + 1] - self.content[t])
- 577            if (all([x is None for x in newcontent])):
- 578                raise Exception("Derivative is undefined at all timeslices")
- 579            return Corr(newcontent, padding=[0, 1])
- 580        elif variant == "backward":
- 581            newcontent = []
- 582            for t in range(1, self.T):
- 583                if (self.content[t - 1] is None) or (self.content[t] is None):
- 584                    newcontent.append(None)
- 585                else:
- 586                    newcontent.append(self.content[t] - self.content[t - 1])
- 587            if (all([x is None for x in newcontent])):
- 588                raise Exception("Derivative is undefined at all timeslices")
- 589            return Corr(newcontent, padding=[1, 0])
- 590        elif variant == "improved":
- 591            newcontent = []
- 592            for t in range(2, self.T - 2):
- 593                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
- 594                    newcontent.append(None)
- 595                else:
- 596                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
- 597            if (all([x is None for x in newcontent])):
- 598                raise Exception('Derivative is undefined at all timeslices')
- 599            return Corr(newcontent, padding=[2, 2])
- 600        elif variant == 'log':
- 601            newcontent = []
- 602            for t in range(self.T):
- 603                if (self.content[t] is None) or (self.content[t] <= 0):
- 604                    newcontent.append(None)
- 605                else:
- 606                    newcontent.append(np.log(self.content[t]))
- 607            if (all([x is None for x in newcontent])):
- 608                raise Exception("Log is undefined at all timeslices")
- 609            logcorr = Corr(newcontent)
- 610            return self * logcorr.deriv('symmetric')
- 611        else:
- 612            raise Exception("Unknown variant.")
- 613
- 614    def second_deriv(self, variant="symmetric"):
- 615        r"""Return the second derivative of the correlator with respect to x0.
- 616
- 617        Parameters
- 618        ----------
- 619        variant : str
- 620            decides which definition of the finite differences derivative is used.
- 621            Available choice:
- 622                - symmetric (default)
- 623                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
- 624                - big_symmetric
- 625                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
- 626                - improved
- 627                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
- 628                - log
- 629                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
- 630        """
- 631        if self.N != 1:
- 632            raise Exception("second_deriv only implemented for one-dimensional correlators.")
- 633        if variant == "symmetric":
- 634            newcontent = []
- 635            for t in range(1, self.T - 1):
- 636                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
- 637                    newcontent.append(None)
- 638                else:
- 639                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
- 640            if (all([x is None for x in newcontent])):
- 641                raise Exception("Derivative is undefined at all timeslices")
- 642            return Corr(newcontent, padding=[1, 1])
- 643        elif variant == "big_symmetric":
- 644            newcontent = []
- 645            for t in range(2, self.T - 2):
- 646                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
- 647                    newcontent.append(None)
- 648                else:
- 649                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
- 650            if (all([x is None for x in newcontent])):
- 651                raise Exception("Derivative is undefined at all timeslices")
- 652            return Corr(newcontent, padding=[2, 2])
- 653        elif variant == "improved":
- 654            newcontent = []
- 655            for t in range(2, self.T - 2):
- 656                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
- 657                    newcontent.append(None)
- 658                else:
- 659                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
- 660            if (all([x is None for x in newcontent])):
- 661                raise Exception("Derivative is undefined at all timeslices")
- 662            return Corr(newcontent, padding=[2, 2])
- 663        elif variant == 'log':
- 664            newcontent = []
- 665            for t in range(self.T):
- 666                if (self.content[t] is None) or (self.content[t] <= 0):
- 667                    newcontent.append(None)
- 668                else:
- 669                    newcontent.append(np.log(self.content[t]))
- 670            if (all([x is None for x in newcontent])):
- 671                raise Exception("Log is undefined at all timeslices")
- 672            logcorr = Corr(newcontent)
- 673            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
- 674        else:
- 675            raise Exception("Unknown variant.")
- 676
- 677    def m_eff(self, variant='log', guess=1.0):
- 678        """Returns the effective mass of the correlator as correlator object
- 679
- 680        Parameters
- 681        ----------
- 682        variant : str
- 683            log : uses the standard effective mass log(C(t) / C(t+1))
- 684            cosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
- 685            sinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
- 686            See, e.g., arXiv:1205.5380
- 687            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
- 688            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
- 689        guess : float
- 690            guess for the root finder, only relevant for the root variant
- 691        """
- 692        if self.N != 1:
- 693            raise Exception('Correlator must be projected before getting m_eff')
- 694        if variant == 'log':
- 695            newcontent = []
- 696            for t in range(self.T - 1):
- 697                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
- 698                    newcontent.append(None)
- 699                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
- 700                    newcontent.append(None)
- 701                else:
- 702                    newcontent.append(self.content[t] / self.content[t + 1])
- 703            if (all([x is None for x in newcontent])):
- 704                raise Exception('m_eff is undefined at all timeslices')
- 705
- 706            return np.log(Corr(newcontent, padding=[0, 1]))
+ 547    def T_symmetry(self, partner, parity=+1):
+ 548        """Return the time symmetry average of the correlator and its partner
+ 549
+ 550        Parameters
+ 551        ----------
+ 552        partner : Corr
+ 553            Time symmetry partner of the Corr
+ 554        parity : int
+ 555            Parity quantum number of the correlator, can be +1 or -1
+ 556        """
+ 557        if self.N != 1:
+ 558            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
+ 559        if not isinstance(partner, Corr):
+ 560            raise Exception("T partner has to be a Corr object.")
+ 561        if parity not in [+1, -1]:
+ 562            raise Exception("Parity has to be +1 or -1.")
+ 563        T_partner = parity * partner.reverse()
+ 564
+ 565        t_slices = []
+ 566        test = (self - T_partner)
+ 567        test.gamma_method()
+ 568        for x0, t_slice in enumerate(test.content):
+ 569            if t_slice is not None:
+ 570                if not t_slice[0].is_zero_within_error(5):
+ 571                    t_slices.append(x0)
+ 572        if t_slices:
+ 573            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
+ 574
+ 575        return (self + T_partner) / 2
+ 576
+ 577    def deriv(self, variant="symmetric"):
+ 578        """Return the first derivative of the correlator with respect to x0.
+ 579
+ 580        Parameters
+ 581        ----------
+ 582        variant : str
+ 583            decides which definition of the finite differences derivative is used.
+ 584            Available choice: symmetric, forward, backward, improved, log, default: symmetric
+ 585        """
+ 586        if self.N != 1:
+ 587            raise Exception("deriv only implemented for one-dimensional correlators.")
+ 588        if variant == "symmetric":
+ 589            newcontent = []
+ 590            for t in range(1, self.T - 1):
+ 591                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+ 592                    newcontent.append(None)
+ 593                else:
+ 594                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
+ 595            if (all([x is None for x in newcontent])):
+ 596                raise Exception('Derivative is undefined at all timeslices')
+ 597            return Corr(newcontent, padding=[1, 1])
+ 598        elif variant == "forward":
+ 599            newcontent = []
+ 600            for t in range(self.T - 1):
+ 601                if (self.content[t] is None) or (self.content[t + 1] is None):
+ 602                    newcontent.append(None)
+ 603                else:
+ 604                    newcontent.append(self.content[t + 1] - self.content[t])
+ 605            if (all([x is None for x in newcontent])):
+ 606                raise Exception("Derivative is undefined at all timeslices")
+ 607            return Corr(newcontent, padding=[0, 1])
+ 608        elif variant == "backward":
+ 609            newcontent = []
+ 610            for t in range(1, self.T):
+ 611                if (self.content[t - 1] is None) or (self.content[t] is None):
+ 612                    newcontent.append(None)
+ 613                else:
+ 614                    newcontent.append(self.content[t] - self.content[t - 1])
+ 615            if (all([x is None for x in newcontent])):
+ 616                raise Exception("Derivative is undefined at all timeslices")
+ 617            return Corr(newcontent, padding=[1, 0])
+ 618        elif variant == "improved":
+ 619            newcontent = []
+ 620            for t in range(2, self.T - 2):
+ 621                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+ 622                    newcontent.append(None)
+ 623                else:
+ 624                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
+ 625            if (all([x is None for x in newcontent])):
+ 626                raise Exception('Derivative is undefined at all timeslices')
+ 627            return Corr(newcontent, padding=[2, 2])
+ 628        elif variant == 'log':
+ 629            newcontent = []
+ 630            for t in range(self.T):
+ 631                if (self.content[t] is None) or (self.content[t] <= 0):
+ 632                    newcontent.append(None)
+ 633                else:
+ 634                    newcontent.append(np.log(self.content[t]))
+ 635            if (all([x is None for x in newcontent])):
+ 636                raise Exception("Log is undefined at all timeslices")
+ 637            logcorr = Corr(newcontent)
+ 638            return self * logcorr.deriv('symmetric')
+ 639        else:
+ 640            raise Exception("Unknown variant.")
+ 641
+ 642    def second_deriv(self, variant="symmetric"):
+ 643        r"""Return the second derivative of the correlator with respect to x0.
+ 644
+ 645        Parameters
+ 646        ----------
+ 647        variant : str
+ 648            decides which definition of the finite differences derivative is used.
+ 649            Available choice:
+ 650                - symmetric (default)
+ 651                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
+ 652                - big_symmetric
+ 653                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
+ 654                - improved
+ 655                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
+ 656                - log
+ 657                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
+ 658        """
+ 659        if self.N != 1:
+ 660            raise Exception("second_deriv only implemented for one-dimensional correlators.")
+ 661        if variant == "symmetric":
+ 662            newcontent = []
+ 663            for t in range(1, self.T - 1):
+ 664                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+ 665                    newcontent.append(None)
+ 666                else:
+ 667                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
+ 668            if (all([x is None for x in newcontent])):
+ 669                raise Exception("Derivative is undefined at all timeslices")
+ 670            return Corr(newcontent, padding=[1, 1])
+ 671        elif variant == "big_symmetric":
+ 672            newcontent = []
+ 673            for t in range(2, self.T - 2):
+ 674                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
+ 675                    newcontent.append(None)
+ 676                else:
+ 677                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
+ 678            if (all([x is None for x in newcontent])):
+ 679                raise Exception("Derivative is undefined at all timeslices")
+ 680            return Corr(newcontent, padding=[2, 2])
+ 681        elif variant == "improved":
+ 682            newcontent = []
+ 683            for t in range(2, self.T - 2):
+ 684                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+ 685                    newcontent.append(None)
+ 686                else:
+ 687                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
+ 688            if (all([x is None for x in newcontent])):
+ 689                raise Exception("Derivative is undefined at all timeslices")
+ 690            return Corr(newcontent, padding=[2, 2])
+ 691        elif variant == 'log':
+ 692            newcontent = []
+ 693            for t in range(self.T):
+ 694                if (self.content[t] is None) or (self.content[t] <= 0):
+ 695                    newcontent.append(None)
+ 696                else:
+ 697                    newcontent.append(np.log(self.content[t]))
+ 698            if (all([x is None for x in newcontent])):
+ 699                raise Exception("Log is undefined at all timeslices")
+ 700            logcorr = Corr(newcontent)
+ 701            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
+ 702        else:
+ 703            raise Exception("Unknown variant.")
+ 704
+ 705    def m_eff(self, variant='log', guess=1.0):
+ 706        """Returns the effective mass of the correlator as correlator object
  707
- 708        elif variant == 'logsym':
- 709            newcontent = []
- 710            for t in range(1, self.T - 1):
- 711                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
- 712                    newcontent.append(None)
- 713                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
- 714                    newcontent.append(None)
- 715                else:
- 716                    newcontent.append(self.content[t - 1] / self.content[t + 1])
- 717            if (all([x is None for x in newcontent])):
- 718                raise Exception('m_eff is undefined at all timeslices')
- 719
- 720            return np.log(Corr(newcontent, padding=[1, 1])) / 2
- 721
- 722        elif variant in ['periodic', 'cosh', 'sinh']:
- 723            if variant in ['periodic', 'cosh']:
- 724                func = anp.cosh
- 725            else:
- 726                func = anp.sinh
- 727
- 728            def root_function(x, d):
- 729                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
- 730
- 731            newcontent = []
- 732            for t in range(self.T - 1):
- 733                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
- 734                    newcontent.append(None)
- 735                # Fill the two timeslices in the middle of the lattice with their predecessors
- 736                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
- 737                    newcontent.append(newcontent[-1])
- 738                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
- 739                    newcontent.append(None)
- 740                else:
- 741                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
- 742            if (all([x is None for x in newcontent])):
- 743                raise Exception('m_eff is undefined at all timeslices')
- 744
- 745            return Corr(newcontent, padding=[0, 1])
- 746
- 747        elif variant == 'arccosh':
- 748            newcontent = []
- 749            for t in range(1, self.T - 1):
- 750                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0):
- 751                    newcontent.append(None)
- 752                else:
- 753                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
- 754            if (all([x is None for x in newcontent])):
- 755                raise Exception("m_eff is undefined at all timeslices")
- 756            return np.arccosh(Corr(newcontent, padding=[1, 1]))
- 757
- 758        else:
- 759            raise Exception('Unknown variant.')
- 760
- 761    def fit(self, function, fitrange=None, silent=False, **kwargs):
- 762        r'''Fits function to the data
- 763
- 764        Parameters
- 765        ----------
- 766        function : obj
- 767            function to fit to the data. See fits.least_squares for details.
- 768        fitrange : list
- 769            Two element list containing the timeslices on which the fit is supposed to start and stop.
- 770            Caution: This range is inclusive as opposed to standard python indexing.
- 771            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
- 772            If not specified, self.prange or all timeslices are used.
- 773        silent : bool
- 774            Decides whether output is printed to the standard output.
- 775        '''
- 776        if self.N != 1:
- 777            raise Exception("Correlator must be projected before fitting")
- 778
- 779        if fitrange is None:
- 780            if self.prange:
- 781                fitrange = self.prange
- 782            else:
- 783                fitrange = [0, self.T - 1]
- 784        else:
- 785            if not isinstance(fitrange, list):
- 786                raise Exception("fitrange has to be a list with two elements")
- 787            if len(fitrange) != 2:
- 788                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
- 789
- 790        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
- 791        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
- 792        result = least_squares(xs, ys, function, silent=silent, **kwargs)
- 793        return result
- 794
- 795    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
- 796        """ Extract a plateau value from a Corr object
- 797
- 798        Parameters
- 799        ----------
- 800        plateau_range : list
- 801            list with two entries, indicating the first and the last timeslice
- 802            of the plateau region.
- 803        method : str
- 804            method to extract the plateau.
- 805                'fit' fits a constant to the plateau region
- 806                'avg', 'average' or 'mean' just average over the given timeslices.
- 807        auto_gamma : bool
- 808            apply gamma_method with default parameters to the Corr. Defaults to None
- 809        """
- 810        if not plateau_range:
- 811            if self.prange:
- 812                plateau_range = self.prange
- 813            else:
- 814                raise Exception("no plateau range provided")
- 815        if self.N != 1:
- 816            raise Exception("Correlator must be projected before getting a plateau.")
- 817        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
- 818            raise Exception("plateau is undefined at all timeslices in plateaurange.")
- 819        if auto_gamma:
- 820            self.gamma_method()
- 821        if method == "fit":
- 822            def const_func(a, t):
- 823                return a[0]
- 824            return self.fit(const_func, plateau_range)[0]
- 825        elif method in ["avg", "average", "mean"]:
- 826            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
- 827            return returnvalue
- 828
- 829        else:
- 830            raise Exception("Unsupported plateau method: " + method)
- 831
- 832    def set_prange(self, prange):
- 833        """Sets the attribute prange of the Corr object."""
- 834        if not len(prange) == 2:
- 835            raise Exception("prange must be a list or array with two values")
- 836        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
- 837            raise Exception("Start and end point must be integers")
- 838        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
- 839            raise Exception("Start and end point must define a range in the interval 0,T")
- 840
- 841        self.prange = prange
- 842        return
- 843
- 844    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
- 845        """Plots the correlator using the tag of the correlator as label if available.
- 846
- 847        Parameters
- 848        ----------
- 849        x_range : list
- 850            list of two values, determining the range of the x-axis e.g. [4, 8].
- 851        comp : Corr or list of Corr
- 852            Correlator or list of correlators which are plotted for comparison.
- 853            The tags of these correlators are used as labels if available.
- 854        logscale : bool
- 855            Sets y-axis to logscale.
- 856        plateau : Obs
- 857            Plateau value to be visualized in the figure.
- 858        fit_res : Fit_result
- 859            Fit_result object to be visualized.
- 860        fit_key : str
- 861            Key for the fit function in Fit_result.fit_function (for combined fits).
- 862        ylabel : str
- 863            Label for the y-axis.
- 864        save : str
- 865            path to file in which the figure should be saved.
- 866        auto_gamma : bool
- 867            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
- 868        hide_sigma : float
- 869            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
- 870        references : list
- 871            List of floating point values that are displayed as horizontal lines for reference.
- 872        title : string
- 873            Optional title of the figure.
- 874        """
- 875        if self.N != 1:
- 876            raise Exception("Correlator must be projected before plotting")
- 877
- 878        if auto_gamma:
- 879            self.gamma_method()
- 880
- 881        if x_range is None:
- 882            x_range = [0, self.T - 1]
- 883
- 884        fig = plt.figure()
- 885        ax1 = fig.add_subplot(111)
- 886
- 887        x, y, y_err = self.plottable()
- 888        if hide_sigma:
- 889            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
- 890        else:
- 891            hide_from = None
- 892        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
- 893        if logscale:
- 894            ax1.set_yscale('log')
- 895        else:
- 896            if y_range is None:
- 897                try:
- 898                    y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
- 899                    y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
- 900                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
- 901                except Exception:
- 902                    pass
- 903            else:
- 904                ax1.set_ylim(y_range)
- 905        if comp:
- 906            if isinstance(comp, (Corr, list)):
- 907                for corr in comp if isinstance(comp, list) else [comp]:
- 908                    if auto_gamma:
- 909                        corr.gamma_method()
- 910                    x, y, y_err = corr.plottable()
- 911                    if hide_sigma:
- 912                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
- 913                    else:
- 914                        hide_from = None
- 915                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
- 916            else:
- 917                raise Exception("'comp' must be a correlator or a list of correlators.")
- 918
- 919        if plateau:
- 920            if isinstance(plateau, Obs):
- 921                if auto_gamma:
- 922                    plateau.gamma_method()
- 923                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
- 924                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
- 925            else:
- 926                raise Exception("'plateau' must be an Obs")
- 927
- 928        if references:
- 929            if isinstance(references, list):
- 930                for ref in references:
- 931                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
- 932            else:
- 933                raise Exception("'references' must be a list of floating pint values.")
- 934
- 935        if self.prange:
- 936            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
- 937            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
- 938
- 939        if fit_res:
- 940            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
- 941            if isinstance(fit_res.fit_function, dict):
- 942                if fit_key:
- 943                    ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
- 944                else:
- 945                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
- 946            else:
- 947                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
- 948
- 949        ax1.set_xlabel(r'$x_0 / a$')
- 950        if ylabel:
- 951            ax1.set_ylabel(ylabel)
- 952        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
- 953
- 954        handles, labels = ax1.get_legend_handles_labels()
- 955        if labels:
- 956            ax1.legend()
- 957
- 958        if title:
- 959            plt.title(title)
- 960
- 961        plt.draw()
+ 708        Parameters
+ 709        ----------
+ 710        variant : str
+ 711            log : uses the standard effective mass log(C(t) / C(t+1))
+ 712            cosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
+ 713            sinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
+ 714            See, e.g., arXiv:1205.5380
+ 715            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+ 716            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
+ 717        guess : float
+ 718            guess for the root finder, only relevant for the root variant
+ 719        """
+ 720        if self.N != 1:
+ 721            raise Exception('Correlator must be projected before getting m_eff')
+ 722        if variant == 'log':
+ 723            newcontent = []
+ 724            for t in range(self.T - 1):
+ 725                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+ 726                    newcontent.append(None)
+ 727                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+ 728                    newcontent.append(None)
+ 729                else:
+ 730                    newcontent.append(self.content[t] / self.content[t + 1])
+ 731            if (all([x is None for x in newcontent])):
+ 732                raise Exception('m_eff is undefined at all timeslices')
+ 733
+ 734            return np.log(Corr(newcontent, padding=[0, 1]))
+ 735
+ 736        elif variant == 'logsym':
+ 737            newcontent = []
+ 738            for t in range(1, self.T - 1):
+ 739                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+ 740                    newcontent.append(None)
+ 741                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
+ 742                    newcontent.append(None)
+ 743                else:
+ 744                    newcontent.append(self.content[t - 1] / self.content[t + 1])
+ 745            if (all([x is None for x in newcontent])):
+ 746                raise Exception('m_eff is undefined at all timeslices')
+ 747
+ 748            return np.log(Corr(newcontent, padding=[1, 1])) / 2
+ 749
+ 750        elif variant in ['periodic', 'cosh', 'sinh']:
+ 751            if variant in ['periodic', 'cosh']:
+ 752                func = anp.cosh
+ 753            else:
+ 754                func = anp.sinh
+ 755
+ 756            def root_function(x, d):
+ 757                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
+ 758
+ 759            newcontent = []
+ 760            for t in range(self.T - 1):
+ 761                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+ 762                    newcontent.append(None)
+ 763                # Fill the two timeslices in the middle of the lattice with their predecessors
+ 764                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
+ 765                    newcontent.append(newcontent[-1])
+ 766                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+ 767                    newcontent.append(None)
+ 768                else:
+ 769                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
+ 770            if (all([x is None for x in newcontent])):
+ 771                raise Exception('m_eff is undefined at all timeslices')
+ 772
+ 773            return Corr(newcontent, padding=[0, 1])
+ 774
+ 775        elif variant == 'arccosh':
+ 776            newcontent = []
+ 777            for t in range(1, self.T - 1):
+ 778                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0):
+ 779                    newcontent.append(None)
+ 780                else:
+ 781                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+ 782            if (all([x is None for x in newcontent])):
+ 783                raise Exception("m_eff is undefined at all timeslices")
+ 784            return np.arccosh(Corr(newcontent, padding=[1, 1]))
+ 785
+ 786        else:
+ 787            raise Exception('Unknown variant.')
+ 788
+ 789    def fit(self, function, fitrange=None, silent=False, **kwargs):
+ 790        r'''Fits function to the data
+ 791
+ 792        Parameters
+ 793        ----------
+ 794        function : obj
+ 795            function to fit to the data. See fits.least_squares for details.
+ 796        fitrange : list
+ 797            Two element list containing the timeslices on which the fit is supposed to start and stop.
+ 798            Caution: This range is inclusive as opposed to standard python indexing.
+ 799            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
+ 800            If not specified, self.prange or all timeslices are used.
+ 801        silent : bool
+ 802            Decides whether output is printed to the standard output.
+ 803        '''
+ 804        if self.N != 1:
+ 805            raise Exception("Correlator must be projected before fitting")
+ 806
+ 807        if fitrange is None:
+ 808            if self.prange:
+ 809                fitrange = self.prange
+ 810            else:
+ 811                fitrange = [0, self.T - 1]
+ 812        else:
+ 813            if not isinstance(fitrange, list):
+ 814                raise Exception("fitrange has to be a list with two elements")
+ 815            if len(fitrange) != 2:
+ 816                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
+ 817
+ 818        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
+ 819        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
+ 820        result = least_squares(xs, ys, function, silent=silent, **kwargs)
+ 821        return result
+ 822
+ 823    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+ 824        """ Extract a plateau value from a Corr object
+ 825
+ 826        Parameters
+ 827        ----------
+ 828        plateau_range : list
+ 829            list with two entries, indicating the first and the last timeslice
+ 830            of the plateau region.
+ 831        method : str
+ 832            method to extract the plateau.
+ 833                'fit' fits a constant to the plateau region
+ 834                'avg', 'average' or 'mean' just average over the given timeslices.
+ 835        auto_gamma : bool
+ 836            apply gamma_method with default parameters to the Corr. Defaults to None
+ 837        """
+ 838        if not plateau_range:
+ 839            if self.prange:
+ 840                plateau_range = self.prange
+ 841            else:
+ 842                raise Exception("no plateau range provided")
+ 843        if self.N != 1:
+ 844            raise Exception("Correlator must be projected before getting a plateau.")
+ 845        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
+ 846            raise Exception("plateau is undefined at all timeslices in plateaurange.")
+ 847        if auto_gamma:
+ 848            self.gamma_method()
+ 849        if method == "fit":
+ 850            def const_func(a, t):
+ 851                return a[0]
+ 852            return self.fit(const_func, plateau_range)[0]
+ 853        elif method in ["avg", "average", "mean"]:
+ 854            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
+ 855            return returnvalue
+ 856
+ 857        else:
+ 858            raise Exception("Unsupported plateau method: " + method)
+ 859
+ 860    def set_prange(self, prange):
+ 861        """Sets the attribute prange of the Corr object."""
+ 862        if not len(prange) == 2:
+ 863            raise Exception("prange must be a list or array with two values")
+ 864        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
+ 865            raise Exception("Start and end point must be integers")
+ 866        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
+ 867            raise Exception("Start and end point must define a range in the interval 0,T")
+ 868
+ 869        self.prange = prange
+ 870        return
+ 871
+ 872    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
+ 873        """Plots the correlator using the tag of the correlator as label if available.
+ 874
+ 875        Parameters
+ 876        ----------
+ 877        x_range : list
+ 878            list of two values, determining the range of the x-axis e.g. [4, 8].
+ 879        comp : Corr or list of Corr
+ 880            Correlator or list of correlators which are plotted for comparison.
+ 881            The tags of these correlators are used as labels if available.
+ 882        logscale : bool
+ 883            Sets y-axis to logscale.
+ 884        plateau : Obs
+ 885            Plateau value to be visualized in the figure.
+ 886        fit_res : Fit_result
+ 887            Fit_result object to be visualized.
+ 888        fit_key : str
+ 889            Key for the fit function in Fit_result.fit_function (for combined fits).
+ 890        ylabel : str
+ 891            Label for the y-axis.
+ 892        save : str
+ 893            path to file in which the figure should be saved.
+ 894        auto_gamma : bool
+ 895            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
+ 896        hide_sigma : float
+ 897            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
+ 898        references : list
+ 899            List of floating point values that are displayed as horizontal lines for reference.
+ 900        title : string
+ 901            Optional title of the figure.
+ 902        """
+ 903        if self.N != 1:
+ 904            raise Exception("Correlator must be projected before plotting")
+ 905
+ 906        if auto_gamma:
+ 907            self.gamma_method()
+ 908
+ 909        if x_range is None:
+ 910            x_range = [0, self.T - 1]
+ 911
+ 912        fig = plt.figure()
+ 913        ax1 = fig.add_subplot(111)
+ 914
+ 915        x, y, y_err = self.plottable()
+ 916        if hide_sigma:
+ 917            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+ 918        else:
+ 919            hide_from = None
+ 920        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
+ 921        if logscale:
+ 922            ax1.set_yscale('log')
+ 923        else:
+ 924            if y_range is None:
+ 925                try:
+ 926                    y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+ 927                    y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+ 928                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
+ 929                except Exception:
+ 930                    pass
+ 931            else:
+ 932                ax1.set_ylim(y_range)
+ 933        if comp:
+ 934            if isinstance(comp, (Corr, list)):
+ 935                for corr in comp if isinstance(comp, list) else [comp]:
+ 936                    if auto_gamma:
+ 937                        corr.gamma_method()
+ 938                    x, y, y_err = corr.plottable()
+ 939                    if hide_sigma:
+ 940                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+ 941                    else:
+ 942                        hide_from = None
+ 943                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
+ 944            else:
+ 945                raise Exception("'comp' must be a correlator or a list of correlators.")
+ 946
+ 947        if plateau:
+ 948            if isinstance(plateau, Obs):
+ 949                if auto_gamma:
+ 950                    plateau.gamma_method()
+ 951                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
+ 952                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+ 953            else:
+ 954                raise Exception("'plateau' must be an Obs")
+ 955
+ 956        if references:
+ 957            if isinstance(references, list):
+ 958                for ref in references:
+ 959                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
+ 960            else:
+ 961                raise Exception("'references' must be a list of floating pint values.")
  962
- 963        if save:
- 964            if isinstance(save, str):
- 965                fig.savefig(save, bbox_inches='tight')
- 966            else:
- 967                raise Exception("'save' has to be a string.")
- 968
- 969    def spaghetti_plot(self, logscale=True):
- 970        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
- 971
- 972        Parameters
- 973        ----------
- 974        logscale : bool
- 975            Determines whether the scale of the y-axis is logarithmic or standard.
- 976        """
- 977        if self.N != 1:
- 978            raise Exception("Correlator needs to be projected first.")
- 979
- 980        mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist]))
- 981        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
- 982
- 983        for name in mc_names:
- 984            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+ 963        if self.prange:
+ 964            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
+ 965            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
+ 966
+ 967        if fit_res:
+ 968            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
+ 969            if isinstance(fit_res.fit_function, dict):
+ 970                if fit_key:
+ 971                    ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
+ 972                else:
+ 973                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
+ 974            else:
+ 975                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
+ 976
+ 977        ax1.set_xlabel(r'$x_0 / a$')
+ 978        if ylabel:
+ 979            ax1.set_ylabel(ylabel)
+ 980        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
+ 981
+ 982        handles, labels = ax1.get_legend_handles_labels()
+ 983        if labels:
+ 984            ax1.legend()
  985
- 986            fig = plt.figure()
- 987            ax = fig.add_subplot(111)
- 988            for dat in data:
- 989                ax.plot(x0_vals, dat, ls='-', marker='')
+ 986        if title:
+ 987            plt.title(title)
+ 988
+ 989        plt.draw()
  990
- 991            if logscale is True:
- 992                ax.set_yscale('log')
- 993
- 994            ax.set_xlabel(r'$x_0 / a$')
- 995            plt.title(name)
- 996            plt.draw()
- 997
- 998    def dump(self, filename, datatype="json.gz", **kwargs):
- 999        """Dumps the Corr into a file of chosen type
+ 991        if save:
+ 992            if isinstance(save, str):
+ 993                fig.savefig(save, bbox_inches='tight')
+ 994            else:
+ 995                raise Exception("'save' has to be a string.")
+ 996
+ 997    def spaghetti_plot(self, logscale=True):
+ 998        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+ 999
 1000        Parameters
 1001        ----------
-1002        filename : str
-1003            Name of the file to be saved.
-1004        datatype : str
-1005            Format of the exported file. Supported formats include
-1006            "json.gz" and "pickle"
-1007        path : str
-1008            specifies a custom path for the file (default '.')
-1009        """
-1010        if datatype == "json.gz":
-1011            from .input.json import dump_to_json
-1012            if 'path' in kwargs:
-1013                file_name = kwargs.get('path') + '/' + filename
-1014            else:
-1015                file_name = filename
-1016            dump_to_json(self, file_name)
-1017        elif datatype == "pickle":
-1018            dump_object(self, filename, **kwargs)
-1019        else:
-1020            raise Exception("Unknown datatype " + str(datatype))
+1002        logscale : bool
+1003            Determines whether the scale of the y-axis is logarithmic or standard.
+1004        """
+1005        if self.N != 1:
+1006            raise Exception("Correlator needs to be projected first.")
+1007
+1008        mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist]))
+1009        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+1010
+1011        for name in mc_names:
+1012            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+1013
+1014            fig = plt.figure()
+1015            ax = fig.add_subplot(111)
+1016            for dat in data:
+1017                ax.plot(x0_vals, dat, ls='-', marker='')
+1018
+1019            if logscale is True:
+1020                ax.set_yscale('log')
 1021
-1022    def print(self, print_range=None):
-1023        print(self.__repr__(print_range))
-1024
-1025    def __repr__(self, print_range=None):
-1026        if print_range is None:
-1027            print_range = [0, None]
-1028
-1029        content_string = ""
-1030        content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n"  # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here
-1031
-1032        if self.tag is not None:
-1033            content_string += "Description: " + self.tag + "\n"
-1034        if self.N != 1:
-1035            return content_string
-1036
-1037        if print_range[1]:
-1038            print_range[1] += 1
-1039        content_string += 'x0/a\tCorr(x0/a)\n------------------\n'
-1040        for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]):
-1041            if sub_corr is None:
-1042                content_string += str(i + print_range[0]) + '\n'
-1043            else:
-1044                content_string += str(i + print_range[0])
-1045                for element in sub_corr:
-1046                    content_string += f"\t{element:+2}"
-1047                content_string += '\n'
-1048        return content_string
+1022            ax.set_xlabel(r'$x_0 / a$')
+1023            plt.title(name)
+1024            plt.draw()
+1025
+1026    def dump(self, filename, datatype="json.gz", **kwargs):
+1027        """Dumps the Corr into a file of chosen type
+1028        Parameters
+1029        ----------
+1030        filename : str
+1031            Name of the file to be saved.
+1032        datatype : str
+1033            Format of the exported file. Supported formats include
+1034            "json.gz" and "pickle"
+1035        path : str
+1036            specifies a custom path for the file (default '.')
+1037        """
+1038        if datatype == "json.gz":
+1039            from .input.json import dump_to_json
+1040            if 'path' in kwargs:
+1041                file_name = kwargs.get('path') + '/' + filename
+1042            else:
+1043                file_name = filename
+1044            dump_to_json(self, file_name)
+1045        elif datatype == "pickle":
+1046            dump_object(self, filename, **kwargs)
+1047        else:
+1048            raise Exception("Unknown datatype " + str(datatype))
 1049
-1050    def __str__(self):
-1051        return self.__repr__()
+1050    def print(self, print_range=None):
+1051        print(self.__repr__(print_range))
 1052
-1053    # We define the basic operations, that can be performed with correlators.
-1054    # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr.
-1055    # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception.
-1056    # One could try and tell Obs to check if the y in __mul__ is a Corr and
-1057
-1058    __array_priority__ = 10000
+1053    def __repr__(self, print_range=None):
+1054        if print_range is None:
+1055            print_range = [0, None]
+1056
+1057        content_string = ""
+1058        content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n"  # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here
 1059
-1060    def __eq__(self, y):
-1061        if isinstance(y, Corr):
-1062            comp = np.asarray(y.content, dtype=object)
-1063        else:
-1064            comp = np.asarray(y)
-1065        return np.asarray(self.content, dtype=object) == comp
-1066
-1067    def __add__(self, y):
-1068        if isinstance(y, Corr):
-1069            if ((self.N != y.N) or (self.T != y.T)):
-1070                raise Exception("Addition of Corrs with different shape")
-1071            newcontent = []
-1072            for t in range(self.T):
-1073                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
-1074                    newcontent.append(None)
-1075                else:
-1076                    newcontent.append(self.content[t] + y.content[t])
-1077            return Corr(newcontent)
-1078
-1079        elif isinstance(y, (Obs, int, float, CObs, complex)):
-1080            newcontent = []
-1081            for t in range(self.T):
-1082                if _check_for_none(self, self.content[t]):
-1083                    newcontent.append(None)
-1084                else:
-1085                    newcontent.append(self.content[t] + y)
-1086            return Corr(newcontent, prange=self.prange)
-1087        elif isinstance(y, np.ndarray):
-1088            if y.shape == (self.T,):
-1089                return Corr(list((np.array(self.content).T + y).T))
-1090            else:
-1091                raise ValueError("operands could not be broadcast together")
-1092        else:
-1093            raise TypeError("Corr + wrong type")
+1060        if self.tag is not None:
+1061            content_string += "Description: " + self.tag + "\n"
+1062        if self.N != 1:
+1063            return content_string
+1064
+1065        if print_range[1]:
+1066            print_range[1] += 1
+1067        content_string += 'x0/a\tCorr(x0/a)\n------------------\n'
+1068        for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]):
+1069            if sub_corr is None:
+1070                content_string += str(i + print_range[0]) + '\n'
+1071            else:
+1072                content_string += str(i + print_range[0])
+1073                for element in sub_corr:
+1074                    content_string += f"\t{element:+2}"
+1075                content_string += '\n'
+1076        return content_string
+1077
+1078    def __str__(self):
+1079        return self.__repr__()
+1080
+1081    # We define the basic operations, that can be performed with correlators.
+1082    # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr.
+1083    # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception.
+1084    # One could try and tell Obs to check if the y in __mul__ is a Corr and
+1085
+1086    __array_priority__ = 10000
+1087
+1088    def __eq__(self, y):
+1089        if isinstance(y, Corr):
+1090            comp = np.asarray(y.content, dtype=object)
+1091        else:
+1092            comp = np.asarray(y)
+1093        return np.asarray(self.content, dtype=object) == comp
 1094
-1095    def __mul__(self, y):
+1095    def __add__(self, y):
 1096        if isinstance(y, Corr):
-1097            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
-1098                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
+1097            if ((self.N != y.N) or (self.T != y.T)):
+1098                raise Exception("Addition of Corrs with different shape")
 1099            newcontent = []
 1100            for t in range(self.T):
 1101                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
 1102                    newcontent.append(None)
 1103                else:
-1104                    newcontent.append(self.content[t] * y.content[t])
+1104                    newcontent.append(self.content[t] + y.content[t])
 1105            return Corr(newcontent)
 1106
 1107        elif isinstance(y, (Obs, int, float, CObs, complex)):
@@ -2782,281 +2867,309 @@
 1110                if _check_for_none(self, self.content[t]):
 1111                    newcontent.append(None)
 1112                else:
-1113                    newcontent.append(self.content[t] * y)
+1113                    newcontent.append(self.content[t] + y)
 1114            return Corr(newcontent, prange=self.prange)
 1115        elif isinstance(y, np.ndarray):
 1116            if y.shape == (self.T,):
-1117                return Corr(list((np.array(self.content).T * y).T))
+1117                return Corr(list((np.array(self.content).T + y).T))
 1118            else:
 1119                raise ValueError("operands could not be broadcast together")
 1120        else:
-1121            raise TypeError("Corr * wrong type")
+1121            raise TypeError("Corr + wrong type")
 1122
-1123    def __matmul__(self, y):
-1124        if isinstance(y, np.ndarray):
-1125            if y.ndim != 2 or y.shape[0] != y.shape[1]:
-1126                raise ValueError("Can only multiply correlators by square matrices.")
-1127            if not self.N == y.shape[0]:
-1128                raise ValueError("matmul: mismatch of matrix dimensions")
-1129            newcontent = []
-1130            for t in range(self.T):
-1131                if _check_for_none(self, self.content[t]):
-1132                    newcontent.append(None)
-1133                else:
-1134                    newcontent.append(self.content[t] @ y)
-1135            return Corr(newcontent)
-1136        elif isinstance(y, Corr):
-1137            if not self.N == y.N:
-1138                raise ValueError("matmul: mismatch of matrix dimensions")
-1139            newcontent = []
-1140            for t in range(self.T):
-1141                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
-1142                    newcontent.append(None)
-1143                else:
-1144                    newcontent.append(self.content[t] @ y.content[t])
-1145            return Corr(newcontent)
-1146
-1147        else:
-1148            return NotImplemented
-1149
-1150    def __rmatmul__(self, y):
-1151        if isinstance(y, np.ndarray):
-1152            if y.ndim != 2 or y.shape[0] != y.shape[1]:
-1153                raise ValueError("Can only multiply correlators by square matrices.")
-1154            if not self.N == y.shape[0]:
-1155                raise ValueError("matmul: mismatch of matrix dimensions")
-1156            newcontent = []
-1157            for t in range(self.T):
-1158                if _check_for_none(self, self.content[t]):
-1159                    newcontent.append(None)
-1160                else:
-1161                    newcontent.append(y @ self.content[t])
-1162            return Corr(newcontent)
-1163        else:
-1164            return NotImplemented
-1165
-1166    def __truediv__(self, y):
-1167        if isinstance(y, Corr):
-1168            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
-1169                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
-1170            newcontent = []
-1171            for t in range(self.T):
-1172                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
-1173                    newcontent.append(None)
-1174                else:
-1175                    newcontent.append(self.content[t] / y.content[t])
-1176            for t in range(self.T):
-1177                if _check_for_none(self, newcontent[t]):
-1178                    continue
-1179                if np.isnan(np.sum(newcontent[t]).value):
-1180                    newcontent[t] = None
-1181
-1182            if all([item is None for item in newcontent]):
-1183                raise Exception("Division returns completely undefined correlator")
-1184            return Corr(newcontent)
-1185
-1186        elif isinstance(y, (Obs, CObs)):
-1187            if isinstance(y, Obs):
-1188                if y.value == 0:
-1189                    raise Exception('Division by zero will return undefined correlator')
-1190            if isinstance(y, CObs):
-1191                if y.is_zero():
-1192                    raise Exception('Division by zero will return undefined correlator')
+1123    def __mul__(self, y):
+1124        if isinstance(y, Corr):
+1125            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
+1126                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
+1127            newcontent = []
+1128            for t in range(self.T):
+1129                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
+1130                    newcontent.append(None)
+1131                else:
+1132                    newcontent.append(self.content[t] * y.content[t])
+1133            return Corr(newcontent)
+1134
+1135        elif isinstance(y, (Obs, int, float, CObs, complex)):
+1136            newcontent = []
+1137            for t in range(self.T):
+1138                if _check_for_none(self, self.content[t]):
+1139                    newcontent.append(None)
+1140                else:
+1141                    newcontent.append(self.content[t] * y)
+1142            return Corr(newcontent, prange=self.prange)
+1143        elif isinstance(y, np.ndarray):
+1144            if y.shape == (self.T,):
+1145                return Corr(list((np.array(self.content).T * y).T))
+1146            else:
+1147                raise ValueError("operands could not be broadcast together")
+1148        else:
+1149            raise TypeError("Corr * wrong type")
+1150
+1151    def __matmul__(self, y):
+1152        if isinstance(y, np.ndarray):
+1153            if y.ndim != 2 or y.shape[0] != y.shape[1]:
+1154                raise ValueError("Can only multiply correlators by square matrices.")
+1155            if not self.N == y.shape[0]:
+1156                raise ValueError("matmul: mismatch of matrix dimensions")
+1157            newcontent = []
+1158            for t in range(self.T):
+1159                if _check_for_none(self, self.content[t]):
+1160                    newcontent.append(None)
+1161                else:
+1162                    newcontent.append(self.content[t] @ y)
+1163            return Corr(newcontent)
+1164        elif isinstance(y, Corr):
+1165            if not self.N == y.N:
+1166                raise ValueError("matmul: mismatch of matrix dimensions")
+1167            newcontent = []
+1168            for t in range(self.T):
+1169                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
+1170                    newcontent.append(None)
+1171                else:
+1172                    newcontent.append(self.content[t] @ y.content[t])
+1173            return Corr(newcontent)
+1174
+1175        else:
+1176            return NotImplemented
+1177
+1178    def __rmatmul__(self, y):
+1179        if isinstance(y, np.ndarray):
+1180            if y.ndim != 2 or y.shape[0] != y.shape[1]:
+1181                raise ValueError("Can only multiply correlators by square matrices.")
+1182            if not self.N == y.shape[0]:
+1183                raise ValueError("matmul: mismatch of matrix dimensions")
+1184            newcontent = []
+1185            for t in range(self.T):
+1186                if _check_for_none(self, self.content[t]):
+1187                    newcontent.append(None)
+1188                else:
+1189                    newcontent.append(y @ self.content[t])
+1190            return Corr(newcontent)
+1191        else:
+1192            return NotImplemented
 1193
-1194            newcontent = []
-1195            for t in range(self.T):
-1196                if _check_for_none(self, self.content[t]):
-1197                    newcontent.append(None)
-1198                else:
-1199                    newcontent.append(self.content[t] / y)
-1200            return Corr(newcontent, prange=self.prange)
-1201
-1202        elif isinstance(y, (int, float)):
-1203            if y == 0:
-1204                raise Exception('Division by zero will return undefined correlator')
-1205            newcontent = []
-1206            for t in range(self.T):
-1207                if _check_for_none(self, self.content[t]):
-1208                    newcontent.append(None)
-1209                else:
-1210                    newcontent.append(self.content[t] / y)
-1211            return Corr(newcontent, prange=self.prange)
-1212        elif isinstance(y, np.ndarray):
-1213            if y.shape == (self.T,):
-1214                return Corr(list((np.array(self.content).T / y).T))
-1215            else:
-1216                raise ValueError("operands could not be broadcast together")
-1217        else:
-1218            raise TypeError('Corr / wrong type')
-1219
-1220    def __neg__(self):
-1221        newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content]
-1222        return Corr(newcontent, prange=self.prange)
-1223
-1224    def __sub__(self, y):
-1225        return self + (-y)
-1226
-1227    def __pow__(self, y):
-1228        if isinstance(y, (Obs, int, float, CObs)):
-1229            newcontent = [None if _check_for_none(self, item) else item**y for item in self.content]
-1230            return Corr(newcontent, prange=self.prange)
-1231        else:
-1232            raise TypeError('Type of exponent not supported')
-1233
-1234    def __abs__(self):
-1235        newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content]
-1236        return Corr(newcontent, prange=self.prange)
-1237
-1238    # The numpy functions:
-1239    def sqrt(self):
-1240        return self ** 0.5
-1241
-1242    def log(self):
-1243        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1244        return Corr(newcontent, prange=self.prange)
-1245
-1246    def exp(self):
-1247        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1248        return Corr(newcontent, prange=self.prange)
-1249
-1250    def _apply_func_to_corr(self, func):
-1251        newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content]
-1252        for t in range(self.T):
-1253            if _check_for_none(self, newcontent[t]):
-1254                continue
-1255            tmp_sum = np.sum(newcontent[t])
-1256            if hasattr(tmp_sum, "value"):
-1257                if np.isnan(tmp_sum.value):
-1258                    newcontent[t] = None
-1259        if all([item is None for item in newcontent]):
-1260            raise Exception('Operation returns undefined correlator')
-1261        return Corr(newcontent)
-1262
-1263    def sin(self):
-1264        return self._apply_func_to_corr(np.sin)
+1194    def __truediv__(self, y):
+1195        if isinstance(y, Corr):
+1196            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
+1197                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
+1198            newcontent = []
+1199            for t in range(self.T):
+1200                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
+1201                    newcontent.append(None)
+1202                else:
+1203                    newcontent.append(self.content[t] / y.content[t])
+1204            for t in range(self.T):
+1205                if _check_for_none(self, newcontent[t]):
+1206                    continue
+1207                if np.isnan(np.sum(newcontent[t]).value):
+1208                    newcontent[t] = None
+1209
+1210            if all([item is None for item in newcontent]):
+1211                raise Exception("Division returns completely undefined correlator")
+1212            return Corr(newcontent)
+1213
+1214        elif isinstance(y, (Obs, CObs)):
+1215            if isinstance(y, Obs):
+1216                if y.value == 0:
+1217                    raise Exception('Division by zero will return undefined correlator')
+1218            if isinstance(y, CObs):
+1219                if y.is_zero():
+1220                    raise Exception('Division by zero will return undefined correlator')
+1221
+1222            newcontent = []
+1223            for t in range(self.T):
+1224                if _check_for_none(self, self.content[t]):
+1225                    newcontent.append(None)
+1226                else:
+1227                    newcontent.append(self.content[t] / y)
+1228            return Corr(newcontent, prange=self.prange)
+1229
+1230        elif isinstance(y, (int, float)):
+1231            if y == 0:
+1232                raise Exception('Division by zero will return undefined correlator')
+1233            newcontent = []
+1234            for t in range(self.T):
+1235                if _check_for_none(self, self.content[t]):
+1236                    newcontent.append(None)
+1237                else:
+1238                    newcontent.append(self.content[t] / y)
+1239            return Corr(newcontent, prange=self.prange)
+1240        elif isinstance(y, np.ndarray):
+1241            if y.shape == (self.T,):
+1242                return Corr(list((np.array(self.content).T / y).T))
+1243            else:
+1244                raise ValueError("operands could not be broadcast together")
+1245        else:
+1246            raise TypeError('Corr / wrong type')
+1247
+1248    def __neg__(self):
+1249        newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content]
+1250        return Corr(newcontent, prange=self.prange)
+1251
+1252    def __sub__(self, y):
+1253        return self + (-y)
+1254
+1255    def __pow__(self, y):
+1256        if isinstance(y, (Obs, int, float, CObs)):
+1257            newcontent = [None if _check_for_none(self, item) else item**y for item in self.content]
+1258            return Corr(newcontent, prange=self.prange)
+1259        else:
+1260            raise TypeError('Type of exponent not supported')
+1261
+1262    def __abs__(self):
+1263        newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content]
+1264        return Corr(newcontent, prange=self.prange)
 1265
-1266    def cos(self):
-1267        return self._apply_func_to_corr(np.cos)
-1268
-1269    def tan(self):
-1270        return self._apply_func_to_corr(np.tan)
-1271
-1272    def sinh(self):
-1273        return self._apply_func_to_corr(np.sinh)
-1274
-1275    def cosh(self):
-1276        return self._apply_func_to_corr(np.cosh)
+1266    # The numpy functions:
+1267    def sqrt(self):
+1268        return self ** 0.5
+1269
+1270    def log(self):
+1271        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1272        return Corr(newcontent, prange=self.prange)
+1273
+1274    def exp(self):
+1275        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1276        return Corr(newcontent, prange=self.prange)
 1277
-1278    def tanh(self):
-1279        return self._apply_func_to_corr(np.tanh)
-1280
-1281    def arcsin(self):
-1282        return self._apply_func_to_corr(np.arcsin)
-1283
-1284    def arccos(self):
-1285        return self._apply_func_to_corr(np.arccos)
-1286
-1287    def arctan(self):
-1288        return self._apply_func_to_corr(np.arctan)
-1289
-1290    def arcsinh(self):
-1291        return self._apply_func_to_corr(np.arcsinh)
-1292
-1293    def arccosh(self):
-1294        return self._apply_func_to_corr(np.arccosh)
-1295
-1296    def arctanh(self):
-1297        return self._apply_func_to_corr(np.arctanh)
-1298
-1299    # Right hand side operations (require tweak in main module to work)
-1300    def __radd__(self, y):
-1301        return self + y
+1278    def _apply_func_to_corr(self, func):
+1279        newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content]
+1280        for t in range(self.T):
+1281            if _check_for_none(self, newcontent[t]):
+1282                continue
+1283            tmp_sum = np.sum(newcontent[t])
+1284            if hasattr(tmp_sum, "value"):
+1285                if np.isnan(tmp_sum.value):
+1286                    newcontent[t] = None
+1287        if all([item is None for item in newcontent]):
+1288            raise Exception('Operation returns undefined correlator')
+1289        return Corr(newcontent)
+1290
+1291    def sin(self):
+1292        return self._apply_func_to_corr(np.sin)
+1293
+1294    def cos(self):
+1295        return self._apply_func_to_corr(np.cos)
+1296
+1297    def tan(self):
+1298        return self._apply_func_to_corr(np.tan)
+1299
+1300    def sinh(self):
+1301        return self._apply_func_to_corr(np.sinh)
 1302
-1303    def __rsub__(self, y):
-1304        return -self + y
+1303    def cosh(self):
+1304        return self._apply_func_to_corr(np.cosh)
 1305
-1306    def __rmul__(self, y):
-1307        return self * y
+1306    def tanh(self):
+1307        return self._apply_func_to_corr(np.tanh)
 1308
-1309    def __rtruediv__(self, y):
-1310        return (self / y) ** (-1)
+1309    def arcsin(self):
+1310        return self._apply_func_to_corr(np.arcsin)
 1311
-1312    @property
-1313    def real(self):
-1314        def return_real(obs_OR_cobs):
-1315            if isinstance(obs_OR_cobs.flatten()[0], CObs):
-1316                return np.vectorize(lambda x: x.real)(obs_OR_cobs)
-1317            else:
-1318                return obs_OR_cobs
-1319
-1320        return self._apply_func_to_corr(return_real)
-1321
-1322    @property
-1323    def imag(self):
-1324        def return_imag(obs_OR_cobs):
-1325            if isinstance(obs_OR_cobs.flatten()[0], CObs):
-1326                return np.vectorize(lambda x: x.imag)(obs_OR_cobs)
-1327            else:
-1328                return obs_OR_cobs * 0  # So it stays the right type
-1329
-1330        return self._apply_func_to_corr(return_imag)
-1331
-1332    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1333        r''' Project large correlation matrix to lowest states
-1334
-1335        This method can be used to reduce the size of an (N x N) correlation matrix
-1336        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1337        is still small.
-1338
-1339        Parameters
-1340        ----------
-1341        Ntrunc: int
-1342            Rank of the target matrix.
-1343        tproj: int
-1344            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1345            The default value is 3.
-1346        t0proj: int
-1347            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1348            discouraged for O(a) improved theories, since the correctness of the procedure
-1349            cannot be granted in this case. The default value is 2.
-1350        basematrix : Corr
-1351            Correlation matrix that is used to determine the eigenvectors of the
-1352            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1353            is is not specified.
-1354
-1355        Notes
-1356        -----
-1357        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1358        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1359        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1360        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1361        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1362        correlation matrix and to remove some noise that is added by irrelevant operators.
-1363        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1364        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1365        '''
+1312    def arccos(self):
+1313        return self._apply_func_to_corr(np.arccos)
+1314
+1315    def arctan(self):
+1316        return self._apply_func_to_corr(np.arctan)
+1317
+1318    def arcsinh(self):
+1319        return self._apply_func_to_corr(np.arcsinh)
+1320
+1321    def arccosh(self):
+1322        return self._apply_func_to_corr(np.arccosh)
+1323
+1324    def arctanh(self):
+1325        return self._apply_func_to_corr(np.arctanh)
+1326
+1327    # Right hand side operations (require tweak in main module to work)
+1328    def __radd__(self, y):
+1329        return self + y
+1330
+1331    def __rsub__(self, y):
+1332        return -self + y
+1333
+1334    def __rmul__(self, y):
+1335        return self * y
+1336
+1337    def __rtruediv__(self, y):
+1338        return (self / y) ** (-1)
+1339
+1340    @property
+1341    def real(self):
+1342        def return_real(obs_OR_cobs):
+1343            if isinstance(obs_OR_cobs.flatten()[0], CObs):
+1344                return np.vectorize(lambda x: x.real)(obs_OR_cobs)
+1345            else:
+1346                return obs_OR_cobs
+1347
+1348        return self._apply_func_to_corr(return_real)
+1349
+1350    @property
+1351    def imag(self):
+1352        def return_imag(obs_OR_cobs):
+1353            if isinstance(obs_OR_cobs.flatten()[0], CObs):
+1354                return np.vectorize(lambda x: x.imag)(obs_OR_cobs)
+1355            else:
+1356                return obs_OR_cobs * 0  # So it stays the right type
+1357
+1358        return self._apply_func_to_corr(return_imag)
+1359
+1360    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1361        r''' Project large correlation matrix to lowest states
+1362
+1363        This method can be used to reduce the size of an (N x N) correlation matrix
+1364        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1365        is still small.
 1366
-1367        if self.N == 1:
-1368            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1369        if basematrix is None:
-1370            basematrix = self
-1371        if Ntrunc >= basematrix.N:
-1372            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1373        if basematrix.N != self.N:
-1374            raise Exception('basematrix and targetmatrix have to be of the same size.')
-1375
-1376        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1377
-1378        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1379        rmat = []
-1380        for t in range(basematrix.T):
-1381            for i in range(Ntrunc):
-1382                for j in range(Ntrunc):
-1383                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1384            rmat.append(np.copy(tmpmat))
-1385
-1386        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1387        return Corr(newcontent)
+1367        Parameters
+1368        ----------
+1369        Ntrunc: int
+1370            Rank of the target matrix.
+1371        tproj: int
+1372            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1373            The default value is 3.
+1374        t0proj: int
+1375            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1376            discouraged for O(a) improved theories, since the correctness of the procedure
+1377            cannot be granted in this case. The default value is 2.
+1378        basematrix : Corr
+1379            Correlation matrix that is used to determine the eigenvectors of the
+1380            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1381            is is not specified.
+1382
+1383        Notes
+1384        -----
+1385        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1386        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1387        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1388        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1389        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1390        correlation matrix and to remove some noise that is added by irrelevant operators.
+1391        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1392        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1393        '''
+1394
+1395        if self.N == 1:
+1396            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1397        if basematrix is None:
+1398            basematrix = self
+1399        if Ntrunc >= basematrix.N:
+1400            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1401        if basematrix.N != self.N:
+1402            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1403
+1404        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1405
+1406        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1407        rmat = []
+1408        for t in range(basematrix.T):
+1409            for i in range(Ntrunc):
+1410                for j in range(Ntrunc):
+1411                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1412            rmat.append(np.copy(tmpmat))
+1413
+1414        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1415        return Corr(newcontent)
 

 
 
@@ -3105,82 +3218,82 @@ the temporal extent of the correlator and N is the dimension of the matrix.
- 
 45    def __init__(self, data_input, padding=[0, 0], prange=None):
- 46        """ Initialize a Corr object.
- 47
- 48        Parameters
- 49        ----------
- 50        data_input : list or array
- 51            list of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
- 52        padding : list, optional
- 53            List with two entries where the first labels the padding
- 54            at the front of the correlator and the second the padding
- 55            at the back.
- 56        prange : list, optional
- 57            List containing the first and last timeslice of the plateau
- 58            region identified for this correlator.
- 59        """
- 60
- 61        if isinstance(data_input, np.ndarray):
- 62            if data_input.ndim == 1:
- 63                data_input = list(data_input)
- 64            elif data_input.ndim == 2:
- 65                if not data_input.shape[0] == data_input.shape[1]:
- 66                    raise ValueError("Array needs to be square.")
- 67                if not all([isinstance(item, Corr) for item in data_input.flatten()]):
- 68                    raise ValueError("If the input is an array, its elements must be of type pe.Corr.")
- 69                if not all([item.N == 1 for item in data_input.flatten()]):
- 70                    raise ValueError("Can only construct matrix correlator from single valued correlators.")
- 71                if not len(set([item.T for item in data_input.flatten()])) == 1:
- 72                    raise ValueError("All input Correlators must be defined over the same timeslices.")
- 73
- 74                T = data_input[0, 0].T
- 75                N = data_input.shape[0]
- 76                input_as_list = []
- 77                for t in range(T):
- 78                    if any([(item.content[t] is None) for item in data_input.flatten()]):
- 79                        if not all([(item.content[t] is None) for item in data_input.flatten()]):
- 80                            warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss.!", RuntimeWarning)
- 81                        input_as_list.append(None)
- 82                    else:
- 83                        array_at_timeslace = np.empty([N, N], dtype="object")
- 84                        for i in range(N):
- 85                            for j in range(N):
- 86                                array_at_timeslace[i, j] = data_input[i, j][t]
- 87                        input_as_list.append(array_at_timeslace)
- 88                data_input = input_as_list
- 89            elif data_input.ndim == 3:
- 90                if not data_input.shape[1] == data_input.shape[2]:
- 91                    raise ValueError("Array needs to be square.")
- 92                data_input = list(data_input)
- 93            else:
- 94                raise ValueError("Arrays with ndim>3 not supported.")
- 95
- 96        if isinstance(data_input, list):
- 97
- 98            if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
- 99                _assert_equal_properties([o for o in data_input if o is not None])
-100                self.content = [np.asarray([item]) if item is not None else None for item in data_input]
-101                self.N = 1
-102            elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]):
-103                self.content = data_input
-104                noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
-105                self.N = noNull[0].shape[0]
-106                if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
-107                    raise ValueError("Smearing matrices are not NxN.")
-108                if (not all([item.shape == noNull[0].shape for item in noNull])):
-109                    raise ValueError("Items in data_input are not of identical shape." + str(noNull))
-110            else:
-111                raise TypeError("'data_input' contains item of wrong type.")
-112        else:
-113            raise TypeError("Data input was not given as list or correct array.")
-114
-115        self.tag = None
-116
-117        # An undefined timeslice is represented by the None object
-118        self.content = [None] * padding[0] + self.content + [None] * padding[1]
-119        self.T = len(self.content)
-120        self.prange = prange
+            
 46    def __init__(self, data_input, padding=[0, 0], prange=None):
+ 47        """ Initialize a Corr object.
+ 48
+ 49        Parameters
+ 50        ----------
+ 51        data_input : list or array
+ 52            list of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
+ 53        padding : list, optional
+ 54            List with two entries where the first labels the padding
+ 55            at the front of the correlator and the second the padding
+ 56            at the back.
+ 57        prange : list, optional
+ 58            List containing the first and last timeslice of the plateau
+ 59            region identified for this correlator.
+ 60        """
+ 61
+ 62        if isinstance(data_input, np.ndarray):
+ 63            if data_input.ndim == 1:
+ 64                data_input = list(data_input)
+ 65            elif data_input.ndim == 2:
+ 66                if not data_input.shape[0] == data_input.shape[1]:
+ 67                    raise ValueError("Array needs to be square.")
+ 68                if not all([isinstance(item, Corr) for item in data_input.flatten()]):
+ 69                    raise ValueError("If the input is an array, its elements must be of type pe.Corr.")
+ 70                if not all([item.N == 1 for item in data_input.flatten()]):
+ 71                    raise ValueError("Can only construct matrix correlator from single valued correlators.")
+ 72                if not len(set([item.T for item in data_input.flatten()])) == 1:
+ 73                    raise ValueError("All input Correlators must be defined over the same timeslices.")
+ 74
+ 75                T = data_input[0, 0].T
+ 76                N = data_input.shape[0]
+ 77                input_as_list = []
+ 78                for t in range(T):
+ 79                    if any([(item.content[t] is None) for item in data_input.flatten()]):
+ 80                        if not all([(item.content[t] is None) for item in data_input.flatten()]):
+ 81                            warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss.!", RuntimeWarning)
+ 82                        input_as_list.append(None)
+ 83                    else:
+ 84                        array_at_timeslace = np.empty([N, N], dtype="object")
+ 85                        for i in range(N):
+ 86                            for j in range(N):
+ 87                                array_at_timeslace[i, j] = data_input[i, j][t]
+ 88                        input_as_list.append(array_at_timeslace)
+ 89                data_input = input_as_list
+ 90            elif data_input.ndim == 3:
+ 91                if not data_input.shape[1] == data_input.shape[2]:
+ 92                    raise ValueError("Array needs to be square.")
+ 93                data_input = list(data_input)
+ 94            else:
+ 95                raise ValueError("Arrays with ndim>3 not supported.")
+ 96
+ 97        if isinstance(data_input, list):
+ 98
+ 99            if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
+100                _assert_equal_properties([o for o in data_input if o is not None])
+101                self.content = [np.asarray([item]) if item is not None else None for item in data_input]
+102                self.N = 1
+103            elif all([isinstance(item, np.ndarray) or item is None for item in data_input]) and any([isinstance(item, np.ndarray) for item in data_input]):
+104                self.content = data_input
+105                noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
+106                self.N = noNull[0].shape[0]
+107                if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
+108                    raise ValueError("Smearing matrices are not NxN.")
+109                if (not all([item.shape == noNull[0].shape for item in noNull])):
+110                    raise ValueError("Items in data_input are not of identical shape." + str(noNull))
+111            else:
+112                raise TypeError("'data_input' contains item of wrong type.")
+113        else:
+114            raise TypeError("Data input was not given as list or correct array.")
+115
+116        self.tag = None
+117
+118        # An undefined timeslice is represented by the None object
+119        self.content = [None] * padding[0] + self.content + [None] * padding[1]
+120        self.T = len(self.content)
+121        self.prange = prange
 

 
 
@@ -3269,16 +3382,16 @@ region identified for this correlator.
- 
141    def gamma_method(self, **kwargs):
-142        """Apply the gamma method to the content of the Corr."""
-143        for item in self.content:
-144            if not (item is None):
-145                if self.N == 1:
-146                    item[0].gamma_method(**kwargs)
-147                else:
-148                    for i in range(self.N):
-149                        for j in range(self.N):
-150                            item[i, j].gamma_method(**kwargs)
+            
142    def gamma_method(self, **kwargs):
+143        """Apply the gamma method to the content of the Corr."""
+144        for item in self.content:
+145            if not (item is None):
+146                if self.N == 1:
+147                    item[0].gamma_method(**kwargs)
+148                else:
+149                    for i in range(self.N):
+150                        for j in range(self.N):
+151                            item[i, j].gamma_method(**kwargs)
 

 
 
@@ -3298,16 +3411,16 @@ region identified for this correlator.
- 
141    def gamma_method(self, **kwargs):
-142        """Apply the gamma method to the content of the Corr."""
-143        for item in self.content:
-144            if not (item is None):
-145                if self.N == 1:
-146                    item[0].gamma_method(**kwargs)
-147                else:
-148                    for i in range(self.N):
-149                        for j in range(self.N):
-150                            item[i, j].gamma_method(**kwargs)
+            
142    def gamma_method(self, **kwargs):
+143        """Apply the gamma method to the content of the Corr."""
+144        for item in self.content:
+145            if not (item is None):
+146                if self.N == 1:
+147                    item[0].gamma_method(**kwargs)
+148                else:
+149                    for i in range(self.N):
+150                        for j in range(self.N):
+151                            item[i, j].gamma_method(**kwargs)
 

 
 
@@ -3327,44 +3440,44 @@ region identified for this correlator.
- 
154    def projected(self, vector_l=None, vector_r=None, normalize=False):
-155        """We need to project the Correlator with a Vector to get a single value at each timeslice.
-156
-157        The method can use one or two vectors.
-158        If two are specified it returns v1@G@v2 (the order might be very important.)
-159        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
-160        """
-161        if self.N == 1:
-162            raise Exception("Trying to project a Corr, that already has N=1.")
-163
-164        if vector_l is None:
-165            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
-166        elif (vector_r is None):
-167            vector_r = vector_l
-168        if isinstance(vector_l, list) and not isinstance(vector_r, list):
-169            if len(vector_l) != self.T:
-170                raise Exception("Length of vector list must be equal to T")
-171            vector_r = [vector_r] * self.T
-172        if isinstance(vector_r, list) and not isinstance(vector_l, list):
-173            if len(vector_r) != self.T:
-174                raise Exception("Length of vector list must be equal to T")
-175            vector_l = [vector_l] * self.T
-176
-177        if not isinstance(vector_l, list):
-178            if not vector_l.shape == vector_r.shape == (self.N,):
-179                raise Exception("Vectors are of wrong shape!")
-180            if normalize:
-181                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
-182            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
-183
-184        else:
-185            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
-186            if normalize:
-187                for t in range(self.T):
-188                    vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t])
-189
-190            newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
-191        return Corr(newcontent)
+            
155    def projected(self, vector_l=None, vector_r=None, normalize=False):
+156        """We need to project the Correlator with a Vector to get a single value at each timeslice.
+157
+158        The method can use one or two vectors.
+159        If two are specified it returns v1@G@v2 (the order might be very important.)
+160        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
+161        """
+162        if self.N == 1:
+163            raise Exception("Trying to project a Corr, that already has N=1.")
+164
+165        if vector_l is None:
+166            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
+167        elif (vector_r is None):
+168            vector_r = vector_l
+169        if isinstance(vector_l, list) and not isinstance(vector_r, list):
+170            if len(vector_l) != self.T:
+171                raise Exception("Length of vector list must be equal to T")
+172            vector_r = [vector_r] * self.T
+173        if isinstance(vector_r, list) and not isinstance(vector_l, list):
+174            if len(vector_r) != self.T:
+175                raise Exception("Length of vector list must be equal to T")
+176            vector_l = [vector_l] * self.T
+177
+178        if not isinstance(vector_l, list):
+179            if not vector_l.shape == vector_r.shape == (self.N,):
+180                raise Exception("Vectors are of wrong shape!")
+181            if normalize:
+182                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
+183            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
+184
+185        else:
+186            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
+187            if normalize:
+188                for t in range(self.T):
+189                    vector_l[t], vector_r[t] = vector_l[t] / np.sqrt((vector_l[t] @ vector_l[t])), vector_r[t] / np.sqrt(vector_r[t] @ vector_r[t])
+190
+191            newcontent = [None if (_check_for_none(self, self.content[t]) or vector_l[t] is None or vector_r[t] is None) else np.asarray([vector_l[t].T @ self.content[t] @ vector_r[t]]) for t in range(self.T)]
+192        return Corr(newcontent)
 

 
 
@@ -3388,20 +3501,20 @@ By default it will return the lowest source, which usually means unsmeared-unsme
- 
193    def item(self, i, j):
-194        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
-195
-196        Parameters
-197        ----------
-198        i : int
-199            First index to be picked.
-200        j : int
-201            Second index to be picked.
-202        """
-203        if self.N == 1:
-204            raise Exception("Trying to pick item from projected Corr")
-205        newcontent = [None if (item is None) else item[i, j] for item in self.content]
-206        return Corr(newcontent)
+            
194    def item(self, i, j):
+195        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
+196
+197        Parameters
+198        ----------
+199        i : int
+200            First index to be picked.
+201        j : int
+202            Second index to be picked.
+203        """
+204        if self.N == 1:
+205            raise Exception("Trying to pick item from projected Corr")
+206        newcontent = [None if (item is None) else item[i, j] for item in self.content]
+207        return Corr(newcontent)
 

 
 
@@ -3430,19 +3543,19 @@ Second index to be picked.
- 
208    def plottable(self):
-209        """Outputs the correlator in a plotable format.
-210
-211        Outputs three lists containing the timeslice index, the value on each
-212        timeslice and the error on each timeslice.
-213        """
-214        if self.N != 1:
-215            raise Exception("Can only make Corr[N=1] plottable")
-216        x_list = [x for x in range(self.T) if not self.content[x] is None]
-217        y_list = [y[0].value for y in self.content if y is not None]
-218        y_err_list = [y[0].dvalue for y in self.content if y is not None]
-219
-220        return x_list, y_list, y_err_list
+            
209    def plottable(self):
+210        """Outputs the correlator in a plotable format.
+211
+212        Outputs three lists containing the timeslice index, the value on each
+213        timeslice and the error on each timeslice.
+214        """
+215        if self.N != 1:
+216            raise Exception("Can only make Corr[N=1] plottable")
+217        x_list = [x for x in range(self.T) if not self.content[x] is None]
+218        y_list = [y[0].value for y in self.content if y is not None]
+219        y_err_list = [y[0].dvalue for y in self.content if y is not None]
+220
+221        return x_list, y_list, y_err_list
 

 
 
@@ -3465,26 +3578,26 @@ timeslice and the error on each timeslice.
- 
222    def symmetric(self):
-223        """ Symmetrize the correlator around x0=0."""
-224        if self.N != 1:
-225            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
-226        if self.T % 2 != 0:
-227            raise Exception("Can not symmetrize odd T")
-228
-229        if self.content[0] is not None:
-230            if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0:
-231                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
-232
-233        newcontent = [self.content[0]]
-234        for t in range(1, self.T):
-235            if (self.content[t] is None) or (self.content[self.T - t] is None):
-236                newcontent.append(None)
-237            else:
-238                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
-239        if (all([x is None for x in newcontent])):
-240            raise Exception("Corr could not be symmetrized: No redundant values")
-241        return Corr(newcontent, prange=self.prange)
+            
223    def symmetric(self):
+224        """ Symmetrize the correlator around x0=0."""
+225        if self.N != 1:
+226            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
+227        if self.T % 2 != 0:
+228            raise Exception("Can not symmetrize odd T")
+229
+230        if self.content[0] is not None:
+231            if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0:
+232                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
+233
+234        newcontent = [self.content[0]]
+235        for t in range(1, self.T):
+236            if (self.content[t] is None) or (self.content[self.T - t] is None):
+237                newcontent.append(None)
+238            else:
+239                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
+240        if (all([x is None for x in newcontent])):
+241            raise Exception("Corr could not be symmetrized: No redundant values")
+242        return Corr(newcontent, prange=self.prange)
 

 
 
@@ -3504,27 +3617,27 @@ timeslice and the error on each timeslice.
- 
243    def anti_symmetric(self):
-244        """Anti-symmetrize the correlator around x0=0."""
-245        if self.N != 1:
-246            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
-247        if self.T % 2 != 0:
-248            raise Exception("Can not symmetrize odd T")
-249
-250        test = 1 * self
-251        test.gamma_method()
-252        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
-253            warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)
-254
-255        newcontent = [self.content[0]]
-256        for t in range(1, self.T):
-257            if (self.content[t] is None) or (self.content[self.T - t] is None):
-258                newcontent.append(None)
-259            else:
-260                newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
-261        if (all([x is None for x in newcontent])):
-262            raise Exception("Corr could not be symmetrized: No redundant values")
-263        return Corr(newcontent, prange=self.prange)
+            
244    def anti_symmetric(self):
+245        """Anti-symmetrize the correlator around x0=0."""
+246        if self.N != 1:
+247            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
+248        if self.T % 2 != 0:
+249            raise Exception("Can not symmetrize odd T")
+250
+251        test = 1 * self
+252        test.gamma_method()
+253        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
+254            warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)
+255
+256        newcontent = [self.content[0]]
+257        for t in range(1, self.T):
+258            if (self.content[t] is None) or (self.content[self.T - t] is None):
+259                newcontent.append(None)
+260            else:
+261                newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
+262        if (all([x is None for x in newcontent])):
+263            raise Exception("Corr could not be symmetrized: No redundant values")
+264        return Corr(newcontent, prange=self.prange)
 

 
 
@@ -3544,20 +3657,20 @@ timeslice and the error on each timeslice.
- 
265    def is_matrix_symmetric(self):
-266        """Checks whether a correlator matrices is symmetric on every timeslice."""
-267        if self.N == 1:
-268            raise TypeError("Only works for correlator matrices.")
-269        for t in range(self.T):
-270            if self[t] is None:
-271                continue
-272            for i in range(self.N):
-273                for j in range(i + 1, self.N):
-274                    if self[t][i, j] is self[t][j, i]:
-275                        continue
-276                    if hash(self[t][i, j]) != hash(self[t][j, i]):
-277                        return False
-278        return True
+            
266    def is_matrix_symmetric(self):
+267        """Checks whether a correlator matrices is symmetric on every timeslice."""
+268        if self.N == 1:
+269            raise TypeError("Only works for correlator matrices.")
+270        for t in range(self.T):
+271            if self[t] is None:
+272                continue
+273            for i in range(self.N):
+274                for j in range(i + 1, self.N):
+275                    if self[t][i, j] is self[t][j, i]:
+276                        continue
+277                    if hash(self[t][i, j]) != hash(self[t][j, i]):
+278                        return False
+279        return True
 

 
 
@@ -3577,17 +3690,17 @@ timeslice and the error on each timeslice.
- 
280    def trace(self):
-281        """Calculates the per-timeslice trace of a correlator matrix."""
-282        if self.N == 1:
-283            raise ValueError("Only works for correlator matrices.")
-284        newcontent = []
-285        for t in range(self.T):
-286            if _check_for_none(self, self.content[t]):
-287                newcontent.append(None)
-288            else:
-289                newcontent.append(np.trace(self.content[t]))
-290        return Corr(newcontent)
+            
281    def trace(self):
+282        """Calculates the per-timeslice trace of a correlator matrix."""
+283        if self.N == 1:
+284            raise ValueError("Only works for correlator matrices.")
+285        newcontent = []
+286        for t in range(self.T):
+287            if _check_for_none(self, self.content[t]):
+288                newcontent.append(None)
+289            else:
+290                newcontent.append(np.trace(self.content[t]))
+291        return Corr(newcontent)
 

 
 
@@ -3607,15 +3720,15 @@ timeslice and the error on each timeslice.
- 
292    def matrix_symmetric(self):
-293        """Symmetrizes the correlator matrices on every timeslice."""
-294        if self.N == 1:
-295            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
-296        if self.is_matrix_symmetric():
-297            return 1.0 * self
-298        else:
-299            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
-300            return 0.5 * (Corr(transposed) + self)
+            
293    def matrix_symmetric(self):
+294        """Symmetrizes the correlator matrices on every timeslice."""
+295        if self.N == 1:
+296            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
+297        if self.is_matrix_symmetric():
+298            return 1.0 * self
+299        else:
+300            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
+301            return 0.5 * (Corr(transposed) + self)
 

 
 
@@ -3629,90 +3742,117 @@ timeslice and the error on each timeslice.

 

             
         def
-        GEVP(self, t0, ts=None, sort='Eigenvalue', **kwargs):
+        GEVP(self, t0, ts=None, sort='Eigenvalue', vector_obs=False, **kwargs):
 
                 
 
     

     
-            
302    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
-303        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
-304
-305        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
-306        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
-307        ```python
-308        C.GEVP(t0=2)[0]  # Ground state vector(s)
-309        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
-310        ```
-311
-312        Parameters
-313        ----------
-314        t0 : int
-315            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
-316        ts : int
-317            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
-318            If sort="Eigenvector" it gives a reference point for the sorting method.
-319        sort : string
-320            If 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.
-321            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-322            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
-323              The reference state is identified by its eigenvalue at $t=t_s$.
-324
-325        Other Parameters
-326        ----------------
-327        state : int
-328           Returns only the vector(s) for a specified state. The lowest state is zero.
-329        '''
-330
-331        if self.N == 1:
-332            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
-333        if ts is not None:
-334            if (ts <= t0):
-335                raise Exception("ts has to be larger than t0.")
-336
-337        if "sorted_list" in kwargs:
-338            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
-339            sort = kwargs.get("sorted_list")
-340
-341        if self.is_matrix_symmetric():
-342            symmetric_corr = self
-343        else:
-344            symmetric_corr = self.matrix_symmetric()
-345
-346        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
-347        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
+            
303    def GEVP(self, t0, ts=None, sort="Eigenvalue", vector_obs=False, **kwargs):
+304        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
+305
+306        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
+307        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
+308        ```python
+309        C.GEVP(t0=2)[0]  # Ground state vector(s)
+310        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
+311        ```
+312
+313        Parameters
+314        ----------
+315        t0 : int
+316            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
+317        ts : int
+318            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
+319            If sort="Eigenvector" it gives a reference point for the sorting method.
+320        sort : string
+321            If 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.
+322            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
+323            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
+324              The reference state is identified by its eigenvalue at $t=t_s$.
+325            - None: The GEVP is solved only at ts, no sorting is necessary
+326        vector_obs : bool
+327            If True, uncertainties are propagated in the eigenvector computation (default False).
+328
+329        Other Parameters
+330        ----------------
+331        state : int
+332           Returns only the vector(s) for a specified state. The lowest state is zero.
+333        method : str
+334           Method used to solve the GEVP.
+335           - "eigh": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
+336           - "cholesky": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
+337        '''
+338
+339        if self.N == 1:
+340            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
+341        if ts is not None:
+342            if (ts <= t0):
+343                raise Exception("ts has to be larger than t0.")
+344
+345        if "sorted_list" in kwargs:
+346            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
+347            sort = kwargs.get("sorted_list")
 348
-349        if sort is None:
-350            if (ts is None):
-351                raise Exception("ts is required if sort=None.")
-352            if (self.content[t0] is None) or (self.content[ts] is None):
-353                raise Exception("Corr not defined at t0/ts.")
-354            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
-355            reordered_vecs = _GEVP_solver(Gt, G0)
-356
-357        elif sort in ["Eigenvalue", "Eigenvector"]:
-358            if sort == "Eigenvalue" and ts is not None:
-359                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
-360            all_vecs = [None] * (t0 + 1)
-361            for t in range(t0 + 1, self.T):
-362                try:
-363                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
-364                    all_vecs.append(_GEVP_solver(Gt, G0))
-365                except Exception:
-366                    all_vecs.append(None)
-367            if sort == "Eigenvector":
-368                if ts is None:
-369                    raise Exception("ts is required for the Eigenvector sorting method.")
-370                all_vecs = _sort_vectors(all_vecs, ts)
-371
-372            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
-373        else:
-374            raise Exception("Unkown value for 'sort'.")
-375
-376        if "state" in kwargs:
-377            return reordered_vecs[kwargs.get("state")]
-378        else:
-379            return reordered_vecs
+349        if self.is_matrix_symmetric():
+350            symmetric_corr = self
+351        else:
+352            symmetric_corr = self.matrix_symmetric()
+353
+354        def _get_mat_at_t(t, vector_obs=vector_obs):
+355            if vector_obs:
+356                return symmetric_corr[t]
+357            else:
+358                return np.vectorize(lambda x: x.value)(symmetric_corr[t])
+359        G0 = _get_mat_at_t(t0)
+360
+361        method = kwargs.get('method', 'eigh')
+362        if vector_obs:
+363            chol = linalg.cholesky(G0)
+364            chol_inv = linalg.inv(chol)
+365            method = 'cholesky'
+366        else:
+367            chol = np.linalg.cholesky(_get_mat_at_t(t0, vector_obs=False))  # Check if matrix G0 is positive-semidefinite.
+368            if method == 'cholesky':
+369                chol_inv = np.linalg.inv(chol)
+370            else:
+371                chol_inv = None
+372
+373        if sort is None:
+374            if (ts is None):
+375                raise Exception("ts is required if sort=None.")
+376            if (self.content[t0] is None) or (self.content[ts] is None):
+377                raise Exception("Corr not defined at t0/ts.")
+378            Gt = _get_mat_at_t(ts)
+379            reordered_vecs = _GEVP_solver(Gt, G0, method=method, chol_inv=chol_inv)
+380            if kwargs.get('auto_gamma', False) and vector_obs:
+381                [[o.gm() for o in ev if isinstance(o, Obs)] for ev in reordered_vecs]
+382
+383        elif sort in ["Eigenvalue", "Eigenvector"]:
+384            if sort == "Eigenvalue" and ts is not None:
+385                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
+386            all_vecs = [None] * (t0 + 1)
+387            for t in range(t0 + 1, self.T):
+388                try:
+389                    Gt = _get_mat_at_t(t)
+390                    all_vecs.append(_GEVP_solver(Gt, G0, method=method, chol_inv=chol_inv))
+391                except Exception:
+392                    all_vecs.append(None)
+393            if sort == "Eigenvector":
+394                if ts is None:
+395                    raise Exception("ts is required for the Eigenvector sorting method.")
+396                all_vecs = _sort_vectors(all_vecs, ts)
+397
+398            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
+399            if kwargs.get('auto_gamma', False) and vector_obs:
+400                [[[o.gm() for o in evn] for evn in ev if evn is not None] for ev in reordered_vecs]
+401        else:
+402            raise Exception("Unknown value for 'sort'. Choose 'Eigenvalue', 'Eigenvector' or None.")
+403
+404        if "state" in kwargs:
+405            return reordered_vecs[kwargs.get("state")]
+406        else:
+407            return reordered_vecs
 

 
 
@@ -3738,10 +3878,13 @@ If sort="Eigenvector" it gives a reference point for the sorting method.
 
  • sort (string):
 If 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.
 
      
-
    • "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
      • 
+
    • "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
      • 
 
    • "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
 The reference state is identified by its eigenvalue at $t=t_s$.
      • 
+
    • None: The GEVP is solved only at ts, no sorting is necessary
      • 
 
    • 
+
  • vector_obs (bool):
+If True, uncertainties are propagated in the eigenvector computation (default False).
    • 
 
 
 
    Other Parameters
    
@@ -3749,6 +3892,12 @@ The reference state is identified by its eigenvalue at $t=t_s$.
 
      
 
    • state (int):
 Returns only the vector(s) for a specified state. The lowest state is zero.
      • 
+
    • method (str):
+Method used to solve the GEVP.
+
        
+
      • "eigh": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
        • 
+
      • "cholesky": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
        • 
+
      • 
 
    
 
    
 
@@ -3759,24 +3908,24 @@ Returns only the vector(s) for a specified state. The lowest state is zero.
 
    
             
         def
-        Eigenvalue(self, t0, ts=None, state=0, sort='Eigenvalue'):
+        Eigenvalue(self, t0, ts=None, state=0, sort='Eigenvalue', **kwargs):
 
                 
 
     
    
     
-            
    381    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
-382        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
-383
-384        Parameters
-385        ----------
-386        state : int
-387            The state one is interested in ordered by energy. The lowest state is zero.
-388
-389        All other parameters are identical to the ones of Corr.GEVP.
-390        """
-391        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
-392        return self.projected(vec)
+            
    409    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue", **kwargs):
+410        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
+411
+412        Parameters
+413        ----------
+414        state : int
+415            The state one is interested in ordered by energy. The lowest state is zero.
+416
+417        All other parameters are identical to the ones of Corr.GEVP.
+418        """
+419        vec = self.GEVP(t0, ts=ts, sort=sort, **kwargs)[state]
+420        return self.projected(vec)
 
    
 
 
@@ -3804,46 +3953,46 @@ The state one is interested in ordered by energy. The lowest state is zero.
 
     
    
     
-            
    394    def Hankel(self, N, periodic=False):
-395        """Constructs an NxN Hankel matrix
-396
-397        C(t) c(t+1) ... c(t+n-1)
-398        C(t+1) c(t+2) ... c(t+n)
-399        .................
-400        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
-401
-402        Parameters
-403        ----------
-404        N : int
-405            Dimension of the Hankel matrix
-406        periodic : bool, optional
-407            determines whether the matrix is extended periodically
-408        """
-409
-410        if self.N != 1:
-411            raise Exception("Multi-operator Prony not implemented!")
-412
-413        array = np.empty([N, N], dtype="object")
-414        new_content = []
-415        for t in range(self.T):
-416            new_content.append(array.copy())
-417
-418        def wrap(i):
-419            while i >= self.T:
-420                i -= self.T
-421            return i
-422
-423        for t in range(self.T):
-424            for i in range(N):
-425                for j in range(N):
-426                    if periodic:
-427                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
-428                    elif (t + i + j) >= self.T:
-429                        new_content[t] = None
-430                    else:
-431                        new_content[t][i, j] = self.content[t + i + j][0]
-432
-433        return Corr(new_content)
+            
    422    def Hankel(self, N, periodic=False):
+423        """Constructs an NxN Hankel matrix
+424
+425        C(t) c(t+1) ... c(t+n-1)
+426        C(t+1) c(t+2) ... c(t+n)
+427        .................
+428        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
+429
+430        Parameters
+431        ----------
+432        N : int
+433            Dimension of the Hankel matrix
+434        periodic : bool, optional
+435            determines whether the matrix is extended periodically
+436        """
+437
+438        if self.N != 1:
+439            raise Exception("Multi-operator Prony not implemented!")
+440
+441        array = np.empty([N, N], dtype="object")
+442        new_content = []
+443        for t in range(self.T):
+444            new_content.append(array.copy())
+445
+446        def wrap(i):
+447            while i >= self.T:
+448                i -= self.T
+449            return i
+450
+451        for t in range(self.T):
+452            for i in range(N):
+453                for j in range(N):
+454                    if periodic:
+455                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
+456                    elif (t + i + j) >= self.T:
+457                        new_content[t] = None
+458                    else:
+459                        new_content[t][i, j] = self.content[t + i + j][0]
+460
+461        return Corr(new_content)
 
    
 
 
@@ -3877,15 +4026,15 @@ determines whether the matrix is extended periodically
 
     
    
     
-            
    435    def roll(self, dt):
-436        """Periodically shift the correlator by dt timeslices
-437
-438        Parameters
-439        ----------
-440        dt : int
-441            number of timeslices
-442        """
-443        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
+            
    463    def roll(self, dt):
+464        """Periodically shift the correlator by dt timeslices
+465
+466        Parameters
+467        ----------
+468        dt : int
+469            number of timeslices
+470        """
+471        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
 
    
 
 
@@ -3912,9 +4061,9 @@ number of timeslices
 
     
    
     
-            
    445    def reverse(self):
-446        """Reverse the time ordering of the Corr"""
-447        return Corr(self.content[:: -1])
+            
    473    def reverse(self):
+474        """Reverse the time ordering of the Corr"""
+475        return Corr(self.content[:: -1])
 
    
 
 
@@ -3934,23 +4083,23 @@ number of timeslices
 
     
    
     
-            
    449    def thin(self, spacing=2, offset=0):
-450        """Thin out a correlator to suppress correlations
-451
-452        Parameters
-453        ----------
-454        spacing : int
-455            Keep only every 'spacing'th entry of the correlator
-456        offset : int
-457            Offset the equal spacing
-458        """
-459        new_content = []
-460        for t in range(self.T):
-461            if (offset + t) % spacing != 0:
-462                new_content.append(None)
-463            else:
-464                new_content.append(self.content[t])
-465        return Corr(new_content)
+            
    477    def thin(self, spacing=2, offset=0):
+478        """Thin out a correlator to suppress correlations
+479
+480        Parameters
+481        ----------
+482        spacing : int
+483            Keep only every 'spacing'th entry of the correlator
+484        offset : int
+485            Offset the equal spacing
+486        """
+487        new_content = []
+488        for t in range(self.T):
+489            if (offset + t) % spacing != 0:
+490                new_content.append(None)
+491            else:
+492                new_content.append(self.content[t])
+493        return Corr(new_content)
 
    
 
 
@@ -3979,34 +4128,34 @@ Offset the equal spacing
 
     
    
     
-            
    467    def correlate(self, partner):
-468        """Correlate the correlator with another correlator or Obs
-469
-470        Parameters
-471        ----------
-472        partner : Obs or Corr
-473            partner to correlate the correlator with.
-474            Can either be an Obs which is correlated with all entries of the
-475            correlator or a Corr of same length.
-476        """
-477        if self.N != 1:
-478            raise Exception("Only one-dimensional correlators can be safely correlated.")
-479        new_content = []
-480        for x0, t_slice in enumerate(self.content):
-481            if _check_for_none(self, t_slice):
-482                new_content.append(None)
-483            else:
-484                if isinstance(partner, Corr):
-485                    if _check_for_none(partner, partner.content[x0]):
-486                        new_content.append(None)
-487                    else:
-488                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
-489                elif isinstance(partner, Obs):  # Should this include CObs?
-490                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
-491                else:
-492                    raise Exception("Can only correlate with an Obs or a Corr.")
-493
-494        return Corr(new_content)
+            
    495    def correlate(self, partner):
+496        """Correlate the correlator with another correlator or Obs
+497
+498        Parameters
+499        ----------
+500        partner : Obs or Corr
+501            partner to correlate the correlator with.
+502            Can either be an Obs which is correlated with all entries of the
+503            correlator or a Corr of same length.
+504        """
+505        if self.N != 1:
+506            raise Exception("Only one-dimensional correlators can be safely correlated.")
+507        new_content = []
+508        for x0, t_slice in enumerate(self.content):
+509            if _check_for_none(self, t_slice):
+510                new_content.append(None)
+511            else:
+512                if isinstance(partner, Corr):
+513                    if _check_for_none(partner, partner.content[x0]):
+514                        new_content.append(None)
+515                    else:
+516                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
+517                elif isinstance(partner, Obs):  # Should this include CObs?
+518                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
+519                else:
+520                    raise Exception("Can only correlate with an Obs or a Corr.")
+521
+522        return Corr(new_content)
 
    
 
 
@@ -4035,28 +4184,28 @@ correlator or a Corr of same length.
 
     
    
     
-            
    496    def reweight(self, weight, **kwargs):
-497        """Reweight the correlator.
-498
-499        Parameters
-500        ----------
-501        weight : Obs
-502            Reweighting factor. An Observable that has to be defined on a superset of the
-503            configurations in obs[i].idl for all i.
-504        all_configs : bool
-505            if True, the reweighted observables are normalized by the average of
-506            the reweighting factor on all configurations in weight.idl and not
-507            on the configurations in obs[i].idl.
-508        """
-509        if self.N != 1:
-510            raise Exception("Reweighting only implemented for one-dimensional correlators.")
-511        new_content = []
-512        for t_slice in self.content:
-513            if _check_for_none(self, t_slice):
-514                new_content.append(None)
-515            else:
-516                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
-517        return Corr(new_content)
+            
    524    def reweight(self, weight, **kwargs):
+525        """Reweight the correlator.
+526
+527        Parameters
+528        ----------
+529        weight : Obs
+530            Reweighting factor. An Observable that has to be defined on a superset of the
+531            configurations in obs[i].idl for all i.
+532        all_configs : bool
+533            if True, the reweighted observables are normalized by the average of
+534            the reweighting factor on all configurations in weight.idl and not
+535            on the configurations in obs[i].idl.
+536        """
+537        if self.N != 1:
+538            raise Exception("Reweighting only implemented for one-dimensional correlators.")
+539        new_content = []
+540        for t_slice in self.content:
+541            if _check_for_none(self, t_slice):
+542                new_content.append(None)
+543            else:
+544                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
+545        return Corr(new_content)
 
    
 
 
@@ -4088,35 +4237,35 @@ on the configurations in obs[i].idl.
 
     
    
     
-            
    519    def T_symmetry(self, partner, parity=+1):
-520        """Return the time symmetry average of the correlator and its partner
-521
-522        Parameters
-523        ----------
-524        partner : Corr
-525            Time symmetry partner of the Corr
-526        parity : int
-527            Parity quantum number of the correlator, can be +1 or -1
-528        """
-529        if self.N != 1:
-530            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
-531        if not isinstance(partner, Corr):
-532            raise Exception("T partner has to be a Corr object.")
-533        if parity not in [+1, -1]:
-534            raise Exception("Parity has to be +1 or -1.")
-535        T_partner = parity * partner.reverse()
-536
-537        t_slices = []
-538        test = (self - T_partner)
-539        test.gamma_method()
-540        for x0, t_slice in enumerate(test.content):
-541            if t_slice is not None:
-542                if not t_slice[0].is_zero_within_error(5):
-543                    t_slices.append(x0)
-544        if t_slices:
-545            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
-546
-547        return (self + T_partner) / 2
+            
    547    def T_symmetry(self, partner, parity=+1):
+548        """Return the time symmetry average of the correlator and its partner
+549
+550        Parameters
+551        ----------
+552        partner : Corr
+553            Time symmetry partner of the Corr
+554        parity : int
+555            Parity quantum number of the correlator, can be +1 or -1
+556        """
+557        if self.N != 1:
+558            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
+559        if not isinstance(partner, Corr):
+560            raise Exception("T partner has to be a Corr object.")
+561        if parity not in [+1, -1]:
+562            raise Exception("Parity has to be +1 or -1.")
+563        T_partner = parity * partner.reverse()
+564
+565        t_slices = []
+566        test = (self - T_partner)
+567        test.gamma_method()
+568        for x0, t_slice in enumerate(test.content):
+569            if t_slice is not None:
+570                if not t_slice[0].is_zero_within_error(5):
+571                    t_slices.append(x0)
+572        if t_slices:
+573            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
+574
+575        return (self + T_partner) / 2
 
    
 
 
@@ -4145,70 +4294,70 @@ Parity quantum number of the correlator, can be +1 or -1
 
     
    
     
-            
    549    def deriv(self, variant="symmetric"):
-550        """Return the first derivative of the correlator with respect to x0.
-551
-552        Parameters
-553        ----------
-554        variant : str
-555            decides which definition of the finite differences derivative is used.
-556            Available choice: symmetric, forward, backward, improved, log, default: symmetric
-557        """
-558        if self.N != 1:
-559            raise Exception("deriv only implemented for one-dimensional correlators.")
-560        if variant == "symmetric":
-561            newcontent = []
-562            for t in range(1, self.T - 1):
-563                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-564                    newcontent.append(None)
-565                else:
-566                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
-567            if (all([x is None for x in newcontent])):
-568                raise Exception('Derivative is undefined at all timeslices')
-569            return Corr(newcontent, padding=[1, 1])
-570        elif variant == "forward":
-571            newcontent = []
-572            for t in range(self.T - 1):
-573                if (self.content[t] is None) or (self.content[t + 1] is None):
-574                    newcontent.append(None)
-575                else:
-576                    newcontent.append(self.content[t + 1] - self.content[t])
-577            if (all([x is None for x in newcontent])):
-578                raise Exception("Derivative is undefined at all timeslices")
-579            return Corr(newcontent, padding=[0, 1])
-580        elif variant == "backward":
-581            newcontent = []
-582            for t in range(1, self.T):
-583                if (self.content[t - 1] is None) or (self.content[t] is None):
-584                    newcontent.append(None)
-585                else:
-586                    newcontent.append(self.content[t] - self.content[t - 1])
-587            if (all([x is None for x in newcontent])):
-588                raise Exception("Derivative is undefined at all timeslices")
-589            return Corr(newcontent, padding=[1, 0])
-590        elif variant == "improved":
-591            newcontent = []
-592            for t in range(2, self.T - 2):
-593                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
-594                    newcontent.append(None)
-595                else:
-596                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
-597            if (all([x is None for x in newcontent])):
-598                raise Exception('Derivative is undefined at all timeslices')
-599            return Corr(newcontent, padding=[2, 2])
-600        elif variant == 'log':
-601            newcontent = []
-602            for t in range(self.T):
-603                if (self.content[t] is None) or (self.content[t] <= 0):
-604                    newcontent.append(None)
-605                else:
-606                    newcontent.append(np.log(self.content[t]))
-607            if (all([x is None for x in newcontent])):
-608                raise Exception("Log is undefined at all timeslices")
-609            logcorr = Corr(newcontent)
-610            return self * logcorr.deriv('symmetric')
-611        else:
-612            raise Exception("Unknown variant.")
+            
    577    def deriv(self, variant="symmetric"):
+578        """Return the first derivative of the correlator with respect to x0.
+579
+580        Parameters
+581        ----------
+582        variant : str
+583            decides which definition of the finite differences derivative is used.
+584            Available choice: symmetric, forward, backward, improved, log, default: symmetric
+585        """
+586        if self.N != 1:
+587            raise Exception("deriv only implemented for one-dimensional correlators.")
+588        if variant == "symmetric":
+589            newcontent = []
+590            for t in range(1, self.T - 1):
+591                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+592                    newcontent.append(None)
+593                else:
+594                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
+595            if (all([x is None for x in newcontent])):
+596                raise Exception('Derivative is undefined at all timeslices')
+597            return Corr(newcontent, padding=[1, 1])
+598        elif variant == "forward":
+599            newcontent = []
+600            for t in range(self.T - 1):
+601                if (self.content[t] is None) or (self.content[t + 1] is None):
+602                    newcontent.append(None)
+603                else:
+604                    newcontent.append(self.content[t + 1] - self.content[t])
+605            if (all([x is None for x in newcontent])):
+606                raise Exception("Derivative is undefined at all timeslices")
+607            return Corr(newcontent, padding=[0, 1])
+608        elif variant == "backward":
+609            newcontent = []
+610            for t in range(1, self.T):
+611                if (self.content[t - 1] is None) or (self.content[t] is None):
+612                    newcontent.append(None)
+613                else:
+614                    newcontent.append(self.content[t] - self.content[t - 1])
+615            if (all([x is None for x in newcontent])):
+616                raise Exception("Derivative is undefined at all timeslices")
+617            return Corr(newcontent, padding=[1, 0])
+618        elif variant == "improved":
+619            newcontent = []
+620            for t in range(2, self.T - 2):
+621                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+622                    newcontent.append(None)
+623                else:
+624                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
+625            if (all([x is None for x in newcontent])):
+626                raise Exception('Derivative is undefined at all timeslices')
+627            return Corr(newcontent, padding=[2, 2])
+628        elif variant == 'log':
+629            newcontent = []
+630            for t in range(self.T):
+631                if (self.content[t] is None) or (self.content[t] <= 0):
+632                    newcontent.append(None)
+633                else:
+634                    newcontent.append(np.log(self.content[t]))
+635            if (all([x is None for x in newcontent])):
+636                raise Exception("Log is undefined at all timeslices")
+637            logcorr = Corr(newcontent)
+638            return self * logcorr.deriv('symmetric')
+639        else:
+640            raise Exception("Unknown variant.")
 
    
 
 
@@ -4236,68 +4385,68 @@ Available choice: symmetric, forward, backward, improved, log, default: symmetri
 
     
    
     
-            
    614    def second_deriv(self, variant="symmetric"):
-615        r"""Return the second derivative of the correlator with respect to x0.
-616
-617        Parameters
-618        ----------
-619        variant : str
-620            decides which definition of the finite differences derivative is used.
-621            Available choice:
-622                - symmetric (default)
-623                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
-624                - big_symmetric
-625                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
-626                - improved
-627                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
-628                - log
-629                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
-630        """
-631        if self.N != 1:
-632            raise Exception("second_deriv only implemented for one-dimensional correlators.")
-633        if variant == "symmetric":
-634            newcontent = []
-635            for t in range(1, self.T - 1):
-636                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-637                    newcontent.append(None)
-638                else:
-639                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
-640            if (all([x is None for x in newcontent])):
-641                raise Exception("Derivative is undefined at all timeslices")
-642            return Corr(newcontent, padding=[1, 1])
-643        elif variant == "big_symmetric":
-644            newcontent = []
-645            for t in range(2, self.T - 2):
-646                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
-647                    newcontent.append(None)
-648                else:
-649                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
-650            if (all([x is None for x in newcontent])):
-651                raise Exception("Derivative is undefined at all timeslices")
-652            return Corr(newcontent, padding=[2, 2])
-653        elif variant == "improved":
-654            newcontent = []
-655            for t in range(2, self.T - 2):
-656                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
-657                    newcontent.append(None)
-658                else:
-659                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
-660            if (all([x is None for x in newcontent])):
-661                raise Exception("Derivative is undefined at all timeslices")
-662            return Corr(newcontent, padding=[2, 2])
-663        elif variant == 'log':
-664            newcontent = []
-665            for t in range(self.T):
-666                if (self.content[t] is None) or (self.content[t] <= 0):
-667                    newcontent.append(None)
-668                else:
-669                    newcontent.append(np.log(self.content[t]))
-670            if (all([x is None for x in newcontent])):
-671                raise Exception("Log is undefined at all timeslices")
-672            logcorr = Corr(newcontent)
-673            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
-674        else:
-675            raise Exception("Unknown variant.")
+            
    642    def second_deriv(self, variant="symmetric"):
+643        r"""Return the second derivative of the correlator with respect to x0.
+644
+645        Parameters
+646        ----------
+647        variant : str
+648            decides which definition of the finite differences derivative is used.
+649            Available choice:
+650                - symmetric (default)
+651                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
+652                - big_symmetric
+653                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
+654                - improved
+655                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
+656                - log
+657                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
+658        """
+659        if self.N != 1:
+660            raise Exception("second_deriv only implemented for one-dimensional correlators.")
+661        if variant == "symmetric":
+662            newcontent = []
+663            for t in range(1, self.T - 1):
+664                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+665                    newcontent.append(None)
+666                else:
+667                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
+668            if (all([x is None for x in newcontent])):
+669                raise Exception("Derivative is undefined at all timeslices")
+670            return Corr(newcontent, padding=[1, 1])
+671        elif variant == "big_symmetric":
+672            newcontent = []
+673            for t in range(2, self.T - 2):
+674                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
+675                    newcontent.append(None)
+676                else:
+677                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
+678            if (all([x is None for x in newcontent])):
+679                raise Exception("Derivative is undefined at all timeslices")
+680            return Corr(newcontent, padding=[2, 2])
+681        elif variant == "improved":
+682            newcontent = []
+683            for t in range(2, self.T - 2):
+684                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+685                    newcontent.append(None)
+686                else:
+687                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
+688            if (all([x is None for x in newcontent])):
+689                raise Exception("Derivative is undefined at all timeslices")
+690            return Corr(newcontent, padding=[2, 2])
+691        elif variant == 'log':
+692            newcontent = []
+693            for t in range(self.T):
+694                if (self.content[t] is None) or (self.content[t] <= 0):
+695                    newcontent.append(None)
+696                else:
+697                    newcontent.append(np.log(self.content[t]))
+698            if (all([x is None for x in newcontent])):
+699                raise Exception("Log is undefined at all timeslices")
+700            logcorr = Corr(newcontent)
+701            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
+702        else:
+703            raise Exception("Unknown variant.")
 
    
 
 
@@ -4333,89 +4482,89 @@ Available choice:
 
     
    
     
-            
    677    def m_eff(self, variant='log', guess=1.0):
-678        """Returns the effective mass of the correlator as correlator object
-679
-680        Parameters
-681        ----------
-682        variant : str
-683            log : uses the standard effective mass log(C(t) / C(t+1))
-684            cosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
-685            sinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
-686            See, e.g., arXiv:1205.5380
-687            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
-688            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
-689        guess : float
-690            guess for the root finder, only relevant for the root variant
-691        """
-692        if self.N != 1:
-693            raise Exception('Correlator must be projected before getting m_eff')
-694        if variant == 'log':
-695            newcontent = []
-696            for t in range(self.T - 1):
-697                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-698                    newcontent.append(None)
-699                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-700                    newcontent.append(None)
-701                else:
-702                    newcontent.append(self.content[t] / self.content[t + 1])
-703            if (all([x is None for x in newcontent])):
-704                raise Exception('m_eff is undefined at all timeslices')
-705
-706            return np.log(Corr(newcontent, padding=[0, 1]))
+            
    705    def m_eff(self, variant='log', guess=1.0):
+706        """Returns the effective mass of the correlator as correlator object
 707
-708        elif variant == 'logsym':
-709            newcontent = []
-710            for t in range(1, self.T - 1):
-711                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-712                    newcontent.append(None)
-713                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
-714                    newcontent.append(None)
-715                else:
-716                    newcontent.append(self.content[t - 1] / self.content[t + 1])
-717            if (all([x is None for x in newcontent])):
-718                raise Exception('m_eff is undefined at all timeslices')
-719
-720            return np.log(Corr(newcontent, padding=[1, 1])) / 2
-721
-722        elif variant in ['periodic', 'cosh', 'sinh']:
-723            if variant in ['periodic', 'cosh']:
-724                func = anp.cosh
-725            else:
-726                func = anp.sinh
-727
-728            def root_function(x, d):
-729                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
-730
-731            newcontent = []
-732            for t in range(self.T - 1):
-733                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
-734                    newcontent.append(None)
-735                # Fill the two timeslices in the middle of the lattice with their predecessors
-736                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
-737                    newcontent.append(newcontent[-1])
-738                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-739                    newcontent.append(None)
-740                else:
-741                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
-742            if (all([x is None for x in newcontent])):
-743                raise Exception('m_eff is undefined at all timeslices')
-744
-745            return Corr(newcontent, padding=[0, 1])
-746
-747        elif variant == 'arccosh':
-748            newcontent = []
-749            for t in range(1, self.T - 1):
-750                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0):
-751                    newcontent.append(None)
-752                else:
-753                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
-754            if (all([x is None for x in newcontent])):
-755                raise Exception("m_eff is undefined at all timeslices")
-756            return np.arccosh(Corr(newcontent, padding=[1, 1]))
-757
-758        else:
-759            raise Exception('Unknown variant.')
+708        Parameters
+709        ----------
+710        variant : str
+711            log : uses the standard effective mass log(C(t) / C(t+1))
+712            cosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
+713            sinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
+714            See, e.g., arXiv:1205.5380
+715            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+716            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
+717        guess : float
+718            guess for the root finder, only relevant for the root variant
+719        """
+720        if self.N != 1:
+721            raise Exception('Correlator must be projected before getting m_eff')
+722        if variant == 'log':
+723            newcontent = []
+724            for t in range(self.T - 1):
+725                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+726                    newcontent.append(None)
+727                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+728                    newcontent.append(None)
+729                else:
+730                    newcontent.append(self.content[t] / self.content[t + 1])
+731            if (all([x is None for x in newcontent])):
+732                raise Exception('m_eff is undefined at all timeslices')
+733
+734            return np.log(Corr(newcontent, padding=[0, 1]))
+735
+736        elif variant == 'logsym':
+737            newcontent = []
+738            for t in range(1, self.T - 1):
+739                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+740                    newcontent.append(None)
+741                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
+742                    newcontent.append(None)
+743                else:
+744                    newcontent.append(self.content[t - 1] / self.content[t + 1])
+745            if (all([x is None for x in newcontent])):
+746                raise Exception('m_eff is undefined at all timeslices')
+747
+748            return np.log(Corr(newcontent, padding=[1, 1])) / 2
+749
+750        elif variant in ['periodic', 'cosh', 'sinh']:
+751            if variant in ['periodic', 'cosh']:
+752                func = anp.cosh
+753            else:
+754                func = anp.sinh
+755
+756            def root_function(x, d):
+757                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
+758
+759            newcontent = []
+760            for t in range(self.T - 1):
+761                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+762                    newcontent.append(None)
+763                # Fill the two timeslices in the middle of the lattice with their predecessors
+764                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
+765                    newcontent.append(newcontent[-1])
+766                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+767                    newcontent.append(None)
+768                else:
+769                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
+770            if (all([x is None for x in newcontent])):
+771                raise Exception('m_eff is undefined at all timeslices')
+772
+773            return Corr(newcontent, padding=[0, 1])
+774
+775        elif variant == 'arccosh':
+776            newcontent = []
+777            for t in range(1, self.T - 1):
+778                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0):
+779                    newcontent.append(None)
+780                else:
+781                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+782            if (all([x is None for x in newcontent])):
+783                raise Exception("m_eff is undefined at all timeslices")
+784            return np.arccosh(Corr(newcontent, padding=[1, 1]))
+785
+786        else:
+787            raise Exception('Unknown variant.')
 
    
 
 
@@ -4449,39 +4598,39 @@ guess for the root finder, only relevant for the root variant
 
     
    
     
-            
    761    def fit(self, function, fitrange=None, silent=False, **kwargs):
-762        r'''Fits function to the data
-763
-764        Parameters
-765        ----------
-766        function : obj
-767            function to fit to the data. See fits.least_squares for details.
-768        fitrange : list
-769            Two element list containing the timeslices on which the fit is supposed to start and stop.
-770            Caution: This range is inclusive as opposed to standard python indexing.
-771            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
-772            If not specified, self.prange or all timeslices are used.
-773        silent : bool
-774            Decides whether output is printed to the standard output.
-775        '''
-776        if self.N != 1:
-777            raise Exception("Correlator must be projected before fitting")
-778
-779        if fitrange is None:
-780            if self.prange:
-781                fitrange = self.prange
-782            else:
-783                fitrange = [0, self.T - 1]
-784        else:
-785            if not isinstance(fitrange, list):
-786                raise Exception("fitrange has to be a list with two elements")
-787            if len(fitrange) != 2:
-788                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
-789
-790        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
-791        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
-792        result = least_squares(xs, ys, function, silent=silent, **kwargs)
-793        return result
+            
    789    def fit(self, function, fitrange=None, silent=False, **kwargs):
+790        r'''Fits function to the data
+791
+792        Parameters
+793        ----------
+794        function : obj
+795            function to fit to the data. See fits.least_squares for details.
+796        fitrange : list
+797            Two element list containing the timeslices on which the fit is supposed to start and stop.
+798            Caution: This range is inclusive as opposed to standard python indexing.
+799            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
+800            If not specified, self.prange or all timeslices are used.
+801        silent : bool
+802            Decides whether output is printed to the standard output.
+803        '''
+804        if self.N != 1:
+805            raise Exception("Correlator must be projected before fitting")
+806
+807        if fitrange is None:
+808            if self.prange:
+809                fitrange = self.prange
+810            else:
+811                fitrange = [0, self.T - 1]
+812        else:
+813            if not isinstance(fitrange, list):
+814                raise Exception("fitrange has to be a list with two elements")
+815            if len(fitrange) != 2:
+816                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
+817
+818        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
+819        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
+820        result = least_squares(xs, ys, function, silent=silent, **kwargs)
+821        return result
 
    
 
 
@@ -4515,42 +4664,42 @@ Decides whether output is printed to the standard output.
 
     
    
     
-            
    795    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
-796        """ Extract a plateau value from a Corr object
-797
-798        Parameters
-799        ----------
-800        plateau_range : list
-801            list with two entries, indicating the first and the last timeslice
-802            of the plateau region.
-803        method : str
-804            method to extract the plateau.
-805                'fit' fits a constant to the plateau region
-806                'avg', 'average' or 'mean' just average over the given timeslices.
-807        auto_gamma : bool
-808            apply gamma_method with default parameters to the Corr. Defaults to None
-809        """
-810        if not plateau_range:
-811            if self.prange:
-812                plateau_range = self.prange
-813            else:
-814                raise Exception("no plateau range provided")
-815        if self.N != 1:
-816            raise Exception("Correlator must be projected before getting a plateau.")
-817        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
-818            raise Exception("plateau is undefined at all timeslices in plateaurange.")
-819        if auto_gamma:
-820            self.gamma_method()
-821        if method == "fit":
-822            def const_func(a, t):
-823                return a[0]
-824            return self.fit(const_func, plateau_range)[0]
-825        elif method in ["avg", "average", "mean"]:
-826            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
-827            return returnvalue
-828
-829        else:
-830            raise Exception("Unsupported plateau method: " + method)
+            
    823    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+824        """ Extract a plateau value from a Corr object
+825
+826        Parameters
+827        ----------
+828        plateau_range : list
+829            list with two entries, indicating the first and the last timeslice
+830            of the plateau region.
+831        method : str
+832            method to extract the plateau.
+833                'fit' fits a constant to the plateau region
+834                'avg', 'average' or 'mean' just average over the given timeslices.
+835        auto_gamma : bool
+836            apply gamma_method with default parameters to the Corr. Defaults to None
+837        """
+838        if not plateau_range:
+839            if self.prange:
+840                plateau_range = self.prange
+841            else:
+842                raise Exception("no plateau range provided")
+843        if self.N != 1:
+844            raise Exception("Correlator must be projected before getting a plateau.")
+845        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
+846            raise Exception("plateau is undefined at all timeslices in plateaurange.")
+847        if auto_gamma:
+848            self.gamma_method()
+849        if method == "fit":
+850            def const_func(a, t):
+851                return a[0]
+852            return self.fit(const_func, plateau_range)[0]
+853        elif method in ["avg", "average", "mean"]:
+854            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
+855            return returnvalue
+856
+857        else:
+858            raise Exception("Unsupported plateau method: " + method)
 
    
 
 
@@ -4584,17 +4733,17 @@ apply gamma_method with default parameters to the Corr. Defaults to None
 
     
    
     
-            
    832    def set_prange(self, prange):
-833        """Sets the attribute prange of the Corr object."""
-834        if not len(prange) == 2:
-835            raise Exception("prange must be a list or array with two values")
-836        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
-837            raise Exception("Start and end point must be integers")
-838        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
-839            raise Exception("Start and end point must define a range in the interval 0,T")
-840
-841        self.prange = prange
-842        return
+            
    860    def set_prange(self, prange):
+861        """Sets the attribute prange of the Corr object."""
+862        if not len(prange) == 2:
+863            raise Exception("prange must be a list or array with two values")
+864        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
+865            raise Exception("Start and end point must be integers")
+866        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
+867            raise Exception("Start and end point must define a range in the interval 0,T")
+868
+869        self.prange = prange
+870        return
 
    
 
 
@@ -4614,130 +4763,130 @@ apply gamma_method with default parameters to the Corr. Defaults to None
 
     
    
     
-            
    844    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
-845        """Plots the correlator using the tag of the correlator as label if available.
-846
-847        Parameters
-848        ----------
-849        x_range : list
-850            list of two values, determining the range of the x-axis e.g. [4, 8].
-851        comp : Corr or list of Corr
-852            Correlator or list of correlators which are plotted for comparison.
-853            The tags of these correlators are used as labels if available.
-854        logscale : bool
-855            Sets y-axis to logscale.
-856        plateau : Obs
-857            Plateau value to be visualized in the figure.
-858        fit_res : Fit_result
-859            Fit_result object to be visualized.
-860        fit_key : str
-861            Key for the fit function in Fit_result.fit_function (for combined fits).
-862        ylabel : str
-863            Label for the y-axis.
-864        save : str
-865            path to file in which the figure should be saved.
-866        auto_gamma : bool
-867            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
-868        hide_sigma : float
-869            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
-870        references : list
-871            List of floating point values that are displayed as horizontal lines for reference.
-872        title : string
-873            Optional title of the figure.
-874        """
-875        if self.N != 1:
-876            raise Exception("Correlator must be projected before plotting")
-877
-878        if auto_gamma:
-879            self.gamma_method()
-880
-881        if x_range is None:
-882            x_range = [0, self.T - 1]
-883
-884        fig = plt.figure()
-885        ax1 = fig.add_subplot(111)
-886
-887        x, y, y_err = self.plottable()
-888        if hide_sigma:
-889            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-890        else:
-891            hide_from = None
-892        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
-893        if logscale:
-894            ax1.set_yscale('log')
-895        else:
-896            if y_range is None:
-897                try:
-898                    y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
-899                    y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
-900                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
-901                except Exception:
-902                    pass
-903            else:
-904                ax1.set_ylim(y_range)
-905        if comp:
-906            if isinstance(comp, (Corr, list)):
-907                for corr in comp if isinstance(comp, list) else [comp]:
-908                    if auto_gamma:
-909                        corr.gamma_method()
-910                    x, y, y_err = corr.plottable()
-911                    if hide_sigma:
-912                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-913                    else:
-914                        hide_from = None
-915                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
-916            else:
-917                raise Exception("'comp' must be a correlator or a list of correlators.")
-918
-919        if plateau:
-920            if isinstance(plateau, Obs):
-921                if auto_gamma:
-922                    plateau.gamma_method()
-923                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
-924                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
-925            else:
-926                raise Exception("'plateau' must be an Obs")
-927
-928        if references:
-929            if isinstance(references, list):
-930                for ref in references:
-931                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
-932            else:
-933                raise Exception("'references' must be a list of floating pint values.")
-934
-935        if self.prange:
-936            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
-937            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
-938
-939        if fit_res:
-940            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
-941            if isinstance(fit_res.fit_function, dict):
-942                if fit_key:
-943                    ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
-944                else:
-945                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
-946            else:
-947                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
-948
-949        ax1.set_xlabel(r'$x_0 / a$')
-950        if ylabel:
-951            ax1.set_ylabel(ylabel)
-952        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
-953
-954        handles, labels = ax1.get_legend_handles_labels()
-955        if labels:
-956            ax1.legend()
-957
-958        if title:
-959            plt.title(title)
-960
-961        plt.draw()
+            
    872    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
+873        """Plots the correlator using the tag of the correlator as label if available.
+874
+875        Parameters
+876        ----------
+877        x_range : list
+878            list of two values, determining the range of the x-axis e.g. [4, 8].
+879        comp : Corr or list of Corr
+880            Correlator or list of correlators which are plotted for comparison.
+881            The tags of these correlators are used as labels if available.
+882        logscale : bool
+883            Sets y-axis to logscale.
+884        plateau : Obs
+885            Plateau value to be visualized in the figure.
+886        fit_res : Fit_result
+887            Fit_result object to be visualized.
+888        fit_key : str
+889            Key for the fit function in Fit_result.fit_function (for combined fits).
+890        ylabel : str
+891            Label for the y-axis.
+892        save : str
+893            path to file in which the figure should be saved.
+894        auto_gamma : bool
+895            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
+896        hide_sigma : float
+897            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
+898        references : list
+899            List of floating point values that are displayed as horizontal lines for reference.
+900        title : string
+901            Optional title of the figure.
+902        """
+903        if self.N != 1:
+904            raise Exception("Correlator must be projected before plotting")
+905
+906        if auto_gamma:
+907            self.gamma_method()
+908
+909        if x_range is None:
+910            x_range = [0, self.T - 1]
+911
+912        fig = plt.figure()
+913        ax1 = fig.add_subplot(111)
+914
+915        x, y, y_err = self.plottable()
+916        if hide_sigma:
+917            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+918        else:
+919            hide_from = None
+920        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
+921        if logscale:
+922            ax1.set_yscale('log')
+923        else:
+924            if y_range is None:
+925                try:
+926                    y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+927                    y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+928                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
+929                except Exception:
+930                    pass
+931            else:
+932                ax1.set_ylim(y_range)
+933        if comp:
+934            if isinstance(comp, (Corr, list)):
+935                for corr in comp if isinstance(comp, list) else [comp]:
+936                    if auto_gamma:
+937                        corr.gamma_method()
+938                    x, y, y_err = corr.plottable()
+939                    if hide_sigma:
+940                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+941                    else:
+942                        hide_from = None
+943                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
+944            else:
+945                raise Exception("'comp' must be a correlator or a list of correlators.")
+946
+947        if plateau:
+948            if isinstance(plateau, Obs):
+949                if auto_gamma:
+950                    plateau.gamma_method()
+951                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
+952                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+953            else:
+954                raise Exception("'plateau' must be an Obs")
+955
+956        if references:
+957            if isinstance(references, list):
+958                for ref in references:
+959                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
+960            else:
+961                raise Exception("'references' must be a list of floating pint values.")
 962
-963        if save:
-964            if isinstance(save, str):
-965                fig.savefig(save, bbox_inches='tight')
-966            else:
-967                raise Exception("'save' has to be a string.")
+963        if self.prange:
+964            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
+965            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
+966
+967        if fit_res:
+968            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
+969            if isinstance(fit_res.fit_function, dict):
+970                if fit_key:
+971                    ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
+972                else:
+973                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
+974            else:
+975                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
+976
+977        ax1.set_xlabel(r'$x_0 / a$')
+978        if ylabel:
+979            ax1.set_ylabel(ylabel)
+980        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
+981
+982        handles, labels = ax1.get_legend_handles_labels()
+983        if labels:
+984            ax1.legend()
+985
+986        if title:
+987            plt.title(title)
+988
+989        plt.draw()
+990
+991        if save:
+992            if isinstance(save, str):
+993                fig.savefig(save, bbox_inches='tight')
+994            else:
+995                raise Exception("'save' has to be a string.")
 
    
 
 
@@ -4787,34 +4936,34 @@ Optional title of the figure.
 
     
    
     
-            
    969    def spaghetti_plot(self, logscale=True):
-970        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-971
-972        Parameters
-973        ----------
-974        logscale : bool
-975            Determines whether the scale of the y-axis is logarithmic or standard.
-976        """
-977        if self.N != 1:
-978            raise Exception("Correlator needs to be projected first.")
-979
-980        mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist]))
-981        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
-982
-983        for name in mc_names:
-984            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
-985
-986            fig = plt.figure()
-987            ax = fig.add_subplot(111)
-988            for dat in data:
-989                ax.plot(x0_vals, dat, ls='-', marker='')
-990
-991            if logscale is True:
-992                ax.set_yscale('log')
-993
-994            ax.set_xlabel(r'$x_0 / a$')
-995            plt.title(name)
-996            plt.draw()
+            
     997    def spaghetti_plot(self, logscale=True):
+ 998        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+ 999
+1000        Parameters
+1001        ----------
+1002        logscale : bool
+1003            Determines whether the scale of the y-axis is logarithmic or standard.
+1004        """
+1005        if self.N != 1:
+1006            raise Exception("Correlator needs to be projected first.")
+1007
+1008        mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist]))
+1009        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+1010
+1011        for name in mc_names:
+1012            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+1013
+1014            fig = plt.figure()
+1015            ax = fig.add_subplot(111)
+1016            for dat in data:
+1017                ax.plot(x0_vals, dat, ls='-', marker='')
+1018
+1019            if logscale is True:
+1020                ax.set_yscale('log')
+1021
+1022            ax.set_xlabel(r'$x_0 / a$')
+1023            plt.title(name)
+1024            plt.draw()
 
    
 
 
@@ -4841,29 +4990,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.
 
     
    
     
-            
     998    def dump(self, filename, datatype="json.gz", **kwargs):
- 999        """Dumps the Corr into a file of chosen type
-1000        Parameters
-1001        ----------
-1002        filename : str
-1003            Name of the file to be saved.
-1004        datatype : str
-1005            Format of the exported file. Supported formats include
-1006            "json.gz" and "pickle"
-1007        path : str
-1008            specifies a custom path for the file (default '.')
-1009        """
-1010        if datatype == "json.gz":
-1011            from .input.json import dump_to_json
-1012            if 'path' in kwargs:
-1013                file_name = kwargs.get('path') + '/' + filename
-1014            else:
-1015                file_name = filename
-1016            dump_to_json(self, file_name)
-1017        elif datatype == "pickle":
-1018            dump_object(self, filename, **kwargs)
-1019        else:
-1020            raise Exception("Unknown datatype " + str(datatype))
+            
    1026    def dump(self, filename, datatype="json.gz", **kwargs):
+1027        """Dumps the Corr into a file of chosen type
+1028        Parameters
+1029        ----------
+1030        filename : str
+1031            Name of the file to be saved.
+1032        datatype : str
+1033            Format of the exported file. Supported formats include
+1034            "json.gz" and "pickle"
+1035        path : str
+1036            specifies a custom path for the file (default '.')
+1037        """
+1038        if datatype == "json.gz":
+1039            from .input.json import dump_to_json
+1040            if 'path' in kwargs:
+1041                file_name = kwargs.get('path') + '/' + filename
+1042            else:
+1043                file_name = filename
+1044            dump_to_json(self, file_name)
+1045        elif datatype == "pickle":
+1046            dump_object(self, filename, **kwargs)
+1047        else:
+1048            raise Exception("Unknown datatype " + str(datatype))
 
    
 
 
@@ -4895,8 +5044,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1022    def print(self, print_range=None):
-1023        print(self.__repr__(print_range))
+            
    1050    def print(self, print_range=None):
+1051        print(self.__repr__(print_range))
 
    
 
 
@@ -4914,8 +5063,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1239    def sqrt(self):
-1240        return self ** 0.5
+            
    1267    def sqrt(self):
+1268        return self ** 0.5
 
    
 
 
@@ -4933,9 +5082,9 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1242    def log(self):
-1243        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1244        return Corr(newcontent, prange=self.prange)
+            
    1270    def log(self):
+1271        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1272        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4953,9 +5102,9 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1246    def exp(self):
-1247        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1248        return Corr(newcontent, prange=self.prange)
+            
    1274    def exp(self):
+1275        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1276        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4973,8 +5122,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1263    def sin(self):
-1264        return self._apply_func_to_corr(np.sin)
+            
    1291    def sin(self):
+1292        return self._apply_func_to_corr(np.sin)
 
    
 
 
@@ -4992,8 +5141,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1266    def cos(self):
-1267        return self._apply_func_to_corr(np.cos)
+            
    1294    def cos(self):
+1295        return self._apply_func_to_corr(np.cos)
 
    
 
 
@@ -5011,8 +5160,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1269    def tan(self):
-1270        return self._apply_func_to_corr(np.tan)
+            
    1297    def tan(self):
+1298        return self._apply_func_to_corr(np.tan)
 
    
 
 
@@ -5030,8 +5179,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1272    def sinh(self):
-1273        return self._apply_func_to_corr(np.sinh)
+            
    1300    def sinh(self):
+1301        return self._apply_func_to_corr(np.sinh)
 
    
 
 
@@ -5049,8 +5198,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1275    def cosh(self):
-1276        return self._apply_func_to_corr(np.cosh)
+            
    1303    def cosh(self):
+1304        return self._apply_func_to_corr(np.cosh)
 
    
 
 
@@ -5068,8 +5217,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1278    def tanh(self):
-1279        return self._apply_func_to_corr(np.tanh)
+            
    1306    def tanh(self):
+1307        return self._apply_func_to_corr(np.tanh)
 
    
 
 
@@ -5087,8 +5236,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1281    def arcsin(self):
-1282        return self._apply_func_to_corr(np.arcsin)
+            
    1309    def arcsin(self):
+1310        return self._apply_func_to_corr(np.arcsin)
 
    
 
 
@@ -5106,8 +5255,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1284    def arccos(self):
-1285        return self._apply_func_to_corr(np.arccos)
+            
    1312    def arccos(self):
+1313        return self._apply_func_to_corr(np.arccos)
 
    
 
 
@@ -5125,8 +5274,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1287    def arctan(self):
-1288        return self._apply_func_to_corr(np.arctan)
+            
    1315    def arctan(self):
+1316        return self._apply_func_to_corr(np.arctan)
 
    
 
 
@@ -5144,8 +5293,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1290    def arcsinh(self):
-1291        return self._apply_func_to_corr(np.arcsinh)
+            
    1318    def arcsinh(self):
+1319        return self._apply_func_to_corr(np.arcsinh)
 
    
 
 
@@ -5163,8 +5312,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1293    def arccosh(self):
-1294        return self._apply_func_to_corr(np.arccosh)
+            
    1321    def arccosh(self):
+1322        return self._apply_func_to_corr(np.arccosh)
 
    
 
 
@@ -5182,8 +5331,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1296    def arctanh(self):
-1297        return self._apply_func_to_corr(np.arctanh)
+            
    1324    def arctanh(self):
+1325        return self._apply_func_to_corr(np.arctanh)
 
    
 
 
@@ -5223,62 +5372,62 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1332    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1333        r''' Project large correlation matrix to lowest states
-1334
-1335        This method can be used to reduce the size of an (N x N) correlation matrix
-1336        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1337        is still small.
-1338
-1339        Parameters
-1340        ----------
-1341        Ntrunc: int
-1342            Rank of the target matrix.
-1343        tproj: int
-1344            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1345            The default value is 3.
-1346        t0proj: int
-1347            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1348            discouraged for O(a) improved theories, since the correctness of the procedure
-1349            cannot be granted in this case. The default value is 2.
-1350        basematrix : Corr
-1351            Correlation matrix that is used to determine the eigenvectors of the
-1352            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1353            is is not specified.
-1354
-1355        Notes
-1356        -----
-1357        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1358        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1359        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1360        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1361        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1362        correlation matrix and to remove some noise that is added by irrelevant operators.
-1363        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1364        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1365        '''
+            
    1360    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1361        r''' Project large correlation matrix to lowest states
+1362
+1363        This method can be used to reduce the size of an (N x N) correlation matrix
+1364        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1365        is still small.
 1366
-1367        if self.N == 1:
-1368            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1369        if basematrix is None:
-1370            basematrix = self
-1371        if Ntrunc >= basematrix.N:
-1372            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1373        if basematrix.N != self.N:
-1374            raise Exception('basematrix and targetmatrix have to be of the same size.')
-1375
-1376        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1377
-1378        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1379        rmat = []
-1380        for t in range(basematrix.T):
-1381            for i in range(Ntrunc):
-1382                for j in range(Ntrunc):
-1383                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1384            rmat.append(np.copy(tmpmat))
-1385
-1386        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1387        return Corr(newcontent)
+1367        Parameters
+1368        ----------
+1369        Ntrunc: int
+1370            Rank of the target matrix.
+1371        tproj: int
+1372            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1373            The default value is 3.
+1374        t0proj: int
+1375            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1376            discouraged for O(a) improved theories, since the correctness of the procedure
+1377            cannot be granted in this case. The default value is 2.
+1378        basematrix : Corr
+1379            Correlation matrix that is used to determine the eigenvectors of the
+1380            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1381            is is not specified.
+1382
+1383        Notes
+1384        -----
+1385        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1386        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1387        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1388        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1389        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1390        correlation matrix and to remove some noise that is added by irrelevant operators.
+1391        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1392        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1393        '''
+1394
+1395        if self.N == 1:
+1396            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1397        if basematrix is None:
+1398            basematrix = self
+1399        if Ntrunc >= basematrix.N:
+1400            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1401        if basematrix.N != self.N:
+1402            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1403
+1404        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1405
+1406        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1407        rmat = []
+1408        for t in range(basematrix.T):
+1409            for i in range(Ntrunc):
+1410                for j in range(Ntrunc):
+1411                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1412            rmat.append(np.copy(tmpmat))
+1413
+1414        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1415        return Corr(newcontent)
 
    
 
 
diff --git a/docs/pyerrors/linalg.html b/docs/pyerrors/linalg.html
index 605e3c13..94902ef3 100644
--- a/docs/pyerrors/linalg.html
+++ b/docs/pyerrors/linalg.html
@@ -76,6 +76,9 @@
             
  • 
                     eig
             
    • 
+            
  • 
+                    eigv
+            
    • 
             
  • 
                     pinv
             
    • 
@@ -376,17 +379,23 @@
     271    return w
 272
 273
-274def pinv(obs, **kwargs):
-275    """Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""
-276    return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs)
-277
+274def eigv(obs, **kwargs):
+275    """Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""
+276    v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs)
+277    return v
 278
-279def svd(obs, **kwargs):
-280    """Computes the singular value decomposition of a matrix of Obs."""
-281    u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs)
-282    s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs)
-283    vh = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[2], obs)
-284    return (u, s, vh)
+279
+280def pinv(obs, **kwargs):
+281    """Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""
+282    return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs)
+283
+284
+285def svd(obs, **kwargs):
+286    """Computes the singular value decomposition of a matrix of Obs."""
+287    u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs)
+288    s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs)
+289    vh = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[2], obs)
+290    return (u, s, vh)
 
    
 
 
@@ -775,6 +784,29 @@ Obs valued.
    + +
    + +
    + + def + eigv(obs, **kwargs): + + + +
    + + 
    275def eigv(obs, **kwargs):
+276    """Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""
+277    v = derived_observable(lambda x, **kwargs: anp.linalg.eigh(x)[1], obs)
+278    return v
+
    + + +

    Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.

    +
    + +
    @@ -787,9 +819,9 @@ Obs valued. - 
    275def pinv(obs, **kwargs):
-276    """Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""
-277    return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs)
+            
    281def pinv(obs, **kwargs):
+282    """Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""
+283    return derived_observable(lambda x, **kwargs: anp.linalg.pinv(x), obs)
 
    
 
 
@@ -809,12 +841,12 @@ Obs valued.
    - 
    280def svd(obs, **kwargs):
-281    """Computes the singular value decomposition of a matrix of Obs."""
-282    u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs)
-283    s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs)
-284    vh = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[2], obs)
-285    return (u, s, vh)
+            
    286def svd(obs, **kwargs):
+287    """Computes the singular value decomposition of a matrix of Obs."""
+288    u = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[0], obs)
+289    s = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[1], obs)
+290    vh = derived_observable(lambda x, **kwargs: anp.linalg.svd(x, full_matrices=False)[2], obs)
+291    return (u, s, vh)
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index 69541536..4b9ba8b8 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
    \n\n
    \n
    python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    (Also works for any feature branch).
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
    \n\n
    For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.
    \n\n
    The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.
    \n\n
    Initialization
    \n\n
    A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs
    \n\n
    \n
    corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
    \n
    \n\n
    A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects
    \n\n
    \n
    matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
    \n
    \n\n
    or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "
    Calculates the per-timeslice trace of a correlator matrix.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • parity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
    \n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
    \n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
    \n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
    \n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
      \n\n
      def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
    Read hadrons hdf5 file and extract entry based on attributes.
    \n\n
    Parameters
    \n\n
      \n
    • filestem (str):\nFull namestem of the files to read, including the full path.
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • group (str):\nlabel of the group to be extracted.
      • \n
    • attrs (dict or int):\nDictionary containing the attributes. For example
      \n\n
      \n
      attrs = {"gamma_snk": "Gamma5",\n        "gamma_src": "Gamma5"}\n
      \n
      \n\n
      Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
    \n\n
    It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
    \n\n
    A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
      • \n
    • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • root (Obs):\nThe root of the data series.
      • \n
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • w0 (Obs):\nExtracted w0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • files (List[str]): A list of files to read data from.
        • \n
      • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
    \n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks_list (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type_list (list[str]):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset_list (list[int]):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf_list (int):\nID of wave function
      • \n
    • wf2_list (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname_list,\tquarks_list=['.*'],\tcorr_type_list=['bi'],\tnoffset_list=[0],\twf_list=[0],\twf2_list=[0],\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\tkeyed_out=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "
    Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nmeasurement path, same as for sfcf read method
      • \n
    • param_hash (str):\nexpected parameter hash
      • \n
    • prefix (str):\ndata prefix to find the appropriate replicum folders in path
      • \n
    • param_prefix (str):\nprefix of the parameter file. Defaults to 'parameters_'
      • \n
    \n\n
    Returns
    \n\n
      \n
    • nums (dict):\ndictionary of faulty parameter files sorted by the replica paths
      • \n
    \n", "signature": "(path, param_hash, prefix, param_prefix='parameters_'):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
    \n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
    Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
    \n\n
    The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\nfunction to integrate, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(p, x):\n   return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
      \n
      \n\n
      where x is the integration variable.
      • \n
    • p (list of floats or Obs):\nparameters of the function func.
      • \n
    • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
      • \n
    • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
      • \n
    • All parameters of scipy.integrate.quad
      • \n
    \n\n
    Returns
    \n\n
      \n
    • y (Obs):\nThe integral of func from a to b.
      • \n
    • abserr (float):\nAn estimate of the absolute error in the result.
      • \n
    • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
      • \n
    • message: A convergence message.
      • \n
    • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
      • \n
    \n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
    \n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
    \n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
    \n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
    Export bootstrap samples from the Obs
    \n\n
    Parameters
    \n\n
      \n
    • samples (int):\nNumber of bootstrap samples to generate.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
      • \n
    • save_rng (str):\nSave the random numbers to a file if a path is specified.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
      • \n
    \n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
    Imports bootstrap samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
      • \n
    \n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
    \n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 8336}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 367}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 40, "bases": 0, "doc": 100}, "pyerrors.correlators.Corr.tag": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.content": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.T": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, 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+    /** 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", "kind": "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 linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
    \n\n
    \n
    python -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    (Also works for any feature branch).
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
    \n\n
    For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.
    \n\n
    The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.
    \n\n
    Initialization
    \n\n
    A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs
    \n\n
    \n
    corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
    \n
    \n\n
    A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects
    \n\n
    \n
    matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
    \n
    \n\n
    or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "
    Calculates the per-timeslice trace of a correlator matrix.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • None: The GEVP is solved only at ts, no sorting is necessary
        • \n
      • \n
    • vector_obs (bool):\nIf True, uncertainties are propagated in the eigenvector computation (default False).
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    • method (str):\nMethod used to solve the GEVP.\n
        \n
      • \"eigh\": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)
        • \n
      • \"cholesky\": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.
        • \n
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', vector_obs=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • parity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
    \n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
    \n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
    \n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
    \n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
      \n\n
      def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "
    Read hadrons hdf5 file and extract entry based on attributes.
    \n\n
    Parameters
    \n\n
      \n
    • filestem (str):\nFull namestem of the files to read, including the full path.
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • group (str):\nlabel of the group to be extracted.
      • \n
    • attrs (dict or int):\nDictionary containing the attributes. For example
      \n\n
      \n
      attrs = {"gamma_snk": "Gamma5",\n        "gamma_src": "Gamma5"}\n
      \n
      \n\n
      Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • part (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(filestem, ens_id, group, attrs=None, idl=None, part='real'):", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
    \n\n
    It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
    \n\n
    A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
      • \n
    • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • root (Obs):\nThe root of the data series.
      • \n
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • w0 (Obs):\nExtracted w0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • files (List[str]): A list of files to read data from.
        • \n
      • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "
    \n", "default_value": "'/'"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks_list (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type_list (list[str]):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset_list (list[int]):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf_list (int):\nID of wave function
      • \n
    • wf2_list (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname_list,\tquarks_list=['.*'],\tcorr_type_list=['bi'],\tnoffset_list=[0],\twf_list=[0],\twf2_list=[0],\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\tkeyed_out=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "
    Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nmeasurement path, same as for sfcf read method
      • \n
    • param_hash (str):\nexpected parameter hash
      • \n
    • prefix (str):\ndata prefix to find the appropriate replicum folders in path
      • \n
    • param_prefix (str):\nprefix of the parameter file. Defaults to 'parameters_'
      • \n
    \n\n
    Returns
    \n\n
      \n
    • nums (dict):\ndictionary of faulty parameter files sorted by the replica paths
      • \n
    \n", "signature": "(path, param_hash, prefix, param_prefix='parameters_'):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
    \n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
    Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
    \n\n
    The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\nfunction to integrate, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(p, x):\n   return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
      \n
      \n\n
      where x is the integration variable.
      • \n
    • p (list of floats or Obs):\nparameters of the function func.
      • \n
    • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
      • \n
    • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
      • \n
    • All parameters of scipy.integrate.quad
      • \n
    \n\n
    Returns
    \n\n
      \n
    • y (Obs):\nThe integral of func from a to b.
      • \n
    • abserr (float):\nAn estimate of the absolute error in the result.
      • \n
    • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
      • \n
    • message: A convergence message.
      • \n
    • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
      • \n
    \n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eigv": {"fullname": "pyerrors.linalg.eigv", "modulename": "pyerrors.linalg", "qualname": "eigv", "kind": "function", "doc": "
    Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.13/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
    \n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
    \n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
    \n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
    Export bootstrap samples from the Obs
    \n\n
    Parameters
    \n\n
      \n
    • samples (int):\nNumber of bootstrap samples to generate.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
      • \n
    • save_rng (str):\nSave the random numbers to a file if a path is specified.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
      • \n
    \n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "
    Vectorized version of the gamma_method applicable to lists or arrays of Obs.
    \n\n
    See docstring of pe.Obs.gamma_method for details.
    \n", "signature": "(x, **kwargs):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
    Imports bootstrap samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
      • \n
    \n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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