diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index a5a75ed2..206809ff 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -254,1391 +254,1413 @@ 11 12 13class Corr: - 14 """The class for a correlator (time dependent sequence of pe.Obs). + 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 GEVP - 22 matrix at every timeslice. Other dependency (eg. spatial) are not supported. + 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 """ - 25 - 26 __slots__ = ["content", "N", "T", "tag", "prange"] - 27 - 28 def __init__(self, data_input, padding=[0, 0], prange=None): - 29 """ Initialize a Corr object. - 30 - 31 Parameters - 32 ---------- - 33 data_input : list or array - 34 list of Obs or list of arrays of Obs or array of Corrs - 35 padding : list, optional - 36 List with two entries where the first labels the padding - 37 at the front of the correlator and the second the padding - 38 at the back. - 39 prange : list, optional - 40 List containing the first and last timeslice of the plateau - 41 region indentified for this correlator. - 42 """ + 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 if isinstance(data_input, np.ndarray): - 45 - 46 # This only works, if the array fulfills the conditions below - 47 if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]: - 48 raise Exception("Incompatible array shape") - 49 if not all([isinstance(item, Corr) for item in data_input.flatten()]): - 50 raise Exception("If the input is an array, its elements must be of type pe.Corr") - 51 if not all([item.N == 1 for item in data_input.flatten()]): - 52 raise Exception("Can only construct matrix correlator from single valued correlators") - 53 if not len(set([item.T for item in data_input.flatten()])) == 1: - 54 raise Exception("All input Correlators must be defined over the same timeslices.") - 55 - 56 T = data_input[0, 0].T - 57 N = data_input.shape[0] - 58 input_as_list = [] - 59 for t in range(T): - 60 if any([(item.content[t] is None) for item in data_input.flatten()]): - 61 if not all([(item.content[t] is None) for item in data_input.flatten()]): - 62 warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning) - 63 input_as_list.append(None) - 64 else: - 65 array_at_timeslace = np.empty([N, N], dtype="object") - 66 for i in range(N): - 67 for j in range(N): - 68 array_at_timeslace[i, j] = data_input[i, j][t] - 69 input_as_list.append(array_at_timeslace) - 70 data_input = input_as_list - 71 - 72 if isinstance(data_input, list): - 73 - 74 if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]): - 75 _assert_equal_properties([o for o in data_input if o is not None]) - 76 self.content = [np.asarray([item]) if item is not None else None for item in data_input] - 77 self.N = 1 - 78 - 79 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]): - 80 self.content = data_input - 81 noNull = [a for a in self.content if not (a is None)] # To check if the matrices are correct for all undefined elements - 82 self.N = noNull[0].shape[0] - 83 if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]: - 84 raise Exception("Smearing matrices are not NxN") - 85 if (not all([item.shape == noNull[0].shape for item in noNull])): - 86 raise Exception("Items in data_input are not of identical shape." + str(noNull)) - 87 else: - 88 raise Exception("data_input contains item of wrong type") - 89 else: - 90 raise Exception("Data input was not given as list or correct array") - 91 - 92 self.tag = None - 93 - 94 # An undefined timeslice is represented by the None object - 95 self.content = [None] * padding[0] + self.content + [None] * padding[1] - 96 self.T = len(self.content) - 97 self.prange = prange - 98 - 99 def __getitem__(self, idx): - 100 """Return the content of timeslice idx""" - 101 if self.content[idx] is None: - 102 return None - 103 elif len(self.content[idx]) == 1: - 104 return self.content[idx][0] - 105 else: - 106 return self.content[idx] - 107 - 108 @property - 109 def reweighted(self): - 110 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]]) - 111 if np.all(bool_array == 1): - 112 return True - 113 elif np.all(bool_array == 0): - 114 return False - 115 else: - 116 raise Exception("Reweighting status of correlator corrupted.") - 117 - 118 def gamma_method(self, **kwargs): - 119 """Apply the gamma method to the content of the Corr.""" - 120 for item in self.content: - 121 if not (item is None): - 122 if self.N == 1: - 123 item[0].gamma_method(**kwargs) - 124 else: - 125 for i in range(self.N): - 126 for j in range(self.N): - 127 item[i, j].gamma_method(**kwargs) - 128 - 129 gm = gamma_method - 130 - 131 def projected(self, vector_l=None, vector_r=None, normalize=False): - 132 """We need to project the Correlator with a Vector to get a single value at each timeslice. - 133 - 134 The method can use one or two vectors. - 135 If two are specified it returns v1@G@v2 (the order might be very important.) - 136 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to - 137 """ - 138 if self.N == 1: - 139 raise Exception("Trying to project a Corr, that already has N=1.") - 140 - 141 if vector_l is None: - 142 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) - 143 elif (vector_r is None): - 144 vector_r = vector_l - 145 if isinstance(vector_l, list) and not isinstance(vector_r, list): - 146 if len(vector_l) != self.T: - 147 raise Exception("Length of vector list must be equal to T") - 148 vector_r = [vector_r] * self.T - 149 if isinstance(vector_r, list) and not isinstance(vector_l, list): - 150 if len(vector_r) != self.T: - 151 raise Exception("Length of vector list must be equal to T") - 152 vector_l = [vector_l] * self.T - 153 - 154 if not isinstance(vector_l, list): - 155 if not vector_l.shape == vector_r.shape == (self.N,): - 156 raise Exception("Vectors are of wrong shape!") - 157 if normalize: - 158 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) - 159 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] - 160 - 161 else: - 162 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. - 163 if normalize: - 164 for t in range(self.T): - 165 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]) - 166 - 167 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)] - 168 return Corr(newcontent) - 169 - 170 def item(self, i, j): - 171 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. - 172 - 173 Parameters - 174 ---------- - 175 i : int - 176 First index to be picked. - 177 j : int - 178 Second index to be picked. - 179 """ - 180 if self.N == 1: - 181 raise Exception("Trying to pick item from projected Corr") - 182 newcontent = [None if (item is None) else item[i, j] for item in self.content] - 183 return Corr(newcontent) - 184 - 185 def plottable(self): - 186 """Outputs the correlator in a plotable format. - 187 - 188 Outputs three lists containing the timeslice index, the value on each - 189 timeslice and the error on each timeslice. - 190 """ - 191 if self.N != 1: - 192 raise Exception("Can only make Corr[N=1] plottable") - 193 x_list = [x for x in range(self.T) if not self.content[x] is None] - 194 y_list = [y[0].value for y in self.content if y is not None] - 195 y_err_list = [y[0].dvalue for y in self.content if y is not None] - 196 - 197 return x_list, y_list, y_err_list - 198 - 199 def symmetric(self): - 200 """ Symmetrize the correlator around x0=0.""" - 201 if self.N != 1: - 202 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') - 203 if self.T % 2 != 0: - 204 raise Exception("Can not symmetrize odd T") - 205 - 206 if self.content[0] is not None: - 207 if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0: - 208 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) + 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 newcontent = [self.content[0]] - 211 for t in range(1, self.T): - 212 if (self.content[t] is None) or (self.content[self.T - t] is None): - 213 newcontent.append(None) - 214 else: - 215 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) - 216 if (all([x is None for x in newcontent])): - 217 raise Exception("Corr could not be symmetrized: No redundant values") - 218 return Corr(newcontent, prange=self.prange) - 219 - 220 def anti_symmetric(self): - 221 """Anti-symmetrize the correlator around x0=0.""" - 222 if self.N != 1: - 223 raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.') - 224 if self.T % 2 != 0: - 225 raise Exception("Can not symmetrize odd T") - 226 - 227 test = 1 * self - 228 test.gamma_method() - 229 if not all([o.is_zero_within_error(3) for o in test.content[0]]): - 230 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) + 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])) + 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 is_matrix_symmetric(self): - 243 """Checks whether a correlator matrices is symmetric on every timeslice.""" - 244 if self.N == 1: - 245 raise TypeError("Only works for correlator matrices.") - 246 for t in range(self.T): - 247 if self[t] is None: - 248 continue - 249 for i in range(self.N): - 250 for j in range(i + 1, self.N): - 251 if self[t][i, j] is self[t][j, i]: - 252 continue - 253 if hash(self[t][i, j]) != hash(self[t][j, i]): - 254 return False - 255 return True - 256 - 257 def trace(self): - 258 """Calculates the per-timeslice trace of a correlator matrix.""" - 259 if self.N == 1: - 260 raise ValueError("Only works for correlator matrices.") - 261 newcontent = [] - 262 for t in range(self.T): - 263 if _check_for_none(self, self.content[t]): - 264 newcontent.append(None) - 265 else: - 266 newcontent.append(np.trace(self.content[t])) - 267 return Corr(newcontent) - 268 - 269 def matrix_symmetric(self): - 270 """Symmetrizes the correlator matrices on every timeslice.""" - 271 if self.N == 1: - 272 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 273 if self.is_matrix_symmetric(): - 274 return 1.0 * self - 275 else: - 276 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 277 return 0.5 * (Corr(transposed) + self) + 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 GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 280 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 281 - 282 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 283 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 284 ```python - 285 C.GEVP(t0=2)[0] # Ground state vector(s) - 286 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 287 ``` - 288 - 289 Parameters - 290 ---------- - 291 t0 : int - 292 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 293 ts : int - 294 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 295 If sort="Eigenvector" it gives a reference point for the sorting method. - 296 sort : string - 297 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. - 298 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 299 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 300 The reference state is identified by its eigenvalue at $t=t_s$. - 301 - 302 Other Parameters - 303 ---------------- - 304 state : int - 305 Returns only the vector(s) for a specified state. The lowest state is zero. - 306 ''' - 307 - 308 if self.N == 1: - 309 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 310 if ts is not None: - 311 if (ts <= t0): - 312 raise Exception("ts has to be larger than t0.") - 313 - 314 if "sorted_list" in kwargs: - 315 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 316 sort = kwargs.get("sorted_list") - 317 - 318 if self.is_matrix_symmetric(): - 319 symmetric_corr = self - 320 else: - 321 symmetric_corr = self.matrix_symmetric() - 322 - 323 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) - 324 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. - 325 - 326 if sort is None: - 327 if (ts is None): - 328 raise Exception("ts is required if sort=None.") - 329 if (self.content[t0] is None) or (self.content[ts] is None): - 330 raise Exception("Corr not defined at t0/ts.") - 331 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) - 332 reordered_vecs = _GEVP_solver(Gt, G0) - 333 - 334 elif sort in ["Eigenvalue", "Eigenvector"]: - 335 if sort == "Eigenvalue" and ts is not None: - 336 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) - 337 all_vecs = [None] * (t0 + 1) - 338 for t in range(t0 + 1, self.T): - 339 try: - 340 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) - 341 all_vecs.append(_GEVP_solver(Gt, G0)) - 342 except Exception: - 343 all_vecs.append(None) - 344 if sort == "Eigenvector": - 345 if ts is None: - 346 raise Exception("ts is required for the Eigenvector sorting method.") - 347 all_vecs = _sort_vectors(all_vecs, ts) - 348 - 349 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 350 else: - 351 raise Exception("Unkown value for 'sort'.") - 352 - 353 if "state" in kwargs: - 354 return reordered_vecs[kwargs.get("state")] - 355 else: - 356 return reordered_vecs - 357 - 358 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 359 """Determines the eigenvalue of the GEVP by solving and projecting the correlator - 360 - 361 Parameters - 362 ---------- - 363 state : int - 364 The state one is interested in ordered by energy. The lowest state is zero. - 365 - 366 All other parameters are identical to the ones of Corr.GEVP. - 367 """ - 368 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 369 return self.projected(vec) + 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. + 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 def Hankel(self, N, periodic=False): - 372 """Constructs an NxN Hankel matrix - 373 - 374 C(t) c(t+1) ... c(t+n-1) - 375 C(t+1) c(t+2) ... c(t+n) - 376 ................. - 377 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) - 378 - 379 Parameters - 380 ---------- - 381 N : int - 382 Dimension of the Hankel matrix - 383 periodic : bool, optional - 384 determines whether the matrix is extended periodically - 385 """ - 386 - 387 if self.N != 1: - 388 raise Exception("Multi-operator Prony not implemented!") - 389 - 390 array = np.empty([N, N], dtype="object") - 391 new_content = [] - 392 for t in range(self.T): - 393 new_content.append(array.copy()) - 394 - 395 def wrap(i): - 396 while i >= self.T: - 397 i -= self.T - 398 return i - 399 - 400 for t in range(self.T): - 401 for i in range(N): - 402 for j in range(N): - 403 if periodic: - 404 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 405 elif (t + i + j) >= self.T: - 406 new_content[t] = None - 407 else: - 408 new_content[t][i, j] = self.content[t + i + j][0] - 409 - 410 return Corr(new_content) + 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 def roll(self, dt): - 413 """Periodically shift the correlator by dt timeslices - 414 - 415 Parameters - 416 ---------- - 417 dt : int - 418 number of timeslices - 419 """ - 420 return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0))) + 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 def reverse(self): - 423 """Reverse the time ordering of the Corr""" - 424 return Corr(self.content[:: -1]) - 425 - 426 def thin(self, spacing=2, offset=0): - 427 """Thin out a correlator to suppress correlations - 428 - 429 Parameters - 430 ---------- - 431 spacing : int - 432 Keep only every 'spacing'th entry of the correlator - 433 offset : int - 434 Offset the equal spacing - 435 """ - 436 new_content = [] - 437 for t in range(self.T): - 438 if (offset + t) % spacing != 0: - 439 new_content.append(None) - 440 else: - 441 new_content.append(self.content[t]) - 442 return Corr(new_content) + 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 + 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 correlate(self, partner): - 445 """Correlate the correlator with another correlator or Obs - 446 - 447 Parameters - 448 ---------- - 449 partner : Obs or Corr - 450 partner to correlate the correlator with. - 451 Can either be an Obs which is correlated with all entries of the - 452 correlator or a Corr of same length. - 453 """ - 454 if self.N != 1: - 455 raise Exception("Only one-dimensional correlators can be safely correlated.") - 456 new_content = [] - 457 for x0, t_slice in enumerate(self.content): - 458 if _check_for_none(self, t_slice): - 459 new_content.append(None) - 460 else: - 461 if isinstance(partner, Corr): - 462 if _check_for_none(partner, partner.content[x0]): - 463 new_content.append(None) - 464 else: - 465 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 466 elif isinstance(partner, Obs): # Should this include CObs? - 467 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 468 else: - 469 raise Exception("Can only correlate with an Obs or a Corr.") - 470 - 471 return Corr(new_content) - 472 - 473 def reweight(self, weight, **kwargs): - 474 """Reweight the correlator. - 475 - 476 Parameters - 477 ---------- - 478 weight : Obs - 479 Reweighting factor. An Observable that has to be defined on a superset of the - 480 configurations in obs[i].idl for all i. - 481 all_configs : bool - 482 if True, the reweighted observables are normalized by the average of - 483 the reweighting factor on all configurations in weight.idl and not - 484 on the configurations in obs[i].idl. - 485 """ - 486 if self.N != 1: - 487 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 488 new_content = [] - 489 for t_slice in self.content: - 490 if _check_for_none(self, t_slice): - 491 new_content.append(None) - 492 else: - 493 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 494 return Corr(new_content) - 495 - 496 def T_symmetry(self, partner, parity=+1): - 497 """Return the time symmetry average of the correlator and its partner - 498 - 499 Parameters - 500 ---------- - 501 partner : Corr - 502 Time symmetry partner of the Corr - 503 partity : int - 504 Parity quantum number of the correlator, can be +1 or -1 - 505 """ - 506 if self.N != 1: - 507 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 508 if not isinstance(partner, Corr): - 509 raise Exception("T partner has to be a Corr object.") - 510 if parity not in [+1, -1]: - 511 raise Exception("Parity has to be +1 or -1.") - 512 T_partner = parity * partner.reverse() - 513 - 514 t_slices = [] - 515 test = (self - T_partner) - 516 test.gamma_method() - 517 for x0, t_slice in enumerate(test.content): - 518 if t_slice is not None: - 519 if not t_slice[0].is_zero_within_error(5): - 520 t_slices.append(x0) - 521 if t_slices: - 522 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) - 523 - 524 return (self + T_partner) / 2 - 525 - 526 def deriv(self, variant="symmetric"): - 527 """Return the first derivative of the correlator with respect to x0. - 528 - 529 Parameters - 530 ---------- - 531 variant : str - 532 decides which definition of the finite differences derivative is used. - 533 Available choice: symmetric, forward, backward, improved, log, default: symmetric - 534 """ - 535 if self.N != 1: - 536 raise Exception("deriv only implemented for one-dimensional correlators.") - 537 if variant == "symmetric": - 538 newcontent = [] - 539 for t in range(1, self.T - 1): - 540 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 541 newcontent.append(None) - 542 else: - 543 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 544 if (all([x is None for x in newcontent])): - 545 raise Exception('Derivative is undefined at all timeslices') - 546 return Corr(newcontent, padding=[1, 1]) - 547 elif variant == "forward": - 548 newcontent = [] - 549 for t in range(self.T - 1): - 550 if (self.content[t] is None) or (self.content[t + 1] is None): - 551 newcontent.append(None) - 552 else: - 553 newcontent.append(self.content[t + 1] - self.content[t]) - 554 if (all([x is None for x in newcontent])): - 555 raise Exception("Derivative is undefined at all timeslices") - 556 return Corr(newcontent, padding=[0, 1]) - 557 elif variant == "backward": - 558 newcontent = [] - 559 for t in range(1, self.T): - 560 if (self.content[t - 1] is None) or (self.content[t] is None): - 561 newcontent.append(None) - 562 else: - 563 newcontent.append(self.content[t] - self.content[t - 1]) - 564 if (all([x is None for x in newcontent])): - 565 raise Exception("Derivative is undefined at all timeslices") - 566 return Corr(newcontent, padding=[1, 0]) - 567 elif variant == "improved": - 568 newcontent = [] - 569 for t in range(2, self.T - 2): - 570 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): - 571 newcontent.append(None) - 572 else: - 573 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 574 if (all([x is None for x in newcontent])): - 575 raise Exception('Derivative is undefined at all timeslices') - 576 return Corr(newcontent, padding=[2, 2]) - 577 elif variant == 'log': - 578 newcontent = [] - 579 for t in range(self.T): - 580 if (self.content[t] is None) or (self.content[t] <= 0): - 581 newcontent.append(None) - 582 else: - 583 newcontent.append(np.log(self.content[t])) - 584 if (all([x is None for x in newcontent])): - 585 raise Exception("Log is undefined at all timeslices") - 586 logcorr = Corr(newcontent) - 587 return self * logcorr.deriv('symmetric') - 588 else: - 589 raise Exception("Unknown variant.") - 590 - 591 def second_deriv(self, variant="symmetric"): - 592 r"""Return the second derivative of the correlator with respect to x0. - 593 - 594 Parameters - 595 ---------- - 596 variant : str - 597 decides which definition of the finite differences derivative is used. - 598 Available choice: - 599 - symmetric (default) - 600 $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$ - 601 - big_symmetric - 602 $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$ - 603 - improved - 604 $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$ - 605 - log - 606 $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$ - 607 """ - 608 if self.N != 1: - 609 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 610 if variant == "symmetric": - 611 newcontent = [] - 612 for t in range(1, self.T - 1): - 613 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 614 newcontent.append(None) - 615 else: - 616 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 617 if (all([x is None for x in newcontent])): - 618 raise Exception("Derivative is undefined at all timeslices") - 619 return Corr(newcontent, padding=[1, 1]) - 620 elif variant == "big_symmetric": - 621 newcontent = [] - 622 for t in range(2, self.T - 2): - 623 if (self.content[t - 2] is None) or (self.content[t + 2] is None): - 624 newcontent.append(None) - 625 else: - 626 newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4) - 627 if (all([x is None for x in newcontent])): - 628 raise Exception("Derivative is undefined at all timeslices") - 629 return Corr(newcontent, padding=[2, 2]) - 630 elif variant == "improved": - 631 newcontent = [] - 632 for t in range(2, self.T - 2): - 633 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): - 634 newcontent.append(None) - 635 else: - 636 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])) - 637 if (all([x is None for x in newcontent])): - 638 raise Exception("Derivative is undefined at all timeslices") - 639 return Corr(newcontent, padding=[2, 2]) - 640 elif variant == 'log': - 641 newcontent = [] - 642 for t in range(self.T): - 643 if (self.content[t] is None) or (self.content[t] <= 0): - 644 newcontent.append(None) - 645 else: - 646 newcontent.append(np.log(self.content[t])) - 647 if (all([x is None for x in newcontent])): - 648 raise Exception("Log is undefined at all timeslices") - 649 logcorr = Corr(newcontent) - 650 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) - 651 else: - 652 raise Exception("Unknown variant.") - 653 - 654 def m_eff(self, variant='log', guess=1.0): - 655 """Returns the effective mass of the correlator as correlator object - 656 - 657 Parameters - 658 ---------- - 659 variant : str - 660 log : uses the standard effective mass log(C(t) / C(t+1)) - 661 cosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. - 662 sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m. - 663 See, e.g., arXiv:1205.5380 - 664 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 665 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 - 666 guess : float - 667 guess for the root finder, only relevant for the root variant - 668 """ - 669 if self.N != 1: - 670 raise Exception('Correlator must be projected before getting m_eff') - 671 if variant == 'log': - 672 newcontent = [] - 673 for t in range(self.T - 1): - 674 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 675 newcontent.append(None) - 676 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 677 newcontent.append(None) - 678 else: - 679 newcontent.append(self.content[t] / self.content[t + 1]) - 680 if (all([x is None for x in newcontent])): - 681 raise Exception('m_eff is undefined at all timeslices') - 682 - 683 return np.log(Corr(newcontent, padding=[0, 1])) - 684 - 685 elif variant == 'logsym': - 686 newcontent = [] - 687 for t in range(1, self.T - 1): - 688 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 689 newcontent.append(None) - 690 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: - 691 newcontent.append(None) - 692 else: - 693 newcontent.append(self.content[t - 1] / self.content[t + 1]) - 694 if (all([x is None for x in newcontent])): - 695 raise Exception('m_eff is undefined at all timeslices') - 696 - 697 return np.log(Corr(newcontent, padding=[1, 1])) / 2 - 698 - 699 elif variant in ['periodic', 'cosh', 'sinh']: - 700 if variant in ['periodic', 'cosh']: - 701 func = anp.cosh - 702 else: - 703 func = anp.sinh + 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 + 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) + 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 def root_function(x, d): - 706 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 707 + 705 return np.log(Corr(newcontent, padding=[0, 1])) + 706 + 707 elif variant == 'logsym': 708 newcontent = [] - 709 for t in range(self.T - 1): - 710 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 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 # Fill the two timeslices in the middle of the lattice with their predecessors - 713 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 714 newcontent.append(newcontent[-1]) - 715 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 716 newcontent.append(None) - 717 else: - 718 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 719 if (all([x is None for x in newcontent])): - 720 raise Exception('m_eff is undefined at all timeslices') - 721 - 722 return Corr(newcontent, padding=[0, 1]) - 723 - 724 elif variant == 'arccosh': - 725 newcontent = [] - 726 for t in range(1, self.T - 1): - 727 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): - 728 newcontent.append(None) - 729 else: - 730 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) - 731 if (all([x is None for x in newcontent])): - 732 raise Exception("m_eff is undefined at all timeslices") - 733 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 734 - 735 else: - 736 raise Exception('Unknown variant.') - 737 - 738 def fit(self, function, fitrange=None, silent=False, **kwargs): - 739 r'''Fits function to the data - 740 - 741 Parameters - 742 ---------- - 743 function : obj - 744 function to fit to the data. See fits.least_squares for details. - 745 fitrange : list - 746 Two element list containing the timeslices on which the fit is supposed to start and stop. - 747 Caution: This range is inclusive as opposed to standard python indexing. - 748 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 749 If not specified, self.prange or all timeslices are used. - 750 silent : bool - 751 Decides whether output is printed to the standard output. - 752 ''' - 753 if self.N != 1: - 754 raise Exception("Correlator must be projected before fitting") - 755 - 756 if fitrange is None: - 757 if self.prange: - 758 fitrange = self.prange - 759 else: - 760 fitrange = [0, self.T - 1] - 761 else: - 762 if not isinstance(fitrange, list): - 763 raise Exception("fitrange has to be a list with two elements") - 764 if len(fitrange) != 2: - 765 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 766 - 767 xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 768 ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 769 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 770 return result - 771 - 772 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 773 """ Extract a plateau value from a Corr object - 774 - 775 Parameters - 776 ---------- - 777 plateau_range : list - 778 list with two entries, indicating the first and the last timeslice - 779 of the plateau region. - 780 method : str - 781 method to extract the plateau. - 782 'fit' fits a constant to the plateau region - 783 'avg', 'average' or 'mean' just average over the given timeslices. - 784 auto_gamma : bool - 785 apply gamma_method with default parameters to the Corr. Defaults to None - 786 """ - 787 if not plateau_range: - 788 if self.prange: - 789 plateau_range = self.prange - 790 else: - 791 raise Exception("no plateau range provided") - 792 if self.N != 1: - 793 raise Exception("Correlator must be projected before getting a plateau.") - 794 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 795 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 796 if auto_gamma: - 797 self.gamma_method() - 798 if method == "fit": - 799 def const_func(a, t): - 800 return a[0] - 801 return self.fit(const_func, plateau_range)[0] - 802 elif method in ["avg", "average", "mean"]: - 803 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 804 return returnvalue - 805 - 806 else: - 807 raise Exception("Unsupported plateau method: " + method) - 808 - 809 def set_prange(self, prange): - 810 """Sets the attribute prange of the Corr object.""" - 811 if not len(prange) == 2: - 812 raise Exception("prange must be a list or array with two values") - 813 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 814 raise Exception("Start and end point must be integers") - 815 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 816 raise Exception("Start and end point must define a range in the interval 0,T") - 817 - 818 self.prange = prange - 819 return - 820 - 821 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): - 822 """Plots the correlator using the tag of the correlator as label if available. - 823 - 824 Parameters - 825 ---------- - 826 x_range : list - 827 list of two values, determining the range of the x-axis e.g. [4, 8]. - 828 comp : Corr or list of Corr - 829 Correlator or list of correlators which are plotted for comparison. - 830 The tags of these correlators are used as labels if available. - 831 logscale : bool - 832 Sets y-axis to logscale. - 833 plateau : Obs - 834 Plateau value to be visualized in the figure. - 835 fit_res : Fit_result - 836 Fit_result object to be visualized. - 837 fit_key : str - 838 Key for the fit function in Fit_result.fit_function (for combined fits). - 839 ylabel : str - 840 Label for the y-axis. - 841 save : str - 842 path to file in which the figure should be saved. - 843 auto_gamma : bool - 844 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 845 hide_sigma : float - 846 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 847 references : list - 848 List of floating point values that are displayed as horizontal lines for reference. - 849 title : string - 850 Optional title of the figure. - 851 """ - 852 if self.N != 1: - 853 raise Exception("Correlator must be projected before plotting") - 854 - 855 if auto_gamma: - 856 self.gamma_method() - 857 - 858 if x_range is None: - 859 x_range = [0, self.T - 1] - 860 - 861 fig = plt.figure() - 862 ax1 = fig.add_subplot(111) - 863 - 864 x, y, y_err = self.plottable() - 865 if hide_sigma: - 866 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 867 else: - 868 hide_from = None - 869 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 870 if logscale: - 871 ax1.set_yscale('log') - 872 else: - 873 if y_range is None: - 874 try: - 875 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)]) - 876 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)]) - 877 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 878 except Exception: - 879 pass - 880 else: - 881 ax1.set_ylim(y_range) - 882 if comp: - 883 if isinstance(comp, (Corr, list)): - 884 for corr in comp if isinstance(comp, list) else [comp]: - 885 if auto_gamma: - 886 corr.gamma_method() - 887 x, y, y_err = corr.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=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 893 else: - 894 raise Exception("'comp' must be a correlator or a list of correlators.") - 895 - 896 if plateau: - 897 if isinstance(plateau, Obs): - 898 if auto_gamma: - 899 plateau.gamma_method() - 900 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 901 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 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 raise Exception("'plateau' must be an Obs") - 904 - 905 if references: - 906 if isinstance(references, list): - 907 for ref in references: - 908 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 909 else: - 910 raise Exception("'references' must be a list of floating pint values.") - 911 - 912 if self.prange: - 913 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0) - 914 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0) - 915 - 916 if fit_res: - 917 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 918 if isinstance(fit_res.fit_function, dict): - 919 if fit_key: - 920 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) - 921 else: - 922 raise ValueError("Please provide a 'fit_key' for visualizing combined fits.") - 923 else: - 924 ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) - 925 - 926 ax1.set_xlabel(r'$x_0 / a$') - 927 if ylabel: - 928 ax1.set_ylabel(ylabel) - 929 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 930 - 931 handles, labels = ax1.get_legend_handles_labels() - 932 if labels: - 933 ax1.legend() - 934 - 935 if title: - 936 plt.title(title) + 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 plt.draw() - 939 - 940 if save: - 941 if isinstance(save, str): - 942 fig.savefig(save, bbox_inches='tight') - 943 else: - 944 raise Exception("'save' has to be a string.") - 945 - 946 def spaghetti_plot(self, logscale=True): - 947 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 948 - 949 Parameters - 950 ---------- - 951 logscale : bool - 952 Determines whether the scale of the y-axis is logarithmic or standard. - 953 """ - 954 if self.N != 1: - 955 raise Exception("Correlator needs to be projected first.") + 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 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])) - 958 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 957 if title: + 958 plt.title(title) 959 - 960 for name in mc_names: - 961 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T - 962 - 963 fig = plt.figure() - 964 ax = fig.add_subplot(111) - 965 for dat in data: - 966 ax.plot(x0_vals, dat, ls='-', marker='') + 960 plt.draw() + 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 if logscale is True: - 969 ax.set_yscale('log') + 968 def spaghetti_plot(self, logscale=True): + 969 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. 970 - 971 ax.set_xlabel(r'$x_0 / a$') - 972 plt.title(name) - 973 plt.draw() - 974 - 975 def dump(self, filename, datatype="json.gz", **kwargs): - 976 """Dumps the Corr into a file of chosen type - 977 Parameters - 978 ---------- - 979 filename : str - 980 Name of the file to be saved. - 981 datatype : str - 982 Format of the exported file. Supported formats include - 983 "json.gz" and "pickle" - 984 path : str - 985 specifies a custom path for the file (default '.') - 986 """ - 987 if datatype == "json.gz": - 988 from .input.json import dump_to_json - 989 if 'path' in kwargs: - 990 file_name = kwargs.get('path') + '/' + filename - 991 else: - 992 file_name = filename - 993 dump_to_json(self, file_name) - 994 elif datatype == "pickle": - 995 dump_object(self, filename, **kwargs) - 996 else: - 997 raise Exception("Unknown datatype " + str(datatype)) - 998 - 999 def print(self, print_range=None): -1000 print(self.__repr__(print_range)) -1001 -1002 def __repr__(self, print_range=None): -1003 if print_range is None: -1004 print_range = [0, None] -1005 -1006 content_string = "" -1007 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 -1008 -1009 if self.tag is not None: -1010 content_string += "Description: " + self.tag + "\n" -1011 if self.N != 1: -1012 return content_string -1013 -1014 if print_range[1]: -1015 print_range[1] += 1 -1016 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' -1017 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): -1018 if sub_corr is None: -1019 content_string += str(i + print_range[0]) + '\n' -1020 else: -1021 content_string += str(i + print_range[0]) -1022 for element in sub_corr: -1023 content_string += f"\t{element:+2}" -1024 content_string += '\n' -1025 return content_string -1026 -1027 def __str__(self): -1028 return self.__repr__() -1029 -1030 # We define the basic operations, that can be performed with correlators. -1031 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. -1032 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. -1033 # One could try and tell Obs to check if the y in __mul__ is a Corr and -1034 -1035 __array_priority__ = 10000 -1036 -1037 def __add__(self, y): -1038 if isinstance(y, Corr): -1039 if ((self.N != y.N) or (self.T != y.T)): -1040 raise Exception("Addition of Corrs with different shape") -1041 newcontent = [] -1042 for t in range(self.T): -1043 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1044 newcontent.append(None) -1045 else: -1046 newcontent.append(self.content[t] + y.content[t]) -1047 return Corr(newcontent) + 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 + 984 + 985 fig = plt.figure() + 986 ax = fig.add_subplot(111) + 987 for dat in data: + 988 ax.plot(x0_vals, dat, ls='-', marker='') + 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 + 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)) +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 1048 -1049 elif isinstance(y, (Obs, int, float, CObs)): -1050 newcontent = [] -1051 for t in range(self.T): -1052 if _check_for_none(self, self.content[t]): -1053 newcontent.append(None) -1054 else: -1055 newcontent.append(self.content[t] + y) -1056 return Corr(newcontent, prange=self.prange) -1057 elif isinstance(y, np.ndarray): -1058 if y.shape == (self.T,): -1059 return Corr(list((np.array(self.content).T + y).T)) -1060 else: -1061 raise ValueError("operands could not be broadcast together") -1062 else: -1063 raise TypeError("Corr + wrong type") -1064 -1065 def __mul__(self, y): -1066 if isinstance(y, Corr): -1067 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1068 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1069 newcontent = [] -1070 for t in range(self.T): -1071 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1072 newcontent.append(None) -1073 else: -1074 newcontent.append(self.content[t] * y.content[t]) -1075 return Corr(newcontent) -1076 -1077 elif isinstance(y, (Obs, int, float, CObs)): -1078 newcontent = [] -1079 for t in range(self.T): -1080 if _check_for_none(self, self.content[t]): -1081 newcontent.append(None) -1082 else: -1083 newcontent.append(self.content[t] * y) -1084 return Corr(newcontent, prange=self.prange) -1085 elif isinstance(y, np.ndarray): -1086 if y.shape == (self.T,): -1087 return Corr(list((np.array(self.content).T * y).T)) -1088 else: -1089 raise ValueError("operands could not be broadcast together") -1090 else: -1091 raise TypeError("Corr * wrong type") -1092 -1093 def __matmul__(self, y): -1094 if isinstance(y, np.ndarray): -1095 if y.ndim != 2 or y.shape[0] != y.shape[1]: -1096 raise ValueError("Can only multiply correlators by square matrices.") -1097 if not self.N == y.shape[0]: -1098 raise ValueError("matmul: mismatch of matrix dimensions") -1099 newcontent = [] -1100 for t in range(self.T): -1101 if _check_for_none(self, self.content[t]): -1102 newcontent.append(None) -1103 else: -1104 newcontent.append(self.content[t] @ y) -1105 return Corr(newcontent) -1106 elif isinstance(y, Corr): -1107 if not self.N == y.N: -1108 raise ValueError("matmul: mismatch of matrix dimensions") -1109 newcontent = [] -1110 for t in range(self.T): -1111 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1112 newcontent.append(None) -1113 else: -1114 newcontent.append(self.content[t] @ y.content[t]) -1115 return Corr(newcontent) -1116 -1117 else: -1118 return NotImplemented -1119 -1120 def __rmatmul__(self, y): -1121 if isinstance(y, np.ndarray): -1122 if y.ndim != 2 or y.shape[0] != y.shape[1]: -1123 raise ValueError("Can only multiply correlators by square matrices.") -1124 if not self.N == y.shape[0]: -1125 raise ValueError("matmul: mismatch of matrix dimensions") -1126 newcontent = [] -1127 for t in range(self.T): -1128 if _check_for_none(self, self.content[t]): -1129 newcontent.append(None) -1130 else: -1131 newcontent.append(y @ self.content[t]) -1132 return Corr(newcontent) -1133 else: -1134 return NotImplemented -1135 -1136 def __truediv__(self, y): -1137 if isinstance(y, Corr): -1138 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1139 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1140 newcontent = [] -1141 for t in range(self.T): -1142 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1143 newcontent.append(None) -1144 else: -1145 newcontent.append(self.content[t] / y.content[t]) -1146 for t in range(self.T): -1147 if _check_for_none(self, newcontent[t]): -1148 continue -1149 if np.isnan(np.sum(newcontent[t]).value): -1150 newcontent[t] = None -1151 -1152 if all([item is None for item in newcontent]): -1153 raise Exception("Division returns completely undefined correlator") +1049 def __str__(self): +1050 return self.__repr__() +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 +1058 +1059 def __add__(self, y): +1060 if isinstance(y, Corr): +1061 if ((self.N != y.N) or (self.T != y.T)): +1062 raise Exception("Addition of Corrs with different shape") +1063 newcontent = [] +1064 for t in range(self.T): +1065 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1066 newcontent.append(None) +1067 else: +1068 newcontent.append(self.content[t] + y.content[t]) +1069 return Corr(newcontent) +1070 +1071 elif isinstance(y, (Obs, int, float, CObs)): +1072 newcontent = [] +1073 for t in range(self.T): +1074 if _check_for_none(self, self.content[t]): +1075 newcontent.append(None) +1076 else: +1077 newcontent.append(self.content[t] + y) +1078 return Corr(newcontent, prange=self.prange) +1079 elif isinstance(y, np.ndarray): +1080 if y.shape == (self.T,): +1081 return Corr(list((np.array(self.content).T + y).T)) +1082 else: +1083 raise ValueError("operands could not be broadcast together") +1084 else: +1085 raise TypeError("Corr + wrong type") +1086 +1087 def __mul__(self, y): +1088 if isinstance(y, Corr): +1089 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1090 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1091 newcontent = [] +1092 for t in range(self.T): +1093 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1094 newcontent.append(None) +1095 else: +1096 newcontent.append(self.content[t] * y.content[t]) +1097 return Corr(newcontent) +1098 +1099 elif isinstance(y, (Obs, int, float, CObs)): +1100 newcontent = [] +1101 for t in range(self.T): +1102 if _check_for_none(self, self.content[t]): +1103 newcontent.append(None) +1104 else: +1105 newcontent.append(self.content[t] * y) +1106 return Corr(newcontent, prange=self.prange) +1107 elif isinstance(y, np.ndarray): +1108 if y.shape == (self.T,): +1109 return Corr(list((np.array(self.content).T * y).T)) +1110 else: +1111 raise ValueError("operands could not be broadcast together") +1112 else: +1113 raise TypeError("Corr * wrong type") +1114 +1115 def __matmul__(self, y): +1116 if isinstance(y, np.ndarray): +1117 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1118 raise ValueError("Can only multiply correlators by square matrices.") +1119 if not self.N == y.shape[0]: +1120 raise ValueError("matmul: mismatch of matrix dimensions") +1121 newcontent = [] +1122 for t in range(self.T): +1123 if _check_for_none(self, self.content[t]): +1124 newcontent.append(None) +1125 else: +1126 newcontent.append(self.content[t] @ y) +1127 return Corr(newcontent) +1128 elif isinstance(y, Corr): +1129 if not self.N == y.N: +1130 raise ValueError("matmul: mismatch of matrix dimensions") +1131 newcontent = [] +1132 for t in range(self.T): +1133 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1134 newcontent.append(None) +1135 else: +1136 newcontent.append(self.content[t] @ y.content[t]) +1137 return Corr(newcontent) +1138 +1139 else: +1140 return NotImplemented +1141 +1142 def __rmatmul__(self, y): +1143 if isinstance(y, np.ndarray): +1144 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1145 raise ValueError("Can only multiply correlators by square matrices.") +1146 if not self.N == y.shape[0]: +1147 raise ValueError("matmul: mismatch of matrix dimensions") +1148 newcontent = [] +1149 for t in range(self.T): +1150 if _check_for_none(self, self.content[t]): +1151 newcontent.append(None) +1152 else: +1153 newcontent.append(y @ self.content[t]) 1154 return Corr(newcontent) -1155 -1156 elif isinstance(y, (Obs, CObs)): -1157 if isinstance(y, Obs): -1158 if y.value == 0: -1159 raise Exception('Division by zero will return undefined correlator') -1160 if isinstance(y, CObs): -1161 if y.is_zero(): -1162 raise Exception('Division by zero will return undefined correlator') -1163 -1164 newcontent = [] -1165 for t in range(self.T): -1166 if _check_for_none(self, self.content[t]): -1167 newcontent.append(None) -1168 else: -1169 newcontent.append(self.content[t] / y) -1170 return Corr(newcontent, prange=self.prange) -1171 -1172 elif isinstance(y, (int, float)): -1173 if y == 0: -1174 raise Exception('Division by zero will return undefined correlator') -1175 newcontent = [] -1176 for t in range(self.T): -1177 if _check_for_none(self, self.content[t]): -1178 newcontent.append(None) -1179 else: -1180 newcontent.append(self.content[t] / y) -1181 return Corr(newcontent, prange=self.prange) -1182 elif isinstance(y, np.ndarray): -1183 if y.shape == (self.T,): -1184 return Corr(list((np.array(self.content).T / y).T)) -1185 else: -1186 raise ValueError("operands could not be broadcast together") -1187 else: -1188 raise TypeError('Corr / wrong type') -1189 -1190 def __neg__(self): -1191 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1192 return Corr(newcontent, prange=self.prange) +1155 else: +1156 return NotImplemented +1157 +1158 def __truediv__(self, y): +1159 if isinstance(y, Corr): +1160 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1161 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1162 newcontent = [] +1163 for t in range(self.T): +1164 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1165 newcontent.append(None) +1166 else: +1167 newcontent.append(self.content[t] / y.content[t]) +1168 for t in range(self.T): +1169 if _check_for_none(self, newcontent[t]): +1170 continue +1171 if np.isnan(np.sum(newcontent[t]).value): +1172 newcontent[t] = None +1173 +1174 if all([item is None for item in newcontent]): +1175 raise Exception("Division returns completely undefined correlator") +1176 return Corr(newcontent) +1177 +1178 elif isinstance(y, (Obs, CObs)): +1179 if isinstance(y, Obs): +1180 if y.value == 0: +1181 raise Exception('Division by zero will return undefined correlator') +1182 if isinstance(y, CObs): +1183 if y.is_zero(): +1184 raise Exception('Division by zero will return undefined correlator') +1185 +1186 newcontent = [] +1187 for t in range(self.T): +1188 if _check_for_none(self, self.content[t]): +1189 newcontent.append(None) +1190 else: +1191 newcontent.append(self.content[t] / y) +1192 return Corr(newcontent, prange=self.prange) 1193 -1194 def __sub__(self, y): -1195 return self + (-y) -1196 -1197 def __pow__(self, y): -1198 if isinstance(y, (Obs, int, float, CObs)): -1199 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1200 return Corr(newcontent, prange=self.prange) -1201 else: -1202 raise TypeError('Type of exponent not supported') -1203 -1204 def __abs__(self): -1205 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1206 return Corr(newcontent, prange=self.prange) -1207 -1208 # The numpy functions: -1209 def sqrt(self): -1210 return self ** 0.5 +1194 elif isinstance(y, (int, float)): +1195 if y == 0: +1196 raise Exception('Division by zero will return undefined correlator') +1197 newcontent = [] +1198 for t in range(self.T): +1199 if _check_for_none(self, self.content[t]): +1200 newcontent.append(None) +1201 else: +1202 newcontent.append(self.content[t] / y) +1203 return Corr(newcontent, prange=self.prange) +1204 elif isinstance(y, np.ndarray): +1205 if y.shape == (self.T,): +1206 return Corr(list((np.array(self.content).T / y).T)) +1207 else: +1208 raise ValueError("operands could not be broadcast together") +1209 else: +1210 raise TypeError('Corr / wrong type') 1211 -1212 def log(self): -1213 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1212 def __neg__(self): +1213 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] 1214 return Corr(newcontent, prange=self.prange) 1215 -1216 def exp(self): -1217 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1218 return Corr(newcontent, prange=self.prange) -1219 -1220 def _apply_func_to_corr(self, func): -1221 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1222 for t in range(self.T): -1223 if _check_for_none(self, newcontent[t]): -1224 continue -1225 tmp_sum = np.sum(newcontent[t]) -1226 if hasattr(tmp_sum, "value"): -1227 if np.isnan(tmp_sum.value): -1228 newcontent[t] = None -1229 if all([item is None for item in newcontent]): -1230 raise Exception('Operation returns undefined correlator') -1231 return Corr(newcontent) -1232 -1233 def sin(self): -1234 return self._apply_func_to_corr(np.sin) -1235 -1236 def cos(self): -1237 return self._apply_func_to_corr(np.cos) -1238 -1239 def tan(self): -1240 return self._apply_func_to_corr(np.tan) +1216 def __sub__(self, y): +1217 return self + (-y) +1218 +1219 def __pow__(self, y): +1220 if isinstance(y, (Obs, int, float, CObs)): +1221 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1222 return Corr(newcontent, prange=self.prange) +1223 else: +1224 raise TypeError('Type of exponent not supported') +1225 +1226 def __abs__(self): +1227 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1228 return Corr(newcontent, prange=self.prange) +1229 +1230 # The numpy functions: +1231 def sqrt(self): +1232 return self ** 0.5 +1233 +1234 def log(self): +1235 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1236 return Corr(newcontent, prange=self.prange) +1237 +1238 def exp(self): +1239 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1240 return Corr(newcontent, prange=self.prange) 1241 -1242 def sinh(self): -1243 return self._apply_func_to_corr(np.sinh) -1244 -1245 def cosh(self): -1246 return self._apply_func_to_corr(np.cosh) -1247 -1248 def tanh(self): -1249 return self._apply_func_to_corr(np.tanh) -1250 -1251 def arcsin(self): -1252 return self._apply_func_to_corr(np.arcsin) -1253 -1254 def arccos(self): -1255 return self._apply_func_to_corr(np.arccos) -1256 -1257 def arctan(self): -1258 return self._apply_func_to_corr(np.arctan) -1259 -1260 def arcsinh(self): -1261 return self._apply_func_to_corr(np.arcsinh) -1262 -1263 def arccosh(self): -1264 return self._apply_func_to_corr(np.arccosh) -1265 -1266 def arctanh(self): -1267 return self._apply_func_to_corr(np.arctanh) -1268 -1269 # Right hand side operations (require tweak in main module to work) -1270 def __radd__(self, y): -1271 return self + y +1242 def _apply_func_to_corr(self, func): +1243 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1244 for t in range(self.T): +1245 if _check_for_none(self, newcontent[t]): +1246 continue +1247 tmp_sum = np.sum(newcontent[t]) +1248 if hasattr(tmp_sum, "value"): +1249 if np.isnan(tmp_sum.value): +1250 newcontent[t] = None +1251 if all([item is None for item in newcontent]): +1252 raise Exception('Operation returns undefined correlator') +1253 return Corr(newcontent) +1254 +1255 def sin(self): +1256 return self._apply_func_to_corr(np.sin) +1257 +1258 def cos(self): +1259 return self._apply_func_to_corr(np.cos) +1260 +1261 def tan(self): +1262 return self._apply_func_to_corr(np.tan) +1263 +1264 def sinh(self): +1265 return self._apply_func_to_corr(np.sinh) +1266 +1267 def cosh(self): +1268 return self._apply_func_to_corr(np.cosh) +1269 +1270 def tanh(self): +1271 return self._apply_func_to_corr(np.tanh) 1272 -1273 def __rsub__(self, y): -1274 return -self + y +1273 def arcsin(self): +1274 return self._apply_func_to_corr(np.arcsin) 1275 -1276 def __rmul__(self, y): -1277 return self * y +1276 def arccos(self): +1277 return self._apply_func_to_corr(np.arccos) 1278 -1279 def __rtruediv__(self, y): -1280 return (self / y) ** (-1) +1279 def arctan(self): +1280 return self._apply_func_to_corr(np.arctan) 1281 -1282 @property -1283 def real(self): -1284 def return_real(obs_OR_cobs): -1285 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1286 return np.vectorize(lambda x: x.real)(obs_OR_cobs) -1287 else: -1288 return obs_OR_cobs -1289 -1290 return self._apply_func_to_corr(return_real) -1291 -1292 @property -1293 def imag(self): -1294 def return_imag(obs_OR_cobs): -1295 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1296 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) -1297 else: -1298 return obs_OR_cobs * 0 # So it stays the right type -1299 -1300 return self._apply_func_to_corr(return_imag) -1301 -1302 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1303 r''' Project large correlation matrix to lowest states -1304 -1305 This method can be used to reduce the size of an (N x N) correlation matrix -1306 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1307 is still small. -1308 -1309 Parameters -1310 ---------- -1311 Ntrunc: int -1312 Rank of the target matrix. -1313 tproj: int -1314 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1315 The default value is 3. -1316 t0proj: int -1317 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1318 discouraged for O(a) improved theories, since the correctness of the procedure -1319 cannot be granted in this case. The default value is 2. -1320 basematrix : Corr -1321 Correlation matrix that is used to determine the eigenvectors of the -1322 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1323 is is not specified. -1324 -1325 Notes -1326 ----- -1327 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1328 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1329 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1330 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1331 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1332 correlation matrix and to remove some noise that is added by irrelevant operators. -1333 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1334 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1335 ''' -1336 -1337 if self.N == 1: -1338 raise Exception('Method cannot be applied to one-dimensional correlators.') -1339 if basematrix is None: -1340 basematrix = self -1341 if Ntrunc >= basematrix.N: -1342 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1343 if basematrix.N != self.N: -1344 raise Exception('basematrix and targetmatrix have to be of the same size.') -1345 -1346 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1347 -1348 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1349 rmat = [] -1350 for t in range(basematrix.T): -1351 for i in range(Ntrunc): -1352 for j in range(Ntrunc): -1353 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1354 rmat.append(np.copy(tmpmat)) -1355 -1356 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1357 return Corr(newcontent) +1282 def arcsinh(self): +1283 return self._apply_func_to_corr(np.arcsinh) +1284 +1285 def arccosh(self): +1286 return self._apply_func_to_corr(np.arccosh) +1287 +1288 def arctanh(self): +1289 return self._apply_func_to_corr(np.arctanh) +1290 +1291 # Right hand side operations (require tweak in main module to work) +1292 def __radd__(self, y): +1293 return self + y +1294 +1295 def __rsub__(self, y): +1296 return -self + y +1297 +1298 def __rmul__(self, y): +1299 return self * y +1300 +1301 def __rtruediv__(self, y): +1302 return (self / y) ** (-1) +1303 +1304 @property +1305 def real(self): +1306 def return_real(obs_OR_cobs): +1307 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1308 return np.vectorize(lambda x: x.real)(obs_OR_cobs) +1309 else: +1310 return obs_OR_cobs +1311 +1312 return self._apply_func_to_corr(return_real) +1313 +1314 @property +1315 def imag(self): +1316 def return_imag(obs_OR_cobs): +1317 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1318 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) +1319 else: +1320 return obs_OR_cobs * 0 # So it stays the right type +1321 +1322 return self._apply_func_to_corr(return_imag) +1323 +1324 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1325 r''' Project large correlation matrix to lowest states +1326 +1327 This method can be used to reduce the size of an (N x N) correlation matrix +1328 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1329 is still small. +1330 +1331 Parameters +1332 ---------- +1333 Ntrunc: int +1334 Rank of the target matrix. +1335 tproj: int +1336 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1337 The default value is 3. +1338 t0proj: int +1339 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1340 discouraged for O(a) improved theories, since the correctness of the procedure +1341 cannot be granted in this case. The default value is 2. +1342 basematrix : Corr +1343 Correlation matrix that is used to determine the eigenvectors of the +1344 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1345 is is not specified. +1346 +1347 Notes +1348 ----- +1349 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1350 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1351 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1352 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1353 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1354 correlation matrix and to remove some noise that is added by irrelevant operators. +1355 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1356 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1357 ''' 1358 -1359 -1360def _sort_vectors(vec_set, ts): -1361 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" -1362 reference_sorting = np.array(vec_set[ts]) -1363 N = reference_sorting.shape[0] -1364 sorted_vec_set = [] -1365 for t in range(len(vec_set)): -1366 if vec_set[t] is None: -1367 sorted_vec_set.append(None) -1368 elif not t == ts: -1369 perms = [list(o) for o in permutations([i for i in range(N)], N)] -1370 best_score = 0 -1371 for perm in perms: -1372 current_score = 1 -1373 for k in range(N): -1374 new_sorting = reference_sorting.copy() -1375 new_sorting[perm[k], :] = vec_set[t][k] -1376 current_score *= abs(np.linalg.det(new_sorting)) -1377 if current_score > best_score: -1378 best_score = current_score -1379 best_perm = perm -1380 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) -1381 else: -1382 sorted_vec_set.append(vec_set[t]) -1383 -1384 return sorted_vec_set -1385 -1386 -1387def _check_for_none(corr, entry): -1388 """Checks if entry for correlator corr is None""" -1389 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 -1390 -1391 -1392def _GEVP_solver(Gt, G0): -1393 """Helper function for solving the GEVP and sorting the eigenvectors. -1394 -1395 The helper function assumes that both provided matrices are symmetric and -1396 only processes the lower triangular part of both matrices. In case the matrices -1397 are not symmetric the upper triangular parts are effectively discarded.""" -1398 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] +1359 if self.N == 1: +1360 raise Exception('Method cannot be applied to one-dimensional correlators.') +1361 if basematrix is None: +1362 basematrix = self +1363 if Ntrunc >= basematrix.N: +1364 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1365 if basematrix.N != self.N: +1366 raise Exception('basematrix and targetmatrix have to be of the same size.') +1367 +1368 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1369 +1370 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1371 rmat = [] +1372 for t in range(basematrix.T): +1373 for i in range(Ntrunc): +1374 for j in range(Ntrunc): +1375 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1376 rmat.append(np.copy(tmpmat)) +1377 +1378 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1379 return Corr(newcontent) +1380 +1381 +1382def _sort_vectors(vec_set, ts): +1383 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" +1384 reference_sorting = np.array(vec_set[ts]) +1385 N = reference_sorting.shape[0] +1386 sorted_vec_set = [] +1387 for t in range(len(vec_set)): +1388 if vec_set[t] is None: +1389 sorted_vec_set.append(None) +1390 elif not t == ts: +1391 perms = [list(o) for o in permutations([i for i in range(N)], N)] +1392 best_score = 0 +1393 for perm in perms: +1394 current_score = 1 +1395 for k in range(N): +1396 new_sorting = reference_sorting.copy() +1397 new_sorting[perm[k], :] = vec_set[t][k] +1398 current_score *= abs(np.linalg.det(new_sorting)) +1399 if current_score > best_score: +1400 best_score = current_score +1401 best_perm = perm +1402 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) +1403 else: +1404 sorted_vec_set.append(vec_set[t]) +1405 +1406 return sorted_vec_set +1407 +1408 +1409def _check_for_none(corr, entry): +1410 """Checks if entry for correlator corr is None""" +1411 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1412 +1413 +1414def _GEVP_solver(Gt, G0): +1415 """Helper function for solving the GEVP and sorting the eigenvectors. +1416 +1417 The helper function assumes that both provided matrices are symmetric and +1418 only processes the lower triangular part of both matrices. In case the matrices +1419 are not symmetric the upper triangular parts are effectively discarded.""" +1420 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] @@ -1655,1350 +1677,1372 @@
  14class Corr:
-  15    """The class for a correlator (time dependent sequence of pe.Obs).
+  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 GEVP
-  23    matrix at every timeslice. Other dependency (eg. spatial) are not supported.
+  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    """
-  26
-  27    __slots__ = ["content", "N", "T", "tag", "prange"]
-  28
-  29    def __init__(self, data_input, padding=[0, 0], prange=None):
-  30        """ Initialize a Corr object.
-  31
-  32        Parameters
-  33        ----------
-  34        data_input : list or array
-  35            list of Obs or list of arrays of Obs or array of Corrs
-  36        padding : list, optional
-  37            List with two entries where the first labels the padding
-  38            at the front of the correlator and the second the padding
-  39            at the back.
-  40        prange : list, optional
-  41            List containing the first and last timeslice of the plateau
-  42            region indentified for this correlator.
-  43        """
+  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        if isinstance(data_input, np.ndarray):
-  46
-  47            # This only works, if the array fulfills the conditions below
-  48            if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]:
-  49                raise Exception("Incompatible array shape")
-  50            if not all([isinstance(item, Corr) for item in data_input.flatten()]):
-  51                raise Exception("If the input is an array, its elements must be of type pe.Corr")
-  52            if not all([item.N == 1 for item in data_input.flatten()]):
-  53                raise Exception("Can only construct matrix correlator from single valued correlators")
-  54            if not len(set([item.T for item in data_input.flatten()])) == 1:
-  55                raise Exception("All input Correlators must be defined over the same timeslices.")
-  56
-  57            T = data_input[0, 0].T
-  58            N = data_input.shape[0]
-  59            input_as_list = []
-  60            for t in range(T):
-  61                if any([(item.content[t] is None) for item in data_input.flatten()]):
-  62                    if not all([(item.content[t] is None) for item in data_input.flatten()]):
-  63                        warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning)
-  64                    input_as_list.append(None)
-  65                else:
-  66                    array_at_timeslace = np.empty([N, N], dtype="object")
-  67                    for i in range(N):
-  68                        for j in range(N):
-  69                            array_at_timeslace[i, j] = data_input[i, j][t]
-  70                    input_as_list.append(array_at_timeslace)
-  71            data_input = input_as_list
-  72
-  73        if isinstance(data_input, list):
-  74
-  75            if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
-  76                _assert_equal_properties([o for o in data_input if o is not None])
-  77                self.content = [np.asarray([item]) if item is not None else None for item in data_input]
-  78                self.N = 1
-  79
-  80            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]):
-  81                self.content = data_input
-  82                noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
-  83                self.N = noNull[0].shape[0]
-  84                if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
-  85                    raise Exception("Smearing matrices are not NxN")
-  86                if (not all([item.shape == noNull[0].shape for item in noNull])):
-  87                    raise Exception("Items in data_input are not of identical shape." + str(noNull))
-  88            else:
-  89                raise Exception("data_input contains item of wrong type")
-  90        else:
-  91            raise Exception("Data input was not given as list or correct array")
-  92
-  93        self.tag = None
-  94
-  95        # An undefined timeslice is represented by the None object
-  96        self.content = [None] * padding[0] + self.content + [None] * padding[1]
-  97        self.T = len(self.content)
-  98        self.prange = prange
-  99
- 100    def __getitem__(self, idx):
- 101        """Return the content of timeslice idx"""
- 102        if self.content[idx] is None:
- 103            return None
- 104        elif len(self.content[idx]) == 1:
- 105            return self.content[idx][0]
- 106        else:
- 107            return self.content[idx]
- 108
- 109    @property
- 110    def reweighted(self):
- 111        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]])
- 112        if np.all(bool_array == 1):
- 113            return True
- 114        elif np.all(bool_array == 0):
- 115            return False
- 116        else:
- 117            raise Exception("Reweighting status of correlator corrupted.")
- 118
- 119    def gamma_method(self, **kwargs):
- 120        """Apply the gamma method to the content of the Corr."""
- 121        for item in self.content:
- 122            if not (item is None):
- 123                if self.N == 1:
- 124                    item[0].gamma_method(**kwargs)
- 125                else:
- 126                    for i in range(self.N):
- 127                        for j in range(self.N):
- 128                            item[i, j].gamma_method(**kwargs)
- 129
- 130    gm = gamma_method
- 131
- 132    def projected(self, vector_l=None, vector_r=None, normalize=False):
- 133        """We need to project the Correlator with a Vector to get a single value at each timeslice.
- 134
- 135        The method can use one or two vectors.
- 136        If two are specified it returns v1@G@v2 (the order might be very important.)
- 137        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
- 138        """
- 139        if self.N == 1:
- 140            raise Exception("Trying to project a Corr, that already has N=1.")
- 141
- 142        if vector_l is None:
- 143            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
- 144        elif (vector_r is None):
- 145            vector_r = vector_l
- 146        if isinstance(vector_l, list) and not isinstance(vector_r, list):
- 147            if len(vector_l) != self.T:
- 148                raise Exception("Length of vector list must be equal to T")
- 149            vector_r = [vector_r] * self.T
- 150        if isinstance(vector_r, list) and not isinstance(vector_l, list):
- 151            if len(vector_r) != self.T:
- 152                raise Exception("Length of vector list must be equal to T")
- 153            vector_l = [vector_l] * self.T
- 154
- 155        if not isinstance(vector_l, list):
- 156            if not vector_l.shape == vector_r.shape == (self.N,):
- 157                raise Exception("Vectors are of wrong shape!")
- 158            if normalize:
- 159                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
- 160            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
- 161
- 162        else:
- 163            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
- 164            if normalize:
- 165                for t in range(self.T):
- 166                    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])
- 167
- 168            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)]
- 169        return Corr(newcontent)
- 170
- 171    def item(self, i, j):
- 172        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
- 173
- 174        Parameters
- 175        ----------
- 176        i : int
- 177            First index to be picked.
- 178        j : int
- 179            Second index to be picked.
- 180        """
- 181        if self.N == 1:
- 182            raise Exception("Trying to pick item from projected Corr")
- 183        newcontent = [None if (item is None) else item[i, j] for item in self.content]
- 184        return Corr(newcontent)
- 185
- 186    def plottable(self):
- 187        """Outputs the correlator in a plotable format.
- 188
- 189        Outputs three lists containing the timeslice index, the value on each
- 190        timeslice and the error on each timeslice.
- 191        """
- 192        if self.N != 1:
- 193            raise Exception("Can only make Corr[N=1] plottable")
- 194        x_list = [x for x in range(self.T) if not self.content[x] is None]
- 195        y_list = [y[0].value for y in self.content if y is not None]
- 196        y_err_list = [y[0].dvalue for y in self.content if y is not None]
- 197
- 198        return x_list, y_list, y_err_list
- 199
- 200    def symmetric(self):
- 201        """ Symmetrize the correlator around x0=0."""
- 202        if self.N != 1:
- 203            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
- 204        if self.T % 2 != 0:
- 205            raise Exception("Can not symmetrize odd T")
- 206
- 207        if self.content[0] is not None:
- 208            if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0:
- 209                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
+  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        newcontent = [self.content[0]]
- 212        for t in range(1, self.T):
- 213            if (self.content[t] is None) or (self.content[self.T - t] is None):
- 214                newcontent.append(None)
- 215            else:
- 216                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
- 217        if (all([x is None for x in newcontent])):
- 218            raise Exception("Corr could not be symmetrized: No redundant values")
- 219        return Corr(newcontent, prange=self.prange)
- 220
- 221    def anti_symmetric(self):
- 222        """Anti-symmetrize the correlator around x0=0."""
- 223        if self.N != 1:
- 224            raise TypeError('anti_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        test = 1 * self
- 229        test.gamma_method()
- 230        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
- 231            warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)
+ 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]))
+ 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 is_matrix_symmetric(self):
- 244        """Checks whether a correlator matrices is symmetric on every timeslice."""
- 245        if self.N == 1:
- 246            raise TypeError("Only works for correlator matrices.")
- 247        for t in range(self.T):
- 248            if self[t] is None:
- 249                continue
- 250            for i in range(self.N):
- 251                for j in range(i + 1, self.N):
- 252                    if self[t][i, j] is self[t][j, i]:
- 253                        continue
- 254                    if hash(self[t][i, j]) != hash(self[t][j, i]):
- 255                        return False
- 256        return True
- 257
- 258    def trace(self):
- 259        """Calculates the per-timeslice trace of a correlator matrix."""
- 260        if self.N == 1:
- 261            raise ValueError("Only works for correlator matrices.")
- 262        newcontent = []
- 263        for t in range(self.T):
- 264            if _check_for_none(self, self.content[t]):
- 265                newcontent.append(None)
- 266            else:
- 267                newcontent.append(np.trace(self.content[t]))
- 268        return Corr(newcontent)
- 269
- 270    def matrix_symmetric(self):
- 271        """Symmetrizes the correlator matrices on every timeslice."""
- 272        if self.N == 1:
- 273            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
- 274        if self.is_matrix_symmetric():
- 275            return 1.0 * self
- 276        else:
- 277            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
- 278            return 0.5 * (Corr(transposed) + self)
+ 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 GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
- 281        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
- 282
- 283        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
- 284        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
- 285        ```python
- 286        C.GEVP(t0=2)[0]  # Ground state vector(s)
- 287        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
- 288        ```
- 289
- 290        Parameters
- 291        ----------
- 292        t0 : int
- 293            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
- 294        ts : int
- 295            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
- 296            If sort="Eigenvector" it gives a reference point for the sorting method.
- 297        sort : string
- 298            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.
- 299            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
- 300            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
- 301              The reference state is identified by its eigenvalue at $t=t_s$.
- 302
- 303        Other Parameters
- 304        ----------------
- 305        state : int
- 306           Returns only the vector(s) for a specified state. The lowest state is zero.
- 307        '''
- 308
- 309        if self.N == 1:
- 310            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
- 311        if ts is not None:
- 312            if (ts <= t0):
- 313                raise Exception("ts has to be larger than t0.")
- 314
- 315        if "sorted_list" in kwargs:
- 316            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
- 317            sort = kwargs.get("sorted_list")
- 318
- 319        if self.is_matrix_symmetric():
- 320            symmetric_corr = self
- 321        else:
- 322            symmetric_corr = self.matrix_symmetric()
- 323
- 324        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
- 325        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
- 326
- 327        if sort is None:
- 328            if (ts is None):
- 329                raise Exception("ts is required if sort=None.")
- 330            if (self.content[t0] is None) or (self.content[ts] is None):
- 331                raise Exception("Corr not defined at t0/ts.")
- 332            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
- 333            reordered_vecs = _GEVP_solver(Gt, G0)
- 334
- 335        elif sort in ["Eigenvalue", "Eigenvector"]:
- 336            if sort == "Eigenvalue" and ts is not None:
- 337                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
- 338            all_vecs = [None] * (t0 + 1)
- 339            for t in range(t0 + 1, self.T):
- 340                try:
- 341                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
- 342                    all_vecs.append(_GEVP_solver(Gt, G0))
- 343                except Exception:
- 344                    all_vecs.append(None)
- 345            if sort == "Eigenvector":
- 346                if ts is None:
- 347                    raise Exception("ts is required for the Eigenvector sorting method.")
- 348                all_vecs = _sort_vectors(all_vecs, ts)
- 349
- 350            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
- 351        else:
- 352            raise Exception("Unkown value for 'sort'.")
- 353
- 354        if "state" in kwargs:
- 355            return reordered_vecs[kwargs.get("state")]
- 356        else:
- 357            return reordered_vecs
- 358
- 359    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
- 360        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
- 361
- 362        Parameters
- 363        ----------
- 364        state : int
- 365            The state one is interested in ordered by energy. The lowest state is zero.
- 366
- 367        All other parameters are identical to the ones of Corr.GEVP.
- 368        """
- 369        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
- 370        return self.projected(vec)
+ 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.
+ 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    def Hankel(self, N, periodic=False):
- 373        """Constructs an NxN Hankel matrix
- 374
- 375        C(t) c(t+1) ... c(t+n-1)
- 376        C(t+1) c(t+2) ... c(t+n)
- 377        .................
- 378        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
- 379
- 380        Parameters
- 381        ----------
- 382        N : int
- 383            Dimension of the Hankel matrix
- 384        periodic : bool, optional
- 385            determines whether the matrix is extended periodically
- 386        """
- 387
- 388        if self.N != 1:
- 389            raise Exception("Multi-operator Prony not implemented!")
- 390
- 391        array = np.empty([N, N], dtype="object")
- 392        new_content = []
- 393        for t in range(self.T):
- 394            new_content.append(array.copy())
- 395
- 396        def wrap(i):
- 397            while i >= self.T:
- 398                i -= self.T
- 399            return i
- 400
- 401        for t in range(self.T):
- 402            for i in range(N):
- 403                for j in range(N):
- 404                    if periodic:
- 405                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
- 406                    elif (t + i + j) >= self.T:
- 407                        new_content[t] = None
- 408                    else:
- 409                        new_content[t][i, j] = self.content[t + i + j][0]
- 410
- 411        return Corr(new_content)
+ 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    def roll(self, dt):
- 414        """Periodically shift the correlator by dt timeslices
- 415
- 416        Parameters
- 417        ----------
- 418        dt : int
- 419            number of timeslices
- 420        """
- 421        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
+ 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    def reverse(self):
- 424        """Reverse the time ordering of the Corr"""
- 425        return Corr(self.content[:: -1])
- 426
- 427    def thin(self, spacing=2, offset=0):
- 428        """Thin out a correlator to suppress correlations
- 429
- 430        Parameters
- 431        ----------
- 432        spacing : int
- 433            Keep only every 'spacing'th entry of the correlator
- 434        offset : int
- 435            Offset the equal spacing
- 436        """
- 437        new_content = []
- 438        for t in range(self.T):
- 439            if (offset + t) % spacing != 0:
- 440                new_content.append(None)
- 441            else:
- 442                new_content.append(self.content[t])
- 443        return Corr(new_content)
+ 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
+ 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 correlate(self, partner):
- 446        """Correlate the correlator with another correlator or Obs
- 447
- 448        Parameters
- 449        ----------
- 450        partner : Obs or Corr
- 451            partner to correlate the correlator with.
- 452            Can either be an Obs which is correlated with all entries of the
- 453            correlator or a Corr of same length.
- 454        """
- 455        if self.N != 1:
- 456            raise Exception("Only one-dimensional correlators can be safely correlated.")
- 457        new_content = []
- 458        for x0, t_slice in enumerate(self.content):
- 459            if _check_for_none(self, t_slice):
- 460                new_content.append(None)
- 461            else:
- 462                if isinstance(partner, Corr):
- 463                    if _check_for_none(partner, partner.content[x0]):
- 464                        new_content.append(None)
- 465                    else:
- 466                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
- 467                elif isinstance(partner, Obs):  # Should this include CObs?
- 468                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
- 469                else:
- 470                    raise Exception("Can only correlate with an Obs or a Corr.")
- 471
- 472        return Corr(new_content)
- 473
- 474    def reweight(self, weight, **kwargs):
- 475        """Reweight the correlator.
- 476
- 477        Parameters
- 478        ----------
- 479        weight : Obs
- 480            Reweighting factor. An Observable that has to be defined on a superset of the
- 481            configurations in obs[i].idl for all i.
- 482        all_configs : bool
- 483            if True, the reweighted observables are normalized by the average of
- 484            the reweighting factor on all configurations in weight.idl and not
- 485            on the configurations in obs[i].idl.
- 486        """
- 487        if self.N != 1:
- 488            raise Exception("Reweighting only implemented for one-dimensional correlators.")
- 489        new_content = []
- 490        for t_slice in self.content:
- 491            if _check_for_none(self, t_slice):
- 492                new_content.append(None)
- 493            else:
- 494                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
- 495        return Corr(new_content)
- 496
- 497    def T_symmetry(self, partner, parity=+1):
- 498        """Return the time symmetry average of the correlator and its partner
- 499
- 500        Parameters
- 501        ----------
- 502        partner : Corr
- 503            Time symmetry partner of the Corr
- 504        partity : int
- 505            Parity quantum number of the correlator, can be +1 or -1
- 506        """
- 507        if self.N != 1:
- 508            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
- 509        if not isinstance(partner, Corr):
- 510            raise Exception("T partner has to be a Corr object.")
- 511        if parity not in [+1, -1]:
- 512            raise Exception("Parity has to be +1 or -1.")
- 513        T_partner = parity * partner.reverse()
- 514
- 515        t_slices = []
- 516        test = (self - T_partner)
- 517        test.gamma_method()
- 518        for x0, t_slice in enumerate(test.content):
- 519            if t_slice is not None:
- 520                if not t_slice[0].is_zero_within_error(5):
- 521                    t_slices.append(x0)
- 522        if t_slices:
- 523            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
- 524
- 525        return (self + T_partner) / 2
- 526
- 527    def deriv(self, variant="symmetric"):
- 528        """Return the first derivative of the correlator with respect to x0.
- 529
- 530        Parameters
- 531        ----------
- 532        variant : str
- 533            decides which definition of the finite differences derivative is used.
- 534            Available choice: symmetric, forward, backward, improved, log, default: symmetric
- 535        """
- 536        if self.N != 1:
- 537            raise Exception("deriv only implemented for one-dimensional correlators.")
- 538        if variant == "symmetric":
- 539            newcontent = []
- 540            for t in range(1, self.T - 1):
- 541                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
- 542                    newcontent.append(None)
- 543                else:
- 544                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
- 545            if (all([x is None for x in newcontent])):
- 546                raise Exception('Derivative is undefined at all timeslices')
- 547            return Corr(newcontent, padding=[1, 1])
- 548        elif variant == "forward":
- 549            newcontent = []
- 550            for t in range(self.T - 1):
- 551                if (self.content[t] is None) or (self.content[t + 1] is None):
- 552                    newcontent.append(None)
- 553                else:
- 554                    newcontent.append(self.content[t + 1] - self.content[t])
- 555            if (all([x is None for x in newcontent])):
- 556                raise Exception("Derivative is undefined at all timeslices")
- 557            return Corr(newcontent, padding=[0, 1])
- 558        elif variant == "backward":
- 559            newcontent = []
- 560            for t in range(1, self.T):
- 561                if (self.content[t - 1] is None) or (self.content[t] is None):
- 562                    newcontent.append(None)
- 563                else:
- 564                    newcontent.append(self.content[t] - self.content[t - 1])
- 565            if (all([x is None for x in newcontent])):
- 566                raise Exception("Derivative is undefined at all timeslices")
- 567            return Corr(newcontent, padding=[1, 0])
- 568        elif variant == "improved":
- 569            newcontent = []
- 570            for t in range(2, self.T - 2):
- 571                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):
- 572                    newcontent.append(None)
- 573                else:
- 574                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
- 575            if (all([x is None for x in newcontent])):
- 576                raise Exception('Derivative is undefined at all timeslices')
- 577            return Corr(newcontent, padding=[2, 2])
- 578        elif variant == 'log':
- 579            newcontent = []
- 580            for t in range(self.T):
- 581                if (self.content[t] is None) or (self.content[t] <= 0):
- 582                    newcontent.append(None)
- 583                else:
- 584                    newcontent.append(np.log(self.content[t]))
- 585            if (all([x is None for x in newcontent])):
- 586                raise Exception("Log is undefined at all timeslices")
- 587            logcorr = Corr(newcontent)
- 588            return self * logcorr.deriv('symmetric')
- 589        else:
- 590            raise Exception("Unknown variant.")
- 591
- 592    def second_deriv(self, variant="symmetric"):
- 593        r"""Return the second derivative of the correlator with respect to x0.
- 594
- 595        Parameters
- 596        ----------
- 597        variant : str
- 598            decides which definition of the finite differences derivative is used.
- 599            Available choice:
- 600                - symmetric (default)
- 601                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
- 602                - big_symmetric
- 603                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
- 604                - improved
- 605                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
- 606                - log
- 607                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
- 608        """
- 609        if self.N != 1:
- 610            raise Exception("second_deriv only implemented for one-dimensional correlators.")
- 611        if variant == "symmetric":
- 612            newcontent = []
- 613            for t in range(1, self.T - 1):
- 614                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
- 615                    newcontent.append(None)
- 616                else:
- 617                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
- 618            if (all([x is None for x in newcontent])):
- 619                raise Exception("Derivative is undefined at all timeslices")
- 620            return Corr(newcontent, padding=[1, 1])
- 621        elif variant == "big_symmetric":
- 622            newcontent = []
- 623            for t in range(2, self.T - 2):
- 624                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
- 625                    newcontent.append(None)
- 626                else:
- 627                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
- 628            if (all([x is None for x in newcontent])):
- 629                raise Exception("Derivative is undefined at all timeslices")
- 630            return Corr(newcontent, padding=[2, 2])
- 631        elif variant == "improved":
- 632            newcontent = []
- 633            for t in range(2, self.T - 2):
- 634                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):
- 635                    newcontent.append(None)
- 636                else:
- 637                    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]))
- 638            if (all([x is None for x in newcontent])):
- 639                raise Exception("Derivative is undefined at all timeslices")
- 640            return Corr(newcontent, padding=[2, 2])
- 641        elif variant == 'log':
- 642            newcontent = []
- 643            for t in range(self.T):
- 644                if (self.content[t] is None) or (self.content[t] <= 0):
- 645                    newcontent.append(None)
- 646                else:
- 647                    newcontent.append(np.log(self.content[t]))
- 648            if (all([x is None for x in newcontent])):
- 649                raise Exception("Log is undefined at all timeslices")
- 650            logcorr = Corr(newcontent)
- 651            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
- 652        else:
- 653            raise Exception("Unknown variant.")
- 654
- 655    def m_eff(self, variant='log', guess=1.0):
- 656        """Returns the effective mass of the correlator as correlator object
- 657
- 658        Parameters
- 659        ----------
- 660        variant : str
- 661            log : uses the standard effective mass log(C(t) / C(t+1))
- 662            cosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
- 663            sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
- 664            See, e.g., arXiv:1205.5380
- 665            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
- 666            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
- 667        guess : float
- 668            guess for the root finder, only relevant for the root variant
- 669        """
- 670        if self.N != 1:
- 671            raise Exception('Correlator must be projected before getting m_eff')
- 672        if variant == 'log':
- 673            newcontent = []
- 674            for t in range(self.T - 1):
- 675                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
- 676                    newcontent.append(None)
- 677                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
- 678                    newcontent.append(None)
- 679                else:
- 680                    newcontent.append(self.content[t] / self.content[t + 1])
- 681            if (all([x is None for x in newcontent])):
- 682                raise Exception('m_eff is undefined at all timeslices')
- 683
- 684            return np.log(Corr(newcontent, padding=[0, 1]))
- 685
- 686        elif variant == 'logsym':
- 687            newcontent = []
- 688            for t in range(1, self.T - 1):
- 689                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
- 690                    newcontent.append(None)
- 691                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
- 692                    newcontent.append(None)
- 693                else:
- 694                    newcontent.append(self.content[t - 1] / self.content[t + 1])
- 695            if (all([x is None for x in newcontent])):
- 696                raise Exception('m_eff is undefined at all timeslices')
- 697
- 698            return np.log(Corr(newcontent, padding=[1, 1])) / 2
- 699
- 700        elif variant in ['periodic', 'cosh', 'sinh']:
- 701            if variant in ['periodic', 'cosh']:
- 702                func = anp.cosh
- 703            else:
- 704                func = anp.sinh
+ 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
+ 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
+ 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            def root_function(x, d):
- 707                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
- 708
+ 706            return np.log(Corr(newcontent, padding=[0, 1]))
+ 707
+ 708        elif variant == 'logsym':
  709            newcontent = []
- 710            for t in range(self.T - 1):
- 711                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+ 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                # Fill the two timeslices in the middle of the lattice with their predecessors
- 714                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
- 715                    newcontent.append(newcontent[-1])
- 716                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
- 717                    newcontent.append(None)
- 718                else:
- 719                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
- 720            if (all([x is None for x in newcontent])):
- 721                raise Exception('m_eff is undefined at all timeslices')
- 722
- 723            return Corr(newcontent, padding=[0, 1])
- 724
- 725        elif variant == 'arccosh':
- 726            newcontent = []
- 727            for t in range(1, self.T - 1):
- 728                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):
- 729                    newcontent.append(None)
- 730                else:
- 731                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
- 732            if (all([x is None for x in newcontent])):
- 733                raise Exception("m_eff is undefined at all timeslices")
- 734            return np.arccosh(Corr(newcontent, padding=[1, 1]))
- 735
- 736        else:
- 737            raise Exception('Unknown variant.')
- 738
- 739    def fit(self, function, fitrange=None, silent=False, **kwargs):
- 740        r'''Fits function to the data
- 741
- 742        Parameters
- 743        ----------
- 744        function : obj
- 745            function to fit to the data. See fits.least_squares for details.
- 746        fitrange : list
- 747            Two element list containing the timeslices on which the fit is supposed to start and stop.
- 748            Caution: This range is inclusive as opposed to standard python indexing.
- 749            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
- 750            If not specified, self.prange or all timeslices are used.
- 751        silent : bool
- 752            Decides whether output is printed to the standard output.
- 753        '''
- 754        if self.N != 1:
- 755            raise Exception("Correlator must be projected before fitting")
- 756
- 757        if fitrange is None:
- 758            if self.prange:
- 759                fitrange = self.prange
- 760            else:
- 761                fitrange = [0, self.T - 1]
- 762        else:
- 763            if not isinstance(fitrange, list):
- 764                raise Exception("fitrange has to be a list with two elements")
- 765            if len(fitrange) != 2:
- 766                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
- 767
- 768        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
- 769        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
- 770        result = least_squares(xs, ys, function, silent=silent, **kwargs)
- 771        return result
- 772
- 773    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
- 774        """ Extract a plateau value from a Corr object
- 775
- 776        Parameters
- 777        ----------
- 778        plateau_range : list
- 779            list with two entries, indicating the first and the last timeslice
- 780            of the plateau region.
- 781        method : str
- 782            method to extract the plateau.
- 783                'fit' fits a constant to the plateau region
- 784                'avg', 'average' or 'mean' just average over the given timeslices.
- 785        auto_gamma : bool
- 786            apply gamma_method with default parameters to the Corr. Defaults to None
- 787        """
- 788        if not plateau_range:
- 789            if self.prange:
- 790                plateau_range = self.prange
- 791            else:
- 792                raise Exception("no plateau range provided")
- 793        if self.N != 1:
- 794            raise Exception("Correlator must be projected before getting a plateau.")
- 795        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
- 796            raise Exception("plateau is undefined at all timeslices in plateaurange.")
- 797        if auto_gamma:
- 798            self.gamma_method()
- 799        if method == "fit":
- 800            def const_func(a, t):
- 801                return a[0]
- 802            return self.fit(const_func, plateau_range)[0]
- 803        elif method in ["avg", "average", "mean"]:
- 804            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
- 805            return returnvalue
- 806
- 807        else:
- 808            raise Exception("Unsupported plateau method: " + method)
- 809
- 810    def set_prange(self, prange):
- 811        """Sets the attribute prange of the Corr object."""
- 812        if not len(prange) == 2:
- 813            raise Exception("prange must be a list or array with two values")
- 814        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
- 815            raise Exception("Start and end point must be integers")
- 816        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
- 817            raise Exception("Start and end point must define a range in the interval 0,T")
- 818
- 819        self.prange = prange
- 820        return
- 821
- 822    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):
- 823        """Plots the correlator using the tag of the correlator as label if available.
- 824
- 825        Parameters
- 826        ----------
- 827        x_range : list
- 828            list of two values, determining the range of the x-axis e.g. [4, 8].
- 829        comp : Corr or list of Corr
- 830            Correlator or list of correlators which are plotted for comparison.
- 831            The tags of these correlators are used as labels if available.
- 832        logscale : bool
- 833            Sets y-axis to logscale.
- 834        plateau : Obs
- 835            Plateau value to be visualized in the figure.
- 836        fit_res : Fit_result
- 837            Fit_result object to be visualized.
- 838        fit_key : str
- 839            Key for the fit function in Fit_result.fit_function (for combined fits).
- 840        ylabel : str
- 841            Label for the y-axis.
- 842        save : str
- 843            path to file in which the figure should be saved.
- 844        auto_gamma : bool
- 845            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
- 846        hide_sigma : float
- 847            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
- 848        references : list
- 849            List of floating point values that are displayed as horizontal lines for reference.
- 850        title : string
- 851            Optional title of the figure.
- 852        """
- 853        if self.N != 1:
- 854            raise Exception("Correlator must be projected before plotting")
- 855
- 856        if auto_gamma:
- 857            self.gamma_method()
- 858
- 859        if x_range is None:
- 860            x_range = [0, self.T - 1]
- 861
- 862        fig = plt.figure()
- 863        ax1 = fig.add_subplot(111)
- 864
- 865        x, y, y_err = self.plottable()
- 866        if hide_sigma:
- 867            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
- 868        else:
- 869            hide_from = None
- 870        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
- 871        if logscale:
- 872            ax1.set_yscale('log')
- 873        else:
- 874            if y_range is None:
- 875                try:
- 876                    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)])
- 877                    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)])
- 878                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
- 879                except Exception:
- 880                    pass
- 881            else:
- 882                ax1.set_ylim(y_range)
- 883        if comp:
- 884            if isinstance(comp, (Corr, list)):
- 885                for corr in comp if isinstance(comp, list) else [comp]:
- 886                    if auto_gamma:
- 887                        corr.gamma_method()
- 888                    x, y, y_err = corr.plottable()
- 889                    if hide_sigma:
- 890                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
- 891                    else:
- 892                        hide_from = None
- 893                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
- 894            else:
- 895                raise Exception("'comp' must be a correlator or a list of correlators.")
- 896
- 897        if plateau:
- 898            if isinstance(plateau, Obs):
- 899                if auto_gamma:
- 900                    plateau.gamma_method()
- 901                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
- 902                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+ 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                raise Exception("'plateau' must be an Obs")
- 905
- 906        if references:
- 907            if isinstance(references, list):
- 908                for ref in references:
- 909                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
- 910            else:
- 911                raise Exception("'references' must be a list of floating pint values.")
- 912
- 913        if self.prange:
- 914            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
- 915            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
- 916
- 917        if fit_res:
- 918            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
- 919            if isinstance(fit_res.fit_function, dict):
- 920                if fit_key:
- 921                    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)
- 922                else:
- 923                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
- 924            else:
- 925                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
- 926
- 927        ax1.set_xlabel(r'$x_0 / a$')
- 928        if ylabel:
- 929            ax1.set_ylabel(ylabel)
- 930        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
- 931
- 932        handles, labels = ax1.get_legend_handles_labels()
- 933        if labels:
- 934            ax1.legend()
- 935
- 936        if title:
- 937            plt.title(title)
+ 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        plt.draw()
- 940
- 941        if save:
- 942            if isinstance(save, str):
- 943                fig.savefig(save, bbox_inches='tight')
- 944            else:
- 945                raise Exception("'save' has to be a string.")
- 946
- 947    def spaghetti_plot(self, logscale=True):
- 948        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
- 949
- 950        Parameters
- 951        ----------
- 952        logscale : bool
- 953            Determines whether the scale of the y-axis is logarithmic or standard.
- 954        """
- 955        if self.N != 1:
- 956            raise Exception("Correlator needs to be projected first.")
+ 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        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]))
- 959        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+ 958        if title:
+ 959            plt.title(title)
  960
- 961        for name in mc_names:
- 962            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
- 963
- 964            fig = plt.figure()
- 965            ax = fig.add_subplot(111)
- 966            for dat in data:
- 967                ax.plot(x0_vals, dat, ls='-', marker='')
+ 961        plt.draw()
+ 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            if logscale is True:
- 970                ax.set_yscale('log')
+ 969    def spaghetti_plot(self, logscale=True):
+ 970        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
  971
- 972            ax.set_xlabel(r'$x_0 / a$')
- 973            plt.title(name)
- 974            plt.draw()
- 975
- 976    def dump(self, filename, datatype="json.gz", **kwargs):
- 977        """Dumps the Corr into a file of chosen type
- 978        Parameters
- 979        ----------
- 980        filename : str
- 981            Name of the file to be saved.
- 982        datatype : str
- 983            Format of the exported file. Supported formats include
- 984            "json.gz" and "pickle"
- 985        path : str
- 986            specifies a custom path for the file (default '.')
- 987        """
- 988        if datatype == "json.gz":
- 989            from .input.json import dump_to_json
- 990            if 'path' in kwargs:
- 991                file_name = kwargs.get('path') + '/' + filename
- 992            else:
- 993                file_name = filename
- 994            dump_to_json(self, file_name)
- 995        elif datatype == "pickle":
- 996            dump_object(self, filename, **kwargs)
- 997        else:
- 998            raise Exception("Unknown datatype " + str(datatype))
- 999
-1000    def print(self, print_range=None):
-1001        print(self.__repr__(print_range))
-1002
-1003    def __repr__(self, print_range=None):
-1004        if print_range is None:
-1005            print_range = [0, None]
-1006
-1007        content_string = ""
-1008        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
-1009
-1010        if self.tag is not None:
-1011            content_string += "Description: " + self.tag + "\n"
-1012        if self.N != 1:
-1013            return content_string
-1014
-1015        if print_range[1]:
-1016            print_range[1] += 1
-1017        content_string += 'x0/a\tCorr(x0/a)\n------------------\n'
-1018        for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]):
-1019            if sub_corr is None:
-1020                content_string += str(i + print_range[0]) + '\n'
-1021            else:
-1022                content_string += str(i + print_range[0])
-1023                for element in sub_corr:
-1024                    content_string += f"\t{element:+2}"
-1025                content_string += '\n'
-1026        return content_string
-1027
-1028    def __str__(self):
-1029        return self.__repr__()
-1030
-1031    # We define the basic operations, that can be performed with correlators.
-1032    # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr.
-1033    # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception.
-1034    # One could try and tell Obs to check if the y in __mul__ is a Corr and
-1035
-1036    __array_priority__ = 10000
-1037
-1038    def __add__(self, y):
-1039        if isinstance(y, Corr):
-1040            if ((self.N != y.N) or (self.T != y.T)):
-1041                raise Exception("Addition of Corrs with different shape")
-1042            newcontent = []
-1043            for t in range(self.T):
-1044                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
-1045                    newcontent.append(None)
-1046                else:
-1047                    newcontent.append(self.content[t] + y.content[t])
-1048            return Corr(newcontent)
+ 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
+ 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))
+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
 1049
-1050        elif isinstance(y, (Obs, int, float, CObs)):
-1051            newcontent = []
-1052            for t in range(self.T):
-1053                if _check_for_none(self, self.content[t]):
-1054                    newcontent.append(None)
-1055                else:
-1056                    newcontent.append(self.content[t] + y)
-1057            return Corr(newcontent, prange=self.prange)
-1058        elif isinstance(y, np.ndarray):
-1059            if y.shape == (self.T,):
-1060                return Corr(list((np.array(self.content).T + y).T))
-1061            else:
-1062                raise ValueError("operands could not be broadcast together")
-1063        else:
-1064            raise TypeError("Corr + wrong type")
-1065
-1066    def __mul__(self, y):
-1067        if isinstance(y, Corr):
-1068            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
-1069                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
-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)):
-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")
-1093
-1094    def __matmul__(self, y):
-1095        if isinstance(y, np.ndarray):
-1096            if y.ndim != 2 or y.shape[0] != y.shape[1]:
-1097                raise ValueError("Can only multiply correlators by square matrices.")
-1098            if not self.N == y.shape[0]:
-1099                raise ValueError("matmul: mismatch of matrix dimensions")
-1100            newcontent = []
-1101            for t in range(self.T):
-1102                if _check_for_none(self, self.content[t]):
-1103                    newcontent.append(None)
-1104                else:
-1105                    newcontent.append(self.content[t] @ y)
-1106            return Corr(newcontent)
-1107        elif isinstance(y, Corr):
-1108            if not self.N == y.N:
-1109                raise ValueError("matmul: mismatch of matrix dimensions")
-1110            newcontent = []
-1111            for t in range(self.T):
-1112                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
-1113                    newcontent.append(None)
-1114                else:
-1115                    newcontent.append(self.content[t] @ y.content[t])
-1116            return Corr(newcontent)
-1117
-1118        else:
-1119            return NotImplemented
-1120
-1121    def __rmatmul__(self, y):
-1122        if isinstance(y, np.ndarray):
-1123            if y.ndim != 2 or y.shape[0] != y.shape[1]:
-1124                raise ValueError("Can only multiply correlators by square matrices.")
-1125            if not self.N == y.shape[0]:
-1126                raise ValueError("matmul: mismatch of matrix dimensions")
-1127            newcontent = []
-1128            for t in range(self.T):
-1129                if _check_for_none(self, self.content[t]):
-1130                    newcontent.append(None)
-1131                else:
-1132                    newcontent.append(y @ self.content[t])
-1133            return Corr(newcontent)
-1134        else:
-1135            return NotImplemented
-1136
-1137    def __truediv__(self, y):
-1138        if isinstance(y, Corr):
-1139            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
-1140                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
-1141            newcontent = []
-1142            for t in range(self.T):
-1143                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
-1144                    newcontent.append(None)
-1145                else:
-1146                    newcontent.append(self.content[t] / y.content[t])
-1147            for t in range(self.T):
-1148                if _check_for_none(self, newcontent[t]):
-1149                    continue
-1150                if np.isnan(np.sum(newcontent[t]).value):
-1151                    newcontent[t] = None
-1152
-1153            if all([item is None for item in newcontent]):
-1154                raise Exception("Division returns completely undefined correlator")
+1050    def __str__(self):
+1051        return self.__repr__()
+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
+1059
+1060    def __add__(self, y):
+1061        if isinstance(y, Corr):
+1062            if ((self.N != y.N) or (self.T != y.T)):
+1063                raise Exception("Addition of Corrs with different shape")
+1064            newcontent = []
+1065            for t in range(self.T):
+1066                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
+1067                    newcontent.append(None)
+1068                else:
+1069                    newcontent.append(self.content[t] + y.content[t])
+1070            return Corr(newcontent)
+1071
+1072        elif isinstance(y, (Obs, int, float, CObs)):
+1073            newcontent = []
+1074            for t in range(self.T):
+1075                if _check_for_none(self, self.content[t]):
+1076                    newcontent.append(None)
+1077                else:
+1078                    newcontent.append(self.content[t] + y)
+1079            return Corr(newcontent, prange=self.prange)
+1080        elif isinstance(y, np.ndarray):
+1081            if y.shape == (self.T,):
+1082                return Corr(list((np.array(self.content).T + y).T))
+1083            else:
+1084                raise ValueError("operands could not be broadcast together")
+1085        else:
+1086            raise TypeError("Corr + wrong type")
+1087
+1088    def __mul__(self, y):
+1089        if isinstance(y, Corr):
+1090            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
+1091                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
+1092            newcontent = []
+1093            for t in range(self.T):
+1094                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
+1095                    newcontent.append(None)
+1096                else:
+1097                    newcontent.append(self.content[t] * y.content[t])
+1098            return Corr(newcontent)
+1099
+1100        elif isinstance(y, (Obs, int, float, CObs)):
+1101            newcontent = []
+1102            for t in range(self.T):
+1103                if _check_for_none(self, self.content[t]):
+1104                    newcontent.append(None)
+1105                else:
+1106                    newcontent.append(self.content[t] * y)
+1107            return Corr(newcontent, prange=self.prange)
+1108        elif isinstance(y, np.ndarray):
+1109            if y.shape == (self.T,):
+1110                return Corr(list((np.array(self.content).T * y).T))
+1111            else:
+1112                raise ValueError("operands could not be broadcast together")
+1113        else:
+1114            raise TypeError("Corr * wrong type")
+1115
+1116    def __matmul__(self, y):
+1117        if isinstance(y, np.ndarray):
+1118            if y.ndim != 2 or y.shape[0] != y.shape[1]:
+1119                raise ValueError("Can only multiply correlators by square matrices.")
+1120            if not self.N == y.shape[0]:
+1121                raise ValueError("matmul: mismatch of matrix dimensions")
+1122            newcontent = []
+1123            for t in range(self.T):
+1124                if _check_for_none(self, self.content[t]):
+1125                    newcontent.append(None)
+1126                else:
+1127                    newcontent.append(self.content[t] @ y)
+1128            return Corr(newcontent)
+1129        elif isinstance(y, Corr):
+1130            if not self.N == y.N:
+1131                raise ValueError("matmul: mismatch of matrix dimensions")
+1132            newcontent = []
+1133            for t in range(self.T):
+1134                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
+1135                    newcontent.append(None)
+1136                else:
+1137                    newcontent.append(self.content[t] @ y.content[t])
+1138            return Corr(newcontent)
+1139
+1140        else:
+1141            return NotImplemented
+1142
+1143    def __rmatmul__(self, y):
+1144        if isinstance(y, np.ndarray):
+1145            if y.ndim != 2 or y.shape[0] != y.shape[1]:
+1146                raise ValueError("Can only multiply correlators by square matrices.")
+1147            if not self.N == y.shape[0]:
+1148                raise ValueError("matmul: mismatch of matrix dimensions")
+1149            newcontent = []
+1150            for t in range(self.T):
+1151                if _check_for_none(self, self.content[t]):
+1152                    newcontent.append(None)
+1153                else:
+1154                    newcontent.append(y @ self.content[t])
 1155            return Corr(newcontent)
-1156
-1157        elif isinstance(y, (Obs, CObs)):
-1158            if isinstance(y, Obs):
-1159                if y.value == 0:
-1160                    raise Exception('Division by zero will return undefined correlator')
-1161            if isinstance(y, CObs):
-1162                if y.is_zero():
-1163                    raise Exception('Division by zero will return undefined correlator')
-1164
-1165            newcontent = []
-1166            for t in range(self.T):
-1167                if _check_for_none(self, self.content[t]):
-1168                    newcontent.append(None)
-1169                else:
-1170                    newcontent.append(self.content[t] / y)
-1171            return Corr(newcontent, prange=self.prange)
-1172
-1173        elif isinstance(y, (int, float)):
-1174            if y == 0:
-1175                raise Exception('Division by zero will return undefined correlator')
-1176            newcontent = []
-1177            for t in range(self.T):
-1178                if _check_for_none(self, self.content[t]):
-1179                    newcontent.append(None)
-1180                else:
-1181                    newcontent.append(self.content[t] / y)
-1182            return Corr(newcontent, prange=self.prange)
-1183        elif isinstance(y, np.ndarray):
-1184            if y.shape == (self.T,):
-1185                return Corr(list((np.array(self.content).T / y).T))
-1186            else:
-1187                raise ValueError("operands could not be broadcast together")
-1188        else:
-1189            raise TypeError('Corr / wrong type')
-1190
-1191    def __neg__(self):
-1192        newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content]
-1193        return Corr(newcontent, prange=self.prange)
+1156        else:
+1157            return NotImplemented
+1158
+1159    def __truediv__(self, y):
+1160        if isinstance(y, Corr):
+1161            if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T):
+1162                raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T")
+1163            newcontent = []
+1164            for t in range(self.T):
+1165                if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]):
+1166                    newcontent.append(None)
+1167                else:
+1168                    newcontent.append(self.content[t] / y.content[t])
+1169            for t in range(self.T):
+1170                if _check_for_none(self, newcontent[t]):
+1171                    continue
+1172                if np.isnan(np.sum(newcontent[t]).value):
+1173                    newcontent[t] = None
+1174
+1175            if all([item is None for item in newcontent]):
+1176                raise Exception("Division returns completely undefined correlator")
+1177            return Corr(newcontent)
+1178
+1179        elif isinstance(y, (Obs, CObs)):
+1180            if isinstance(y, Obs):
+1181                if y.value == 0:
+1182                    raise Exception('Division by zero will return undefined correlator')
+1183            if isinstance(y, CObs):
+1184                if y.is_zero():
+1185                    raise Exception('Division by zero will return undefined correlator')
+1186
+1187            newcontent = []
+1188            for t in range(self.T):
+1189                if _check_for_none(self, self.content[t]):
+1190                    newcontent.append(None)
+1191                else:
+1192                    newcontent.append(self.content[t] / y)
+1193            return Corr(newcontent, prange=self.prange)
 1194
-1195    def __sub__(self, y):
-1196        return self + (-y)
-1197
-1198    def __pow__(self, y):
-1199        if isinstance(y, (Obs, int, float, CObs)):
-1200            newcontent = [None if _check_for_none(self, item) else item**y for item in self.content]
-1201            return Corr(newcontent, prange=self.prange)
-1202        else:
-1203            raise TypeError('Type of exponent not supported')
-1204
-1205    def __abs__(self):
-1206        newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content]
-1207        return Corr(newcontent, prange=self.prange)
-1208
-1209    # The numpy functions:
-1210    def sqrt(self):
-1211        return self ** 0.5
+1195        elif isinstance(y, (int, float)):
+1196            if y == 0:
+1197                raise Exception('Division by zero will return undefined correlator')
+1198            newcontent = []
+1199            for t in range(self.T):
+1200                if _check_for_none(self, self.content[t]):
+1201                    newcontent.append(None)
+1202                else:
+1203                    newcontent.append(self.content[t] / y)
+1204            return Corr(newcontent, prange=self.prange)
+1205        elif isinstance(y, np.ndarray):
+1206            if y.shape == (self.T,):
+1207                return Corr(list((np.array(self.content).T / y).T))
+1208            else:
+1209                raise ValueError("operands could not be broadcast together")
+1210        else:
+1211            raise TypeError('Corr / wrong type')
 1212
-1213    def log(self):
-1214        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1213    def __neg__(self):
+1214        newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content]
 1215        return Corr(newcontent, prange=self.prange)
 1216
-1217    def exp(self):
-1218        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1219        return Corr(newcontent, prange=self.prange)
-1220
-1221    def _apply_func_to_corr(self, func):
-1222        newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content]
-1223        for t in range(self.T):
-1224            if _check_for_none(self, newcontent[t]):
-1225                continue
-1226            tmp_sum = np.sum(newcontent[t])
-1227            if hasattr(tmp_sum, "value"):
-1228                if np.isnan(tmp_sum.value):
-1229                    newcontent[t] = None
-1230        if all([item is None for item in newcontent]):
-1231            raise Exception('Operation returns undefined correlator')
-1232        return Corr(newcontent)
-1233
-1234    def sin(self):
-1235        return self._apply_func_to_corr(np.sin)
-1236
-1237    def cos(self):
-1238        return self._apply_func_to_corr(np.cos)
-1239
-1240    def tan(self):
-1241        return self._apply_func_to_corr(np.tan)
+1217    def __sub__(self, y):
+1218        return self + (-y)
+1219
+1220    def __pow__(self, y):
+1221        if isinstance(y, (Obs, int, float, CObs)):
+1222            newcontent = [None if _check_for_none(self, item) else item**y for item in self.content]
+1223            return Corr(newcontent, prange=self.prange)
+1224        else:
+1225            raise TypeError('Type of exponent not supported')
+1226
+1227    def __abs__(self):
+1228        newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content]
+1229        return Corr(newcontent, prange=self.prange)
+1230
+1231    # The numpy functions:
+1232    def sqrt(self):
+1233        return self ** 0.5
+1234
+1235    def log(self):
+1236        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1237        return Corr(newcontent, prange=self.prange)
+1238
+1239    def exp(self):
+1240        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1241        return Corr(newcontent, prange=self.prange)
 1242
-1243    def sinh(self):
-1244        return self._apply_func_to_corr(np.sinh)
-1245
-1246    def cosh(self):
-1247        return self._apply_func_to_corr(np.cosh)
-1248
-1249    def tanh(self):
-1250        return self._apply_func_to_corr(np.tanh)
-1251
-1252    def arcsin(self):
-1253        return self._apply_func_to_corr(np.arcsin)
-1254
-1255    def arccos(self):
-1256        return self._apply_func_to_corr(np.arccos)
-1257
-1258    def arctan(self):
-1259        return self._apply_func_to_corr(np.arctan)
-1260
-1261    def arcsinh(self):
-1262        return self._apply_func_to_corr(np.arcsinh)
-1263
-1264    def arccosh(self):
-1265        return self._apply_func_to_corr(np.arccosh)
-1266
-1267    def arctanh(self):
-1268        return self._apply_func_to_corr(np.arctanh)
-1269
-1270    # Right hand side operations (require tweak in main module to work)
-1271    def __radd__(self, y):
-1272        return self + y
+1243    def _apply_func_to_corr(self, func):
+1244        newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content]
+1245        for t in range(self.T):
+1246            if _check_for_none(self, newcontent[t]):
+1247                continue
+1248            tmp_sum = np.sum(newcontent[t])
+1249            if hasattr(tmp_sum, "value"):
+1250                if np.isnan(tmp_sum.value):
+1251                    newcontent[t] = None
+1252        if all([item is None for item in newcontent]):
+1253            raise Exception('Operation returns undefined correlator')
+1254        return Corr(newcontent)
+1255
+1256    def sin(self):
+1257        return self._apply_func_to_corr(np.sin)
+1258
+1259    def cos(self):
+1260        return self._apply_func_to_corr(np.cos)
+1261
+1262    def tan(self):
+1263        return self._apply_func_to_corr(np.tan)
+1264
+1265    def sinh(self):
+1266        return self._apply_func_to_corr(np.sinh)
+1267
+1268    def cosh(self):
+1269        return self._apply_func_to_corr(np.cosh)
+1270
+1271    def tanh(self):
+1272        return self._apply_func_to_corr(np.tanh)
 1273
-1274    def __rsub__(self, y):
-1275        return -self + y
+1274    def arcsin(self):
+1275        return self._apply_func_to_corr(np.arcsin)
 1276
-1277    def __rmul__(self, y):
-1278        return self * y
+1277    def arccos(self):
+1278        return self._apply_func_to_corr(np.arccos)
 1279
-1280    def __rtruediv__(self, y):
-1281        return (self / y) ** (-1)
+1280    def arctan(self):
+1281        return self._apply_func_to_corr(np.arctan)
 1282
-1283    @property
-1284    def real(self):
-1285        def return_real(obs_OR_cobs):
-1286            if isinstance(obs_OR_cobs.flatten()[0], CObs):
-1287                return np.vectorize(lambda x: x.real)(obs_OR_cobs)
-1288            else:
-1289                return obs_OR_cobs
-1290
-1291        return self._apply_func_to_corr(return_real)
-1292
-1293    @property
-1294    def imag(self):
-1295        def return_imag(obs_OR_cobs):
-1296            if isinstance(obs_OR_cobs.flatten()[0], CObs):
-1297                return np.vectorize(lambda x: x.imag)(obs_OR_cobs)
-1298            else:
-1299                return obs_OR_cobs * 0  # So it stays the right type
-1300
-1301        return self._apply_func_to_corr(return_imag)
-1302
-1303    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1304        r''' Project large correlation matrix to lowest states
-1305
-1306        This method can be used to reduce the size of an (N x N) correlation matrix
-1307        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1308        is still small.
-1309
-1310        Parameters
-1311        ----------
-1312        Ntrunc: int
-1313            Rank of the target matrix.
-1314        tproj: int
-1315            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1316            The default value is 3.
-1317        t0proj: int
-1318            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1319            discouraged for O(a) improved theories, since the correctness of the procedure
-1320            cannot be granted in this case. The default value is 2.
-1321        basematrix : Corr
-1322            Correlation matrix that is used to determine the eigenvectors of the
-1323            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1324            is is not specified.
-1325
-1326        Notes
-1327        -----
-1328        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1329        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1330        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1331        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1332        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1333        correlation matrix and to remove some noise that is added by irrelevant operators.
-1334        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1335        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1336        '''
-1337
-1338        if self.N == 1:
-1339            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1340        if basematrix is None:
-1341            basematrix = self
-1342        if Ntrunc >= basematrix.N:
-1343            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1344        if basematrix.N != self.N:
-1345            raise Exception('basematrix and targetmatrix have to be of the same size.')
-1346
-1347        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1348
-1349        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1350        rmat = []
-1351        for t in range(basematrix.T):
-1352            for i in range(Ntrunc):
-1353                for j in range(Ntrunc):
-1354                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1355            rmat.append(np.copy(tmpmat))
-1356
-1357        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1358        return Corr(newcontent)
+1283    def arcsinh(self):
+1284        return self._apply_func_to_corr(np.arcsinh)
+1285
+1286    def arccosh(self):
+1287        return self._apply_func_to_corr(np.arccosh)
+1288
+1289    def arctanh(self):
+1290        return self._apply_func_to_corr(np.arctanh)
+1291
+1292    # Right hand side operations (require tweak in main module to work)
+1293    def __radd__(self, y):
+1294        return self + y
+1295
+1296    def __rsub__(self, y):
+1297        return -self + y
+1298
+1299    def __rmul__(self, y):
+1300        return self * y
+1301
+1302    def __rtruediv__(self, y):
+1303        return (self / y) ** (-1)
+1304
+1305    @property
+1306    def real(self):
+1307        def return_real(obs_OR_cobs):
+1308            if isinstance(obs_OR_cobs.flatten()[0], CObs):
+1309                return np.vectorize(lambda x: x.real)(obs_OR_cobs)
+1310            else:
+1311                return obs_OR_cobs
+1312
+1313        return self._apply_func_to_corr(return_real)
+1314
+1315    @property
+1316    def imag(self):
+1317        def return_imag(obs_OR_cobs):
+1318            if isinstance(obs_OR_cobs.flatten()[0], CObs):
+1319                return np.vectorize(lambda x: x.imag)(obs_OR_cobs)
+1320            else:
+1321                return obs_OR_cobs * 0  # So it stays the right type
+1322
+1323        return self._apply_func_to_corr(return_imag)
+1324
+1325    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1326        r''' Project large correlation matrix to lowest states
+1327
+1328        This method can be used to reduce the size of an (N x N) correlation matrix
+1329        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1330        is still small.
+1331
+1332        Parameters
+1333        ----------
+1334        Ntrunc: int
+1335            Rank of the target matrix.
+1336        tproj: int
+1337            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1338            The default value is 3.
+1339        t0proj: int
+1340            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1341            discouraged for O(a) improved theories, since the correctness of the procedure
+1342            cannot be granted in this case. The default value is 2.
+1343        basematrix : Corr
+1344            Correlation matrix that is used to determine the eigenvectors of the
+1345            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1346            is is not specified.
+1347
+1348        Notes
+1349        -----
+1350        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1351        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1352        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1353        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1354        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1355        correlation matrix and to remove some noise that is added by irrelevant operators.
+1356        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1357        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1358        '''
+1359
+1360        if self.N == 1:
+1361            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1362        if basematrix is None:
+1363            basematrix = self
+1364        if Ntrunc >= basematrix.N:
+1365            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1366        if basematrix.N != self.N:
+1367            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1368
+1369        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1370
+1371        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1372        rmat = []
+1373        for t in range(basematrix.T):
+1374            for i in range(Ntrunc):
+1375                for j in range(Ntrunc):
+1376                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1377            rmat.append(np.copy(tmpmat))
+1378
+1379        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1380        return Corr(newcontent)
 
@@ -3009,8 +3053,31 @@ But it is simply more convenient to have a dedicated object for correlators. One often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient to iterate over all timeslices for every operation. This is especially true, when dealing with matrices.

-

The correlator can have two types of content: An Obs at every timeslice OR a GEVP -matrix at every timeslice. Other dependency (eg. spatial) are not supported.

+

The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice. +Other dependency (eg. spatial) are not supported.

+ +

The Corr class can also deal with missing measurements or paddings for fixed boundary conditions. +The missing entries are represented via the None object.

+ +
Initialization
+ +

A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs

+ +
+
corr11 = pe.Corr([obs1, obs2])
+corr11 = pe.Corr(np.array([obs1, obs2]))
+
+
+ +

A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects

+ +
+
matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))
+
+
+ +

or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is +the temporal extent of the correlator and N is the dimension of the matrix.

@@ -3024,76 +3091,82 @@ matrix at every timeslice. Other dependency (eg. spatial) are not supported.

-
29    def __init__(self, data_input, padding=[0, 0], prange=None):
-30        """ Initialize a Corr object.
-31
-32        Parameters
-33        ----------
-34        data_input : list or array
-35            list of Obs or list of arrays of Obs or array of Corrs
-36        padding : list, optional
-37            List with two entries where the first labels the padding
-38            at the front of the correlator and the second the padding
-39            at the back.
-40        prange : list, optional
-41            List containing the first and last timeslice of the plateau
-42            region indentified for this correlator.
-43        """
-44
-45        if isinstance(data_input, np.ndarray):
-46
-47            # This only works, if the array fulfills the conditions below
-48            if not len(data_input.shape) == 2 and data_input.shape[0] == data_input.shape[1]:
-49                raise Exception("Incompatible array shape")
-50            if not all([isinstance(item, Corr) for item in data_input.flatten()]):
-51                raise Exception("If the input is an array, its elements must be of type pe.Corr")
-52            if not all([item.N == 1 for item in data_input.flatten()]):
-53                raise Exception("Can only construct matrix correlator from single valued correlators")
-54            if not len(set([item.T for item in data_input.flatten()])) == 1:
-55                raise Exception("All input Correlators must be defined over the same timeslices.")
-56
-57            T = data_input[0, 0].T
-58            N = data_input.shape[0]
-59            input_as_list = []
-60            for t in range(T):
-61                if any([(item.content[t] is None) for item in data_input.flatten()]):
-62                    if not all([(item.content[t] is None) for item in data_input.flatten()]):
-63                        warnings.warn("Input ill-defined at different timeslices. Conversion leads to data loss!", RuntimeWarning)
-64                    input_as_list.append(None)
-65                else:
-66                    array_at_timeslace = np.empty([N, N], dtype="object")
-67                    for i in range(N):
-68                        for j in range(N):
-69                            array_at_timeslace[i, j] = data_input[i, j][t]
-70                    input_as_list.append(array_at_timeslace)
-71            data_input = input_as_list
-72
-73        if isinstance(data_input, list):
-74
-75            if all([isinstance(item, (Obs, CObs)) or item is None for item in data_input]):
-76                _assert_equal_properties([o for o in data_input if o is not None])
-77                self.content = [np.asarray([item]) if item is not None else None for item in data_input]
-78                self.N = 1
-79
-80            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]):
-81                self.content = data_input
-82                noNull = [a for a in self.content if not (a is None)]  # To check if the matrices are correct for all undefined elements
-83                self.N = noNull[0].shape[0]
-84                if self.N > 1 and noNull[0].shape[0] != noNull[0].shape[1]:
-85                    raise Exception("Smearing matrices are not NxN")
-86                if (not all([item.shape == noNull[0].shape for item in noNull])):
-87                    raise Exception("Items in data_input are not of identical shape." + str(noNull))
-88            else:
-89                raise Exception("data_input contains item of wrong type")
-90        else:
-91            raise Exception("Data input was not given as list or correct array")
-92
-93        self.tag = None
-94
-95        # An undefined timeslice is represented by the None object
-96        self.content = [None] * padding[0] + self.content + [None] * padding[1]
-97        self.T = len(self.content)
-98        self.prange = prange
+            
 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
 
@@ -3103,14 +3176,14 @@ matrix at every timeslice. Other dependency (eg. spatial) are not supported.

  • data_input (list or array): -list of Obs or list of arrays of Obs or array of Corrs
  • +list of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
  • padding (list, optional): List with two entries where the first labels the padding at the front of the correlator and the second the padding at the back.
  • prange (list, optional): List containing the first and last timeslice of the plateau -region indentified for this correlator.
  • +region identified for this correlator.
@@ -3182,16 +3255,16 @@ region indentified for this correlator. -
119    def gamma_method(self, **kwargs):
-120        """Apply the gamma method to the content of the Corr."""
-121        for item in self.content:
-122            if not (item is None):
-123                if self.N == 1:
-124                    item[0].gamma_method(**kwargs)
-125                else:
-126                    for i in range(self.N):
-127                        for j in range(self.N):
-128                            item[i, j].gamma_method(**kwargs)
+            
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)
 
@@ -3211,16 +3284,16 @@ region indentified for this correlator.
-
119    def gamma_method(self, **kwargs):
-120        """Apply the gamma method to the content of the Corr."""
-121        for item in self.content:
-122            if not (item is None):
-123                if self.N == 1:
-124                    item[0].gamma_method(**kwargs)
-125                else:
-126                    for i in range(self.N):
-127                        for j in range(self.N):
-128                            item[i, j].gamma_method(**kwargs)
+            
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)
 
@@ -3240,44 +3313,44 @@ region indentified for this correlator.
-
132    def projected(self, vector_l=None, vector_r=None, normalize=False):
-133        """We need to project the Correlator with a Vector to get a single value at each timeslice.
-134
-135        The method can use one or two vectors.
-136        If two are specified it returns v1@G@v2 (the order might be very important.)
-137        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
-138        """
-139        if self.N == 1:
-140            raise Exception("Trying to project a Corr, that already has N=1.")
-141
-142        if vector_l is None:
-143            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
-144        elif (vector_r is None):
-145            vector_r = vector_l
-146        if isinstance(vector_l, list) and not isinstance(vector_r, list):
-147            if len(vector_l) != self.T:
-148                raise Exception("Length of vector list must be equal to T")
-149            vector_r = [vector_r] * self.T
-150        if isinstance(vector_r, list) and not isinstance(vector_l, list):
-151            if len(vector_r) != self.T:
-152                raise Exception("Length of vector list must be equal to T")
-153            vector_l = [vector_l] * self.T
-154
-155        if not isinstance(vector_l, list):
-156            if not vector_l.shape == vector_r.shape == (self.N,):
-157                raise Exception("Vectors are of wrong shape!")
-158            if normalize:
-159                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
-160            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
-161
-162        else:
-163            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
-164            if normalize:
-165                for t in range(self.T):
-166                    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])
-167
-168            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)]
-169        return Corr(newcontent)
+            
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)
 
@@ -3301,20 +3374,20 @@ By default it will return the lowest source, which usually means unsmeared-unsme
-
171    def item(self, i, j):
-172        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
-173
-174        Parameters
-175        ----------
-176        i : int
-177            First index to be picked.
-178        j : int
-179            Second index to be picked.
-180        """
-181        if self.N == 1:
-182            raise Exception("Trying to pick item from projected Corr")
-183        newcontent = [None if (item is None) else item[i, j] for item in self.content]
-184        return Corr(newcontent)
+            
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)
 
@@ -3343,19 +3416,19 @@ Second index to be picked.
-
186    def plottable(self):
-187        """Outputs the correlator in a plotable format.
-188
-189        Outputs three lists containing the timeslice index, the value on each
-190        timeslice and the error on each timeslice.
-191        """
-192        if self.N != 1:
-193            raise Exception("Can only make Corr[N=1] plottable")
-194        x_list = [x for x in range(self.T) if not self.content[x] is None]
-195        y_list = [y[0].value for y in self.content if y is not None]
-196        y_err_list = [y[0].dvalue for y in self.content if y is not None]
-197
-198        return x_list, y_list, y_err_list
+            
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
 
@@ -3378,26 +3451,26 @@ timeslice and the error on each timeslice.

-
200    def symmetric(self):
-201        """ Symmetrize the correlator around x0=0."""
-202        if self.N != 1:
-203            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
-204        if self.T % 2 != 0:
-205            raise Exception("Can not symmetrize odd T")
-206
-207        if self.content[0] is not None:
-208            if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0:
-209                warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
-210
-211        newcontent = [self.content[0]]
-212        for t in range(1, self.T):
-213            if (self.content[t] is None) or (self.content[self.T - t] is None):
-214                newcontent.append(None)
-215            else:
-216                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
-217        if (all([x is None for x in newcontent])):
-218            raise Exception("Corr could not be symmetrized: No redundant values")
-219        return Corr(newcontent, prange=self.prange)
+            
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)
 
@@ -3417,27 +3490,27 @@ timeslice and the error on each timeslice.

-
221    def anti_symmetric(self):
-222        """Anti-symmetrize the correlator around x0=0."""
-223        if self.N != 1:
-224            raise TypeError('anti_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        test = 1 * self
-229        test.gamma_method()
-230        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
-231            warnings.warn("Correlator does not seem to be anti-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)
+            
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)
 
@@ -3457,20 +3530,20 @@ timeslice and the error on each timeslice.

-
243    def is_matrix_symmetric(self):
-244        """Checks whether a correlator matrices is symmetric on every timeslice."""
-245        if self.N == 1:
-246            raise TypeError("Only works for correlator matrices.")
-247        for t in range(self.T):
-248            if self[t] is None:
-249                continue
-250            for i in range(self.N):
-251                for j in range(i + 1, self.N):
-252                    if self[t][i, j] is self[t][j, i]:
-253                        continue
-254                    if hash(self[t][i, j]) != hash(self[t][j, i]):
-255                        return False
-256        return True
+            
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
 
@@ -3490,17 +3563,17 @@ timeslice and the error on each timeslice.

-
258    def trace(self):
-259        """Calculates the per-timeslice trace of a correlator matrix."""
-260        if self.N == 1:
-261            raise ValueError("Only works for correlator matrices.")
-262        newcontent = []
-263        for t in range(self.T):
-264            if _check_for_none(self, self.content[t]):
-265                newcontent.append(None)
-266            else:
-267                newcontent.append(np.trace(self.content[t]))
-268        return Corr(newcontent)
+            
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)
 
@@ -3520,15 +3593,15 @@ timeslice and the error on each timeslice.

-
270    def matrix_symmetric(self):
-271        """Symmetrizes the correlator matrices on every timeslice."""
-272        if self.N == 1:
-273            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
-274        if self.is_matrix_symmetric():
-275            return 1.0 * self
-276        else:
-277            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
-278            return 0.5 * (Corr(transposed) + self)
+            
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)
 
@@ -3548,84 +3621,84 @@ timeslice and the error on each timeslice.

-
280    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
-281        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
-282
-283        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
-284        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
-285        ```python
-286        C.GEVP(t0=2)[0]  # Ground state vector(s)
-287        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
-288        ```
-289
-290        Parameters
-291        ----------
-292        t0 : int
-293            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
-294        ts : int
-295            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
-296            If sort="Eigenvector" it gives a reference point for the sorting method.
-297        sort : string
-298            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.
-299            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-300            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
-301              The reference state is identified by its eigenvalue at $t=t_s$.
-302
-303        Other Parameters
-304        ----------------
-305        state : int
-306           Returns only the vector(s) for a specified state. The lowest state is zero.
-307        '''
-308
-309        if self.N == 1:
-310            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
-311        if ts is not None:
-312            if (ts <= t0):
-313                raise Exception("ts has to be larger than t0.")
-314
-315        if "sorted_list" in kwargs:
-316            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
-317            sort = kwargs.get("sorted_list")
-318
-319        if self.is_matrix_symmetric():
-320            symmetric_corr = self
-321        else:
-322            symmetric_corr = self.matrix_symmetric()
-323
-324        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
-325        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
-326
-327        if sort is None:
-328            if (ts is None):
-329                raise Exception("ts is required if sort=None.")
-330            if (self.content[t0] is None) or (self.content[ts] is None):
-331                raise Exception("Corr not defined at t0/ts.")
-332            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
-333            reordered_vecs = _GEVP_solver(Gt, G0)
-334
-335        elif sort in ["Eigenvalue", "Eigenvector"]:
-336            if sort == "Eigenvalue" and ts is not None:
-337                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
-338            all_vecs = [None] * (t0 + 1)
-339            for t in range(t0 + 1, self.T):
-340                try:
-341                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
-342                    all_vecs.append(_GEVP_solver(Gt, G0))
-343                except Exception:
-344                    all_vecs.append(None)
-345            if sort == "Eigenvector":
-346                if ts is None:
-347                    raise Exception("ts is required for the Eigenvector sorting method.")
-348                all_vecs = _sort_vectors(all_vecs, ts)
-349
-350            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
-351        else:
-352            raise Exception("Unkown value for 'sort'.")
-353
-354        if "state" in kwargs:
-355            return reordered_vecs[kwargs.get("state")]
-356        else:
-357            return reordered_vecs
+            
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.
+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
 
@@ -3678,18 +3751,18 @@ Returns only the vector(s) for a specified state. The lowest state is zero.
-
359    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
-360        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
-361
-362        Parameters
-363        ----------
-364        state : int
-365            The state one is interested in ordered by energy. The lowest state is zero.
-366
-367        All other parameters are identical to the ones of Corr.GEVP.
-368        """
-369        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
-370        return self.projected(vec)
+            
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)
 
@@ -3717,46 +3790,46 @@ The state one is interested in ordered by energy. The lowest state is zero.
-
372    def Hankel(self, N, periodic=False):
-373        """Constructs an NxN Hankel matrix
-374
-375        C(t) c(t+1) ... c(t+n-1)
-376        C(t+1) c(t+2) ... c(t+n)
-377        .................
-378        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
-379
-380        Parameters
-381        ----------
-382        N : int
-383            Dimension of the Hankel matrix
-384        periodic : bool, optional
-385            determines whether the matrix is extended periodically
-386        """
-387
-388        if self.N != 1:
-389            raise Exception("Multi-operator Prony not implemented!")
-390
-391        array = np.empty([N, N], dtype="object")
-392        new_content = []
-393        for t in range(self.T):
-394            new_content.append(array.copy())
-395
-396        def wrap(i):
-397            while i >= self.T:
-398                i -= self.T
-399            return i
-400
-401        for t in range(self.T):
-402            for i in range(N):
-403                for j in range(N):
-404                    if periodic:
-405                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
-406                    elif (t + i + j) >= self.T:
-407                        new_content[t] = None
-408                    else:
-409                        new_content[t][i, j] = self.content[t + i + j][0]
-410
-411        return Corr(new_content)
+            
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)
 
@@ -3790,15 +3863,15 @@ determines whether the matrix is extended periodically
-
413    def roll(self, dt):
-414        """Periodically shift the correlator by dt timeslices
-415
-416        Parameters
-417        ----------
-418        dt : int
-419            number of timeslices
-420        """
-421        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
+            
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)))
 
@@ -3825,9 +3898,9 @@ number of timeslices
-
423    def reverse(self):
-424        """Reverse the time ordering of the Corr"""
-425        return Corr(self.content[:: -1])
+            
445    def reverse(self):
+446        """Reverse the time ordering of the Corr"""
+447        return Corr(self.content[:: -1])
 
@@ -3847,23 +3920,23 @@ number of timeslices
-
427    def thin(self, spacing=2, offset=0):
-428        """Thin out a correlator to suppress correlations
-429
-430        Parameters
-431        ----------
-432        spacing : int
-433            Keep only every 'spacing'th entry of the correlator
-434        offset : int
-435            Offset the equal spacing
-436        """
-437        new_content = []
-438        for t in range(self.T):
-439            if (offset + t) % spacing != 0:
-440                new_content.append(None)
-441            else:
-442                new_content.append(self.content[t])
-443        return Corr(new_content)
+            
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)
 
@@ -3892,34 +3965,34 @@ Offset the equal spacing
-
445    def correlate(self, partner):
-446        """Correlate the correlator with another correlator or Obs
-447
-448        Parameters
-449        ----------
-450        partner : Obs or Corr
-451            partner to correlate the correlator with.
-452            Can either be an Obs which is correlated with all entries of the
-453            correlator or a Corr of same length.
-454        """
-455        if self.N != 1:
-456            raise Exception("Only one-dimensional correlators can be safely correlated.")
-457        new_content = []
-458        for x0, t_slice in enumerate(self.content):
-459            if _check_for_none(self, t_slice):
-460                new_content.append(None)
-461            else:
-462                if isinstance(partner, Corr):
-463                    if _check_for_none(partner, partner.content[x0]):
-464                        new_content.append(None)
-465                    else:
-466                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
-467                elif isinstance(partner, Obs):  # Should this include CObs?
-468                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
-469                else:
-470                    raise Exception("Can only correlate with an Obs or a Corr.")
-471
-472        return Corr(new_content)
+            
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)
 
@@ -3948,28 +4021,28 @@ correlator or a Corr of same length.
-
474    def reweight(self, weight, **kwargs):
-475        """Reweight the correlator.
-476
-477        Parameters
-478        ----------
-479        weight : Obs
-480            Reweighting factor. An Observable that has to be defined on a superset of the
-481            configurations in obs[i].idl for all i.
-482        all_configs : bool
-483            if True, the reweighted observables are normalized by the average of
-484            the reweighting factor on all configurations in weight.idl and not
-485            on the configurations in obs[i].idl.
-486        """
-487        if self.N != 1:
-488            raise Exception("Reweighting only implemented for one-dimensional correlators.")
-489        new_content = []
-490        for t_slice in self.content:
-491            if _check_for_none(self, t_slice):
-492                new_content.append(None)
-493            else:
-494                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
-495        return Corr(new_content)
+            
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)
 
@@ -4001,35 +4074,35 @@ on the configurations in obs[i].idl.
-
497    def T_symmetry(self, partner, parity=+1):
-498        """Return the time symmetry average of the correlator and its partner
-499
-500        Parameters
-501        ----------
-502        partner : Corr
-503            Time symmetry partner of the Corr
-504        partity : int
-505            Parity quantum number of the correlator, can be +1 or -1
-506        """
-507        if self.N != 1:
-508            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
-509        if not isinstance(partner, Corr):
-510            raise Exception("T partner has to be a Corr object.")
-511        if parity not in [+1, -1]:
-512            raise Exception("Parity has to be +1 or -1.")
-513        T_partner = parity * partner.reverse()
-514
-515        t_slices = []
-516        test = (self - T_partner)
-517        test.gamma_method()
-518        for x0, t_slice in enumerate(test.content):
-519            if t_slice is not None:
-520                if not t_slice[0].is_zero_within_error(5):
-521                    t_slices.append(x0)
-522        if t_slices:
-523            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
-524
-525        return (self + T_partner) / 2
+            
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
 
@@ -4040,7 +4113,7 @@ on the configurations in obs[i].idl.
  • partner (Corr): Time symmetry partner of the Corr
  • -
  • partity (int): +
  • parity (int): Parity quantum number of the correlator, can be +1 or -1
@@ -4058,70 +4131,70 @@ Parity quantum number of the correlator, can be +1 or -1 -
527    def deriv(self, variant="symmetric"):
-528        """Return the first derivative of the correlator with respect to x0.
-529
-530        Parameters
-531        ----------
-532        variant : str
-533            decides which definition of the finite differences derivative is used.
-534            Available choice: symmetric, forward, backward, improved, log, default: symmetric
-535        """
-536        if self.N != 1:
-537            raise Exception("deriv only implemented for one-dimensional correlators.")
-538        if variant == "symmetric":
-539            newcontent = []
-540            for t in range(1, self.T - 1):
-541                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-542                    newcontent.append(None)
-543                else:
-544                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
-545            if (all([x is None for x in newcontent])):
-546                raise Exception('Derivative is undefined at all timeslices')
-547            return Corr(newcontent, padding=[1, 1])
-548        elif variant == "forward":
-549            newcontent = []
-550            for t in range(self.T - 1):
-551                if (self.content[t] is None) or (self.content[t + 1] is None):
-552                    newcontent.append(None)
-553                else:
-554                    newcontent.append(self.content[t + 1] - self.content[t])
-555            if (all([x is None for x in newcontent])):
-556                raise Exception("Derivative is undefined at all timeslices")
-557            return Corr(newcontent, padding=[0, 1])
-558        elif variant == "backward":
-559            newcontent = []
-560            for t in range(1, self.T):
-561                if (self.content[t - 1] is None) or (self.content[t] is None):
-562                    newcontent.append(None)
-563                else:
-564                    newcontent.append(self.content[t] - self.content[t - 1])
-565            if (all([x is None for x in newcontent])):
-566                raise Exception("Derivative is undefined at all timeslices")
-567            return Corr(newcontent, padding=[1, 0])
-568        elif variant == "improved":
-569            newcontent = []
-570            for t in range(2, self.T - 2):
-571                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):
-572                    newcontent.append(None)
-573                else:
-574                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
-575            if (all([x is None for x in newcontent])):
-576                raise Exception('Derivative is undefined at all timeslices')
-577            return Corr(newcontent, padding=[2, 2])
-578        elif variant == 'log':
-579            newcontent = []
-580            for t in range(self.T):
-581                if (self.content[t] is None) or (self.content[t] <= 0):
-582                    newcontent.append(None)
-583                else:
-584                    newcontent.append(np.log(self.content[t]))
-585            if (all([x is None for x in newcontent])):
-586                raise Exception("Log is undefined at all timeslices")
-587            logcorr = Corr(newcontent)
-588            return self * logcorr.deriv('symmetric')
-589        else:
-590            raise Exception("Unknown variant.")
+            
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.")
 
@@ -4149,68 +4222,68 @@ Available choice: symmetric, forward, backward, improved, log, default: symmetri
-
592    def second_deriv(self, variant="symmetric"):
-593        r"""Return the second derivative of the correlator with respect to x0.
-594
-595        Parameters
-596        ----------
-597        variant : str
-598            decides which definition of the finite differences derivative is used.
-599            Available choice:
-600                - symmetric (default)
-601                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
-602                - big_symmetric
-603                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
-604                - improved
-605                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
-606                - log
-607                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
-608        """
-609        if self.N != 1:
-610            raise Exception("second_deriv only implemented for one-dimensional correlators.")
-611        if variant == "symmetric":
-612            newcontent = []
-613            for t in range(1, self.T - 1):
-614                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-615                    newcontent.append(None)
-616                else:
-617                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
-618            if (all([x is None for x in newcontent])):
-619                raise Exception("Derivative is undefined at all timeslices")
-620            return Corr(newcontent, padding=[1, 1])
-621        elif variant == "big_symmetric":
-622            newcontent = []
-623            for t in range(2, self.T - 2):
-624                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
-625                    newcontent.append(None)
-626                else:
-627                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
-628            if (all([x is None for x in newcontent])):
-629                raise Exception("Derivative is undefined at all timeslices")
-630            return Corr(newcontent, padding=[2, 2])
-631        elif variant == "improved":
-632            newcontent = []
-633            for t in range(2, self.T - 2):
-634                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):
-635                    newcontent.append(None)
-636                else:
-637                    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]))
-638            if (all([x is None for x in newcontent])):
-639                raise Exception("Derivative is undefined at all timeslices")
-640            return Corr(newcontent, padding=[2, 2])
-641        elif variant == 'log':
-642            newcontent = []
-643            for t in range(self.T):
-644                if (self.content[t] is None) or (self.content[t] <= 0):
-645                    newcontent.append(None)
-646                else:
-647                    newcontent.append(np.log(self.content[t]))
-648            if (all([x is None for x in newcontent])):
-649                raise Exception("Log is undefined at all timeslices")
-650            logcorr = Corr(newcontent)
-651            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
-652        else:
-653            raise Exception("Unknown variant.")
+            
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.")
 
@@ -4246,89 +4319,89 @@ Available choice:
-
655    def m_eff(self, variant='log', guess=1.0):
-656        """Returns the effective mass of the correlator as correlator object
-657
-658        Parameters
-659        ----------
-660        variant : str
-661            log : uses the standard effective mass log(C(t) / C(t+1))
-662            cosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
-663            sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
-664            See, e.g., arXiv:1205.5380
-665            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
-666            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
-667        guess : float
-668            guess for the root finder, only relevant for the root variant
-669        """
-670        if self.N != 1:
-671            raise Exception('Correlator must be projected before getting m_eff')
-672        if variant == 'log':
-673            newcontent = []
-674            for t in range(self.T - 1):
-675                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-676                    newcontent.append(None)
-677                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-678                    newcontent.append(None)
-679                else:
-680                    newcontent.append(self.content[t] / self.content[t + 1])
-681            if (all([x is None for x in newcontent])):
-682                raise Exception('m_eff is undefined at all timeslices')
-683
-684            return np.log(Corr(newcontent, padding=[0, 1]))
-685
-686        elif variant == 'logsym':
-687            newcontent = []
-688            for t in range(1, self.T - 1):
-689                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-690                    newcontent.append(None)
-691                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
-692                    newcontent.append(None)
-693                else:
-694                    newcontent.append(self.content[t - 1] / self.content[t + 1])
-695            if (all([x is None for x in newcontent])):
-696                raise Exception('m_eff is undefined at all timeslices')
-697
-698            return np.log(Corr(newcontent, padding=[1, 1])) / 2
-699
-700        elif variant in ['periodic', 'cosh', 'sinh']:
-701            if variant in ['periodic', 'cosh']:
-702                func = anp.cosh
-703            else:
-704                func = anp.sinh
+            
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            def root_function(x, d):
-707                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
-708
+706            return np.log(Corr(newcontent, padding=[0, 1]))
+707
+708        elif variant == 'logsym':
 709            newcontent = []
-710            for t in range(self.T - 1):
-711                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+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                # Fill the two timeslices in the middle of the lattice with their predecessors
-714                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
-715                    newcontent.append(newcontent[-1])
-716                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-717                    newcontent.append(None)
-718                else:
-719                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
-720            if (all([x is None for x in newcontent])):
-721                raise Exception('m_eff is undefined at all timeslices')
-722
-723            return Corr(newcontent, padding=[0, 1])
-724
-725        elif variant == 'arccosh':
-726            newcontent = []
-727            for t in range(1, self.T - 1):
-728                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):
-729                    newcontent.append(None)
-730                else:
-731                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
-732            if (all([x is None for x in newcontent])):
-733                raise Exception("m_eff is undefined at all timeslices")
-734            return np.arccosh(Corr(newcontent, padding=[1, 1]))
-735
-736        else:
-737            raise Exception('Unknown variant.')
+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.')
 
@@ -4339,8 +4412,8 @@ Available choice:
  • variant (str): log : uses the standard effective mass log(C(t) / C(t+1)) -cosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. -sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m. +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. +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. See, e.g., arXiv:1205.5380 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
  • @@ -4362,39 +4435,39 @@ guess for the root finder, only relevant for the root variant
-
739    def fit(self, function, fitrange=None, silent=False, **kwargs):
-740        r'''Fits function to the data
-741
-742        Parameters
-743        ----------
-744        function : obj
-745            function to fit to the data. See fits.least_squares for details.
-746        fitrange : list
-747            Two element list containing the timeslices on which the fit is supposed to start and stop.
-748            Caution: This range is inclusive as opposed to standard python indexing.
-749            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
-750            If not specified, self.prange or all timeslices are used.
-751        silent : bool
-752            Decides whether output is printed to the standard output.
-753        '''
-754        if self.N != 1:
-755            raise Exception("Correlator must be projected before fitting")
-756
-757        if fitrange is None:
-758            if self.prange:
-759                fitrange = self.prange
-760            else:
-761                fitrange = [0, self.T - 1]
-762        else:
-763            if not isinstance(fitrange, list):
-764                raise Exception("fitrange has to be a list with two elements")
-765            if len(fitrange) != 2:
-766                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
-767
-768        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
-769        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
-770        result = least_squares(xs, ys, function, silent=silent, **kwargs)
-771        return result
+            
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
 
@@ -4428,42 +4501,42 @@ Decides whether output is printed to the standard output.
-
773    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
-774        """ Extract a plateau value from a Corr object
-775
-776        Parameters
-777        ----------
-778        plateau_range : list
-779            list with two entries, indicating the first and the last timeslice
-780            of the plateau region.
-781        method : str
-782            method to extract the plateau.
-783                'fit' fits a constant to the plateau region
-784                'avg', 'average' or 'mean' just average over the given timeslices.
-785        auto_gamma : bool
-786            apply gamma_method with default parameters to the Corr. Defaults to None
-787        """
-788        if not plateau_range:
-789            if self.prange:
-790                plateau_range = self.prange
-791            else:
-792                raise Exception("no plateau range provided")
-793        if self.N != 1:
-794            raise Exception("Correlator must be projected before getting a plateau.")
-795        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
-796            raise Exception("plateau is undefined at all timeslices in plateaurange.")
-797        if auto_gamma:
-798            self.gamma_method()
-799        if method == "fit":
-800            def const_func(a, t):
-801                return a[0]
-802            return self.fit(const_func, plateau_range)[0]
-803        elif method in ["avg", "average", "mean"]:
-804            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
-805            return returnvalue
-806
-807        else:
-808            raise Exception("Unsupported plateau method: " + method)
+            
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)
 
@@ -4497,17 +4570,17 @@ apply gamma_method with default parameters to the Corr. Defaults to None
-
810    def set_prange(self, prange):
-811        """Sets the attribute prange of the Corr object."""
-812        if not len(prange) == 2:
-813            raise Exception("prange must be a list or array with two values")
-814        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
-815            raise Exception("Start and end point must be integers")
-816        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
-817            raise Exception("Start and end point must define a range in the interval 0,T")
-818
-819        self.prange = prange
-820        return
+            
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
 
@@ -4527,130 +4600,130 @@ apply gamma_method with default parameters to the Corr. Defaults to None
-
822    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):
-823        """Plots the correlator using the tag of the correlator as label if available.
-824
-825        Parameters
-826        ----------
-827        x_range : list
-828            list of two values, determining the range of the x-axis e.g. [4, 8].
-829        comp : Corr or list of Corr
-830            Correlator or list of correlators which are plotted for comparison.
-831            The tags of these correlators are used as labels if available.
-832        logscale : bool
-833            Sets y-axis to logscale.
-834        plateau : Obs
-835            Plateau value to be visualized in the figure.
-836        fit_res : Fit_result
-837            Fit_result object to be visualized.
-838        fit_key : str
-839            Key for the fit function in Fit_result.fit_function (for combined fits).
-840        ylabel : str
-841            Label for the y-axis.
-842        save : str
-843            path to file in which the figure should be saved.
-844        auto_gamma : bool
-845            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
-846        hide_sigma : float
-847            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
-848        references : list
-849            List of floating point values that are displayed as horizontal lines for reference.
-850        title : string
-851            Optional title of the figure.
-852        """
-853        if self.N != 1:
-854            raise Exception("Correlator must be projected before plotting")
-855
-856        if auto_gamma:
-857            self.gamma_method()
-858
-859        if x_range is None:
-860            x_range = [0, self.T - 1]
-861
-862        fig = plt.figure()
-863        ax1 = fig.add_subplot(111)
-864
-865        x, y, y_err = self.plottable()
-866        if hide_sigma:
-867            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-868        else:
-869            hide_from = None
-870        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
-871        if logscale:
-872            ax1.set_yscale('log')
-873        else:
-874            if y_range is None:
-875                try:
-876                    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)])
-877                    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)])
-878                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
-879                except Exception:
-880                    pass
-881            else:
-882                ax1.set_ylim(y_range)
-883        if comp:
-884            if isinstance(comp, (Corr, list)):
-885                for corr in comp if isinstance(comp, list) else [comp]:
-886                    if auto_gamma:
-887                        corr.gamma_method()
-888                    x, y, y_err = corr.plottable()
-889                    if hide_sigma:
-890                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-891                    else:
-892                        hide_from = None
-893                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
-894            else:
-895                raise Exception("'comp' must be a correlator or a list of correlators.")
-896
-897        if plateau:
-898            if isinstance(plateau, Obs):
-899                if auto_gamma:
-900                    plateau.gamma_method()
-901                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
-902                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+            
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                raise Exception("'plateau' must be an Obs")
-905
-906        if references:
-907            if isinstance(references, list):
-908                for ref in references:
-909                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
-910            else:
-911                raise Exception("'references' must be a list of floating pint values.")
-912
-913        if self.prange:
-914            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
-915            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
-916
-917        if fit_res:
-918            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
-919            if isinstance(fit_res.fit_function, dict):
-920                if fit_key:
-921                    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)
-922                else:
-923                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
-924            else:
-925                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
-926
-927        ax1.set_xlabel(r'$x_0 / a$')
-928        if ylabel:
-929            ax1.set_ylabel(ylabel)
-930        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
-931
-932        handles, labels = ax1.get_legend_handles_labels()
-933        if labels:
-934            ax1.legend()
-935
-936        if title:
-937            plt.title(title)
+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        plt.draw()
-940
-941        if save:
-942            if isinstance(save, str):
-943                fig.savefig(save, bbox_inches='tight')
-944            else:
-945                raise Exception("'save' has to be a string.")
+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()
+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.")
 
@@ -4700,34 +4773,34 @@ Optional title of the figure.
-
947    def spaghetti_plot(self, logscale=True):
-948        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-949
-950        Parameters
-951        ----------
-952        logscale : bool
-953            Determines whether the scale of the y-axis is logarithmic or standard.
-954        """
-955        if self.N != 1:
-956            raise Exception("Correlator needs to be projected first.")
-957
-958        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]))
-959        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
-960
-961        for name in mc_names:
-962            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
-963
-964            fig = plt.figure()
-965            ax = fig.add_subplot(111)
-966            for dat in data:
-967                ax.plot(x0_vals, dat, ls='-', marker='')
-968
-969            if logscale is True:
-970                ax.set_yscale('log')
+            
969    def spaghetti_plot(self, logscale=True):
+970        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
 971
-972            ax.set_xlabel(r'$x_0 / a$')
-973            plt.title(name)
-974            plt.draw()
+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()
 
@@ -4754,29 +4827,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.
-
976    def dump(self, filename, datatype="json.gz", **kwargs):
-977        """Dumps the Corr into a file of chosen type
-978        Parameters
-979        ----------
-980        filename : str
-981            Name of the file to be saved.
-982        datatype : str
-983            Format of the exported file. Supported formats include
-984            "json.gz" and "pickle"
-985        path : str
-986            specifies a custom path for the file (default '.')
-987        """
-988        if datatype == "json.gz":
-989            from .input.json import dump_to_json
-990            if 'path' in kwargs:
-991                file_name = kwargs.get('path') + '/' + filename
-992            else:
-993                file_name = filename
-994            dump_to_json(self, file_name)
-995        elif datatype == "pickle":
-996            dump_object(self, filename, **kwargs)
-997        else:
-998            raise Exception("Unknown datatype " + str(datatype))
+            
 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))
 
@@ -4808,8 +4881,8 @@ specifies a custom path for the file (default '.')
-
1000    def print(self, print_range=None):
-1001        print(self.__repr__(print_range))
+            
1022    def print(self, print_range=None):
+1023        print(self.__repr__(print_range))
 
@@ -4827,8 +4900,8 @@ specifies a custom path for the file (default '.')
-
1210    def sqrt(self):
-1211        return self ** 0.5
+            
1232    def sqrt(self):
+1233        return self ** 0.5
 
@@ -4846,9 +4919,9 @@ specifies a custom path for the file (default '.')
-
1213    def log(self):
-1214        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1215        return Corr(newcontent, prange=self.prange)
+            
1235    def log(self):
+1236        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1237        return Corr(newcontent, prange=self.prange)
 
@@ -4866,9 +4939,9 @@ specifies a custom path for the file (default '.')
-
1217    def exp(self):
-1218        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1219        return Corr(newcontent, prange=self.prange)
+            
1239    def exp(self):
+1240        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1241        return Corr(newcontent, prange=self.prange)
 
@@ -4886,8 +4959,8 @@ specifies a custom path for the file (default '.')
-
1234    def sin(self):
-1235        return self._apply_func_to_corr(np.sin)
+            
1256    def sin(self):
+1257        return self._apply_func_to_corr(np.sin)
 
@@ -4905,8 +4978,8 @@ specifies a custom path for the file (default '.')
-
1237    def cos(self):
-1238        return self._apply_func_to_corr(np.cos)
+            
1259    def cos(self):
+1260        return self._apply_func_to_corr(np.cos)
 
@@ -4924,8 +4997,8 @@ specifies a custom path for the file (default '.')
-
1240    def tan(self):
-1241        return self._apply_func_to_corr(np.tan)
+            
1262    def tan(self):
+1263        return self._apply_func_to_corr(np.tan)
 
@@ -4943,8 +5016,8 @@ specifies a custom path for the file (default '.')
-
1243    def sinh(self):
-1244        return self._apply_func_to_corr(np.sinh)
+            
1265    def sinh(self):
+1266        return self._apply_func_to_corr(np.sinh)
 
@@ -4962,8 +5035,8 @@ specifies a custom path for the file (default '.')
-
1246    def cosh(self):
-1247        return self._apply_func_to_corr(np.cosh)
+            
1268    def cosh(self):
+1269        return self._apply_func_to_corr(np.cosh)
 
@@ -4981,8 +5054,8 @@ specifies a custom path for the file (default '.')
-
1249    def tanh(self):
-1250        return self._apply_func_to_corr(np.tanh)
+            
1271    def tanh(self):
+1272        return self._apply_func_to_corr(np.tanh)
 
@@ -5000,8 +5073,8 @@ specifies a custom path for the file (default '.')
-
1252    def arcsin(self):
-1253        return self._apply_func_to_corr(np.arcsin)
+            
1274    def arcsin(self):
+1275        return self._apply_func_to_corr(np.arcsin)
 
@@ -5019,8 +5092,8 @@ specifies a custom path for the file (default '.')
-
1255    def arccos(self):
-1256        return self._apply_func_to_corr(np.arccos)
+            
1277    def arccos(self):
+1278        return self._apply_func_to_corr(np.arccos)
 
@@ -5038,8 +5111,8 @@ specifies a custom path for the file (default '.')
-
1258    def arctan(self):
-1259        return self._apply_func_to_corr(np.arctan)
+            
1280    def arctan(self):
+1281        return self._apply_func_to_corr(np.arctan)
 
@@ -5057,8 +5130,8 @@ specifies a custom path for the file (default '.')
-
1261    def arcsinh(self):
-1262        return self._apply_func_to_corr(np.arcsinh)
+            
1283    def arcsinh(self):
+1284        return self._apply_func_to_corr(np.arcsinh)
 
@@ -5076,8 +5149,8 @@ specifies a custom path for the file (default '.')
-
1264    def arccosh(self):
-1265        return self._apply_func_to_corr(np.arccosh)
+            
1286    def arccosh(self):
+1287        return self._apply_func_to_corr(np.arccosh)
 
@@ -5095,8 +5168,8 @@ specifies a custom path for the file (default '.')
-
1267    def arctanh(self):
-1268        return self._apply_func_to_corr(np.arctanh)
+            
1289    def arctanh(self):
+1290        return self._apply_func_to_corr(np.arctanh)
 
@@ -5136,62 +5209,62 @@ specifies a custom path for the file (default '.')
-
1303    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1304        r''' Project large correlation matrix to lowest states
-1305
-1306        This method can be used to reduce the size of an (N x N) correlation matrix
-1307        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1308        is still small.
-1309
-1310        Parameters
-1311        ----------
-1312        Ntrunc: int
-1313            Rank of the target matrix.
-1314        tproj: int
-1315            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1316            The default value is 3.
-1317        t0proj: int
-1318            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1319            discouraged for O(a) improved theories, since the correctness of the procedure
-1320            cannot be granted in this case. The default value is 2.
-1321        basematrix : Corr
-1322            Correlation matrix that is used to determine the eigenvectors of the
-1323            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1324            is is not specified.
-1325
-1326        Notes
-1327        -----
-1328        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1329        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1330        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1331        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1332        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1333        correlation matrix and to remove some noise that is added by irrelevant operators.
-1334        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1335        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1336        '''
-1337
-1338        if self.N == 1:
-1339            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1340        if basematrix is None:
-1341            basematrix = self
-1342        if Ntrunc >= basematrix.N:
-1343            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1344        if basematrix.N != self.N:
-1345            raise Exception('basematrix and targetmatrix have to be of the same size.')
-1346
-1347        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1348
-1349        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1350        rmat = []
-1351        for t in range(basematrix.T):
-1352            for i in range(Ntrunc):
-1353                for j in range(Ntrunc):
-1354                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1355            rmat.append(np.copy(tmpmat))
-1356
-1357        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1358        return Corr(newcontent)
+            
1325    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1326        r''' Project large correlation matrix to lowest states
+1327
+1328        This method can be used to reduce the size of an (N x N) correlation matrix
+1329        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1330        is still small.
+1331
+1332        Parameters
+1333        ----------
+1334        Ntrunc: int
+1335            Rank of the target matrix.
+1336        tproj: int
+1337            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1338            The default value is 3.
+1339        t0proj: int
+1340            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1341            discouraged for O(a) improved theories, since the correctness of the procedure
+1342            cannot be granted in this case. The default value is 2.
+1343        basematrix : Corr
+1344            Correlation matrix that is used to determine the eigenvectors of the
+1345            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1346            is is not specified.
+1347
+1348        Notes
+1349        -----
+1350        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1351        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1352        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1353        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1354        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1355        correlation matrix and to remove some noise that is added by irrelevant operators.
+1356        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1357        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1358        '''
+1359
+1360        if self.N == 1:
+1361            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1362        if basematrix is None:
+1363            basematrix = self
+1364        if Ntrunc >= basematrix.N:
+1365            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1366        if basematrix.N != self.N:
+1367            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1368
+1369        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1370
+1371        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1372        rmat = []
+1373        for t in range(basematrix.T):
+1374            for i in range(Ntrunc):
+1375                for j in range(Ntrunc):
+1376                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1377            rmat.append(np.copy(tmpmat))
+1378
+1379        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1380        return Corr(newcontent)
 
diff --git a/docs/search.js b/docs/search.js index 2f20ed0a..05872e08 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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configuration"),this.buildDefaultConfig(n)}},t.Configuration.prototype.buildDefaultConfig=function(e){this.reset(),e.forEach(function(e){this.config[e]={boost:1,bool:"OR",expand:!1}},this)},t.Configuration.prototype.buildUserConfig=function(e,n){var i="OR",o=!1;if(this.reset(),"bool"in e&&(i=e.bool||i),"expand"in e&&(o=e.expand||o),"fields"in e)for(var r in e.fields)if(n.indexOf(r)>-1){var s=e.fields[r],u=o;void 0!=s.expand&&(u=s.expand),this.config[r]={boost:s.boost||0===s.boost?s.boost:1,bool:s.bool||i,expand:u}}else t.utils.warn("field name in user configuration not found in index instance fields");else this.addAllFields2UserConfig(i,o,n)},t.Configuration.prototype.addAllFields2UserConfig=function(e,t,n){n.forEach(function(n){this.config[n]={boost:1,bool:e,expand:t}},this)},t.Configuration.prototype.get=function(){return 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.

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Installation

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Install the most recent release using pip and pypi:

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\n
python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
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\n\n

Install the most recent release using conda and conda-forge:

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

Install the current develop version:

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

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\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
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\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.

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\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.

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\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

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When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs

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\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 GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.

\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "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
  • \n
  • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
  • \n
  • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
  • \n
\n", "signature": "(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
  • partity (int):\nParity quantum number of the correlator, can be +1 or -1
  • \n
\n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "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 periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\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_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "

Read hadrons meson hdf5 file and extract the meson labeled 'meson'

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
  • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
  • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "

Read hadrons FlowObservables hdf5 file and extract t0

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
  • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "

Read hadrons DistillationContraction hdf5 files in given directory structure

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
  • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "

ndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)

\n\n

An array object represents a multidimensional, homogeneous array\nof fixed-size items. An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)

\n\n

Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.

\n\n

For more information, refer to the numpy module and examine the\nmethods and attributes of an array.

\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
  • \n
  • shape (tuple of ints):\nShape of created array.
  • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
  • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
  • \n
  • offset (int, optional):\nOffset of array data in buffer.
  • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
  • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
  • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
  • \n
  • data (buffer):\nThe array's elements, in memory.
  • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
  • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
  • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator. The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
  • \n
  • imag (ndarray):\nImaginary part of the array.
  • \n
  • real (ndarray):\nReal part of the array.
  • \n
  • size (int):\nNumber of elements in the array.
  • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
  • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
  • \n
  • ndim (int):\nThe array's number of dimensions.
  • \n
  • shape (tuple of ints):\nShape of the array.
  • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2). This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
  • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
  • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view). The base array is where the\narray data is actually stored.
  • \n
\n\n
See Also
\n\n

array: Construct an array.
\nzeros: Create an array, each element of which is zero.
\nempty: Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype: Create a data-type.
\nnumpy.typing.NDArray: An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.

\n\n
Notes
\n\n

There are two modes of creating an array using __new__:

\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
  2. \n
  3. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
  4. \n
\n\n

No __init__ method is needed because the array is fully initialized\nafter the __new__ method.

\n\n
Examples
\n\n

These examples illustrate the low-level ndarray constructor. Refer\nto the See Also section above for easier ways of constructing an\nndarray.

\n\n

First mode, buffer is None:

\n\n
\n
>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n
\n\n

Second mode:

\n\n
\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "

Gamma_5 hermitean conjugate

\n\n

Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.

\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "

Read hadrons ExternalLeg hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • result (Npr_matrix):\nread Cobs-matrix
  • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "

Read hadrons Bilinear hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict[Npr_matrix]):\nextracted Bilinears
  • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "

Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
  • vertices (list):\nVertex functions to be extracted.
  • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict):\nextracted fourquark matrizes
  • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "

\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "

Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
  • \n
  • description (str):\nOptional string that describes the contents of the json file.
  • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
  • \n
\n\n
Returns
\n\n
    \n
  • json_string (str):\nString for export to .json(.gz) file
  • \n
\n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "

Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
  • \n
  • fname (str):\nFilename of the output file.
  • \n
  • description (str):\nOptional string that describes the contents of the json file.
  • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
  • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
  • \n
\n\n
Returns
\n\n
    \n
  • Null
  • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "

Reconstruct a list of Obs or structures containing Obs from a json string.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
  • \n
  • verbose (bool):\nPrint additional information that was written to the file.
  • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
  • \n
  • or
  • \n
  • result (Obs):\nonly one observable if the list only has one entry
  • \n
  • or
  • \n
  • result (dict):\nif full_output=True
  • \n
\n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "

Import a list of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
  • \n
  • verbose (bool):\nPrint additional information that was written to the file.
  • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
  • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
  • \n
  • or
  • \n
  • result (Obs):\nonly one observable if the list only has one entry
  • \n
  • or
  • \n
  • result (dict):\nif full_output=True
  • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "

Export a dict of Obs or structures containing Obs to a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
  • \n
  • fname (str):\nFilename of the output file.
  • \n
  • description (str):\nOptional string that describes the contents of the json file.
  • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
  • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
  • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "

Import a dict of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
  • \n
  • verbose (bool):\nPrint additional information that was written to the file.
  • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
  • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
  • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
  • \n
\n\n
Returns
\n\n
    \n
  • data (Obs / list / Corr):\nRead data
  • \n
  • or
  • \n
  • data (dict):\nRead data and meta-data
  • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "

\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "

Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).

\n\n

It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.

\n\n

A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.

\n\n
Parameters
\n\n
    \n
  • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
  • \n
  • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
  • \n
\n\n
Returns
\n\n
    \n
  • root (Obs):\nThe root of the data series.
  • \n
\n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "

Read pbp format from given folder structure.

\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of observables read
  • \n
\n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "

\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "

Read rwms format from given folder structure. Returns a list of length nrw

\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
  • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
  • \n
  • version (str):\nversion of openQCD, default 2.0
  • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
  • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
  • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
  • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
  • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
  • \n
\n\n
Returns
\n\n
    \n
  • rwms (Obs):\nReweighting factors read
  • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "

Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.

\n\n

It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.

\n\n

It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
  • \n
  • prefix (str):\nEnsemble prefix
  • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
  • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
  • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
  • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
  • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
  • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
  • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
  • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
  • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
  • \n
\n\n
Returns
\n\n
    \n
  • t0 (Obs):\nExtracted t0
  • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "

Extract w0/a from given .ms.dat files. Returns w0 as Obs.

\n\n

It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt - (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.

\n\n

It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
  • \n
  • prefix (str):\nEnsemble prefix
  • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
  • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
  • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
  • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
  • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
  • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
  • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
  • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
  • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
  • \n
\n\n
Returns
\n\n
    \n
  • w0 (Obs):\nExtracted w0
  • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "

Read the topologial charge based on openQCD gradient flow measurements.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
  • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
  • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
  • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
  • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
  • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
  • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
  • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
  • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
  • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
  • \n
\n\n
Returns
\n\n
    \n
  • result (Obs):\nRead topological charge
  • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "

Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.

\n\n

Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
  • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
  • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
  • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
  • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
  • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
  • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
  • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "

Returns the projection to the topological charge sector defined by target.

\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
  • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
  • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
  • \n
\n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "

Constructs reweighting factors to a specified topological sector.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
  • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
  • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
  • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
  • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
  • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
  • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
  • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
  • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
  • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
  • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
  • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
  • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
  • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "

Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.

\n\n
Parameters
\n\n
    \n
  • path (str):\nThe directory to search for the files in.
  • \n
  • prefix (str):\nThe prefix to match the files against.
  • \n
  • qc (str):\nThe quark combination extension to match the files against.
  • \n
  • corr (str):\nThe correlator to extract data for.
  • \n
  • sep (str, optional):\nThe separator to use when parsing the replika names.
  • \n
  • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:

    \n\n
      \n
    • names (List[str]): A list of names to use for the replicas.
    • \n
    • files (List[str]): A list of files to read data from.
    • \n
    • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
    • \n
  • \n
\n\n
Returns
\n\n
    \n
  • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
  • \n
  • or
  • \n
  • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
  • \n
\n\n
Raises
\n\n
    \n
  • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
  • \n
  • IOError: If there is an error reading a file.
  • \n
  • struct.error: If there is an error unpacking binary data.
  • \n
\n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "

\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "

Write DataFrame including Obs or Corr valued columns to sqlite database.

\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be written to the database.
  • \n
  • table_name (str):\nName of the table in the database.
  • \n
  • db (str):\nPath to the sqlite database.
  • \n
  • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
  • \n
  • gz (bool):\nIf True the json strings are gzipped.
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "

Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.

\n\n
Parameters
\n\n
    \n
  • sql (str):\nSQL query to be executed.
  • \n
  • db (str):\nPath to the sqlite database.
  • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
  • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
  • \n
\n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "

Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.

\n\n

Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.

\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be dumped to a file.
  • \n
  • fname (str):\nFilename of the output file.
  • \n
  • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "

Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
  • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
  • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
  • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
  • \n
\n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "

\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "

Read sfcf files from given folder structure.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
  • \n
  • prefix (str):\nPrefix of the sfcf files.
  • \n
  • name (str):\nName of the correlation function to read.
  • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
  • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
    • \n
    • 'bb' for boundary-boundary
    • \n
    • 'bib' for boundary-inner-boundary
    • \n
  • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
  • \n
  • wf (int):\nID of wave function
  • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
  • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
  • \n
  • ens_name (str):\nreplaces the name of the ensemble
  • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
  • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
  • \n
  • replica (list):\nlist of replica to be read, default is all
  • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
  • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
  • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "

\n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "

Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.

\n\n
Parameters
\n\n
    \n
  • ll (list):\nlist to sort
  • \n
\n\n
Returns
\n\n
    \n
  • ll (list):\nsorted list
  • \n
\n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "

Checks if list of configurations is contained in an idl

\n\n
Parameters
\n\n
    \n
  • idl (range or list):\nidl of the current replicum
  • \n
  • che (list):\nlist of configurations to be checked against
  • \n
\n\n
Returns
\n\n
    \n
  • miss_str (str):\nstring with integers of which idls are missing
  • \n
\n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "

\n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "

Performs a (one-dimensional) numeric integration of f(p, x) from a to b.

\n\n

The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.

\n\n
Parameters
\n\n
    \n
  • func (object):\nfunction to integrate, has to be of the form

    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(p, x):\n   return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
    \n
    \n\n

    where x is the integration variable.

  • \n
  • p (list of floats or Obs):\nparameters of the function func.
  • \n
  • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
  • \n
  • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
  • \n
  • All parameters of scipy.integrate.quad
  • \n
\n\n
Returns
\n\n
    \n
  • y (Obs):\nThe integral of func from a to b.
  • \n
  • abserr (float):\nAn estimate of the absolute error in the result.
  • \n
  • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
  • \n
  • message: A convergence message.
  • \n
  • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
  • \n
\n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "

\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "

Matrix multiply all operands.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
  • \n
  • This implementation is faster compared to standard multiplication via the @ operator.
  • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "

Matrix multiply both operands making use of the jackknife approximation.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
  • \n
  • For large matrices this is considerably faster compared to matmul.
  • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "

Wrapper for numpy.einsum

\n\n
Parameters
\n\n
    \n
  • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
  • \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
  • \n
\n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "

Inverse of Obs or CObs valued matrices.

\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "

Cholesky decomposition of Obs valued matrices.

\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "

Determinant of Obs valued matrices.

\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "

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

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "

Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "

Computes the Moore-Penrose pseudoinverse of a matrix of Obs.

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "

Computes the singular value decomposition of a matrix of Obs.

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "

\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "

Print information about version of python, pyerrors and dependencies.

\n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "

pyerrors wrapper for the errorbars method of matplotlib

\n\n
Parameters
\n\n
    \n
  • x (list):\nA list of x-values which can be Obs.
  • \n
  • y (list):\nA list of y-values which can be Obs.
  • \n
  • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
  • \n
\n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "

Dump object into pickle file.

\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
  • \n
  • name (str):\nname of the file
  • \n
  • path (str):\nspecifies a custom path for the file (default '.')
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "

Load object from pickle file.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
  • \n
\n\n
Returns
\n\n
    \n
  • object (Obs):\nLoaded Object
  • \n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "

Generate an Obs object with given value, dvalue and name for test purposes

\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
  • \n
  • dvalue (float):\nerror of the Obs to be generated.
  • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
  • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
  • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nGenerated Observable
  • \n
\n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "

Generate observables with given covariance and autocorrelation times.

\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
  • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
  • \n
  • name (str):\nensemble name for the data to be geneated.
  • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
  • \n
  • samples (int):\nnumber of samples to be generated for each observable.
  • \n
\n\n
Returns
\n\n
    \n
  • corr_obs (list[Obs]):\nGenerated observable list
  • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "

\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "

Matrix pencil method to extract k energy levels from data

\n\n

Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)

\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
  • \n
  • k (int):\nNumber of states to extract (default 1).
  • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
  • \n
\n\n
Returns
\n\n
    \n
  • energy_levels (list[Obs]):\nExtracted energy levels
  • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "

\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "

Class for a general observable.

\n\n

Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.

\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
  • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
  • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
  • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
  • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
  • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
  • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "

Initialize Obs object.

\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
  • \n
  • names (list):\nlist of strings labeling the individual samples
  • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
  • \n
\n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "

\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "

\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "

\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "

\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "

\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "

\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "

Estimate the error and related properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
  • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
  • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
  • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
  • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "

Estimate the error and related properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
  • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
  • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
  • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
  • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "

Output detailed properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
  • \n
\n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "

Reweight the obs with given rewighting factors.

\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
  • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
  • \n
\n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "

Checks whether the observable is zero within 'sigma' standard errors.

\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
  • \n
  • Works only properly when the gamma method was run.
  • \n
\n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "

Checks whether the observable is zero within a given tolerance.

\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
  • \n
\n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "

Plot integrated autocorrelation time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
  • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "

Plot normalized autocorrelation function time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
  • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "

Plot replica distribution for each ensemble with more than one replicum.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "

Plot derived Monte Carlo history for each ensemble

\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
  • \n
\n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "

Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
  • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "

Dump the Obs to a file 'name' of chosen format.

\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
  • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
  • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
  • \n
  • path (str):\nspecifies a custom path for the file (default '.')
  • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "

Export jackknife samples from the Obs

\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
  • \n
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "

Export bootstrap samples from the Obs

\n\n
Parameters
\n\n
    \n
  • samples (int):\nNumber of bootstrap samples to generate.
  • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
  • \n
  • save_rng (str):\nSave the random numbers to a file if a path is specified.
  • \n
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
  • \n
\n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "

Class for a complex valued observable.

\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "

\n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "

Executes the gamma_method for the real and the imaginary part.

\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "

Checks whether both real and imaginary part are zero within machine precision.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.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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"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

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    \n
  • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
  • \n
\n\n

where applicable.

\n\n

There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.

\n\n

Installation

\n\n

Install the most recent release using pip and pypi:

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python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
\n
\n\n

Install the most recent release using conda and conda-forge:

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

Install the current develop version:

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

(Also works for any feature branch).

\n\n

Basic example

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

The Obs class

\n\n

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

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

Error propagation

\n\n

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

\n\n

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

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

Error estimation

\n\n

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

\n\n
\n
my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
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\n\n

The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.

\n\n

We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.

\n\n
\n
my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
\n
\n\n

The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.

\n\n

If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.

\n\n

Exponential tails

\n\n

Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.

\n\n
\n
my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
\n
\n\n

For the full API see pyerrors.obs.Obs.gamma_method.

\n\n

Multiple ensembles/replica

\n\n

Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.

\n\n
\n
obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
\n
\n\n

Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.

\n\n

pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.

\n\n
\n
obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
\n
\n\n

Error estimation for multiple ensembles

\n\n

In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.

\n\n
\n
pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
\n
\n\n

In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.

\n\n

Irregular Monte Carlo chains

\n\n

Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.

\n\n
\n
# Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
\n
\n\n

Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.

\n\n

Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.

\n\n

For the full API see pyerrors.obs.Obs.

\n\n

Correlators

\n\n

When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs

\n\n
\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
\n
\n\n

In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.

\n\n
\n
my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
\n
\n\n

The individual entries of a correlator can be accessed via slicing

\n\n
\n
print(my_corr[3])\n> 0.3227(33)\n
\n
\n\n

Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.

\n\n
\n
my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
\n
\n\n

pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:

\n\n
    \n
  • Corr.gamma_method applies the gamma method to all entries of the correlator.
  • \n
  • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
  • \n
  • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
  • \n
  • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
  • \n
  • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
  • \n
  • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
  • \n
  • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
  • \n
  • Corr.plateau extracts a plateau value from the correlator in a given range.
  • \n
  • Corr.roll periodically shifts the correlator.
  • \n
  • Corr.reverse reverses the time ordering of the correlator.
  • \n
  • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
  • \n
  • Corr.reweight reweights the correlator.
  • \n
\n\n

pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).

\n\n

For the full API see pyerrors.correlators.Corr.

\n\n

Complex valued observables

\n\n

pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.

\n\n
\n
my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
\n
\n\n

Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.

\n\n
\n
my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
\n
\n\n

The Covobs class

\n\n

In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.

\n\n

This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.

\n\n
\n
import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
\n
\n\n

The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.

\n\n

Correlated auxiliary data is defined similarly to above, e.g., via

\n\n
\n
RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
\n
\n\n

where RAP now is a list of two Obs that contains the two correlated parameters.

\n\n

Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via

\n\n
\n
o.covobs[k].grad\n
\n
\n\n

Error propagation in iterative algorithms

\n\n

pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.

\n\n

Least squares fits

\n\n

Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.

\n\n

Fit functions have to be of the following form

\n\n
\n
import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
\n
\n\n

It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.

\n\n

Fits can then be performed via

\n\n
\n
fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
\n
\n\n

where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.

\n\n

Data stored in Corr objects can be fitted directly using the Corr.fit method.

\n\n
\n
my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
\n
\n\n

this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.

\n\n

For fit functions with multiple independent variables the fit function can be of the form

\n\n
\n
def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
\n
\n\n

pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.

\n\n

For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.

\n\n

Total least squares fits

\n\n

pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.

\n\n

For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.

\n\n

Matrix operations

\n\n

pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:

\n\n
    \n
  • inv for the matrix inverse.
  • \n
  • cholseky for the Cholesky decomposition.
  • \n
  • det for the matrix determinant.
  • \n
  • eigh for eigenvalues and eigenvectors of hermitean matrices.
  • \n
  • eig for eigenvalues of general matrices.
  • \n
  • pinv for the Moore-Penrose pseudoinverse.
  • \n
  • svd for the singular-value-decomposition.
  • \n
\n\n

For the full API see pyerrors.linalg.

\n\n

Export data

\n\n

\n\n

The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:

\n\n
    \n
  • What observables are stored? Possibly: How exactly are they defined.
  • \n
  • How does each single ensemble or external quantity contribute to the error of the observable?
  • \n
  • Who did write the file when and on which machine?
  • \n
\n\n

This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example

\n\n
\n
my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
\n
\n\n

The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.

\n\n

json.gz format specification

\n\n

The first entries of the file provide optional auxiliary information:

\n\n
    \n
  • program is a string that indicates which program was used to write the file.
  • \n
  • version is a string that specifies the version of the format.
  • \n
  • who is a string that specifies the user name of the creator of the file.
  • \n
  • date is a string and contains the creation date of the file.
  • \n
  • host is a string and contains the hostname of the machine where the file has been written.
  • \n
  • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
  • \n
\n\n

The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.

\n\n

Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:

\n\n
    \n
  • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
  • \n
  • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
  • \n
  • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
  • \n
  • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
  • \n
  • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
  • \n
  • data is an array that contains the data from MC chains. We will define it below.
  • \n
  • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
  • \n
\n\n

The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:

\n\n
    \n
  • id, a string that contains the name of the ensemble
  • \n
  • replica, an array that contains an entry per replica of the ensemble.
  • \n
\n\n

Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.

\n\n

Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.

\n\n

The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:

\n\n
    \n
  • id, a string that identifies the covariance matrix
  • \n
  • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
  • \n
  • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
  • \n
  • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
  • \n
\n\n

A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.

\n\n

Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.

\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "

\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "

The class for a correlator (time dependent sequence of pe.Obs).

\n\n

Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.

\n\n

The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.

\n\n

The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the None object.

\n\n
Initialization
\n\n

A simple correlator can be initialized with a list or a one-dimensional array of Obs or Cobs

\n\n
\n
corr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
\n
\n\n

A matrix-valued correlator can either be initialized via a two-dimensional array of Corr objects

\n\n
\n
matrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
\n
\n\n

or alternatively via a three-dimensional array of Obs or CObs of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.

\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "

Initialize a Corr object.

\n\n
Parameters
\n\n
    \n
  • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).
  • \n
  • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
  • \n
  • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.
  • \n
\n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "

\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "

Apply the gamma method to the content of the Corr.

\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "

Apply the gamma method to the content of the Corr.

\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "

We need to project the Correlator with a Vector to get a single value at each timeslice.

\n\n

The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to

\n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "

Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.

\n\n
Parameters
\n\n
    \n
  • i (int):\nFirst index to be picked.
  • \n
  • j (int):\nSecond index to be picked.
  • \n
\n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "

Outputs the correlator in a plotable format.

\n\n

Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "

Symmetrize the correlator around x0=0.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "

Anti-symmetrize the correlator around x0=0.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "

Checks whether a correlator matrices is symmetric on every timeslice.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "

Calculates the per-timeslice trace of a correlator matrix.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "

Symmetrizes the correlator matrices on every timeslice.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "

Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.

\n\n

The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing

\n\n
\n
C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
\n
\n\n
Parameters
\n\n
    \n
  • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
  • \n
  • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
  • \n
  • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
      \n
    • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
    • \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_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "

Read hadrons meson hdf5 file and extract the meson labeled 'meson'

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
  • \n
  • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • corr (Corr):\nCorrelator of the source sink combination in question.
  • \n
\n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "

Read hadrons FlowObservables hdf5 file and extract t0

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
  • \n
\n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "

Read hadrons DistillationContraction hdf5 files in given directory structure

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the directories to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • result (dict):\nextracted DistillationContration data
  • \n
\n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "

ndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)

\n\n

An array object represents a multidimensional, homogeneous array\nof fixed-size items. An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)

\n\n

Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.

\n\n

For more information, refer to the numpy module and examine the\nmethods and attributes of an array.

\n\n
Parameters
\n\n
    \n
  • (for the __new__ method; see Notes below)
  • \n
  • shape (tuple of ints):\nShape of created array.
  • \n
  • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
  • \n
  • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
  • \n
  • offset (int, optional):\nOffset of array data in buffer.
  • \n
  • strides (tuple of ints, optional):\nStrides of data in memory.
  • \n
  • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
  • \n
\n\n
Attributes
\n\n
    \n
  • T (ndarray):\nTranspose of the array.
  • \n
  • data (buffer):\nThe array's elements, in memory.
  • \n
  • dtype (dtype object):\nDescribes the format of the elements in the array.
  • \n
  • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
  • \n
  • flat (numpy.flatiter object):\nFlattened version of the array as an iterator. The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
  • \n
  • imag (ndarray):\nImaginary part of the array.
  • \n
  • real (ndarray):\nReal part of the array.
  • \n
  • size (int):\nNumber of elements in the array.
  • \n
  • itemsize (int):\nThe memory use of each array element in bytes.
  • \n
  • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
  • \n
  • ndim (int):\nThe array's number of dimensions.
  • \n
  • shape (tuple of ints):\nShape of the array.
  • \n
  • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2). This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
  • \n
  • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
  • \n
  • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view). The base array is where the\narray data is actually stored.
  • \n
\n\n
See Also
\n\n

array: Construct an array.
\nzeros: Create an array, each element of which is zero.
\nempty: Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").
\ndtype: Create a data-type.
\nnumpy.typing.NDArray: An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.

\n\n
Notes
\n\n

There are two modes of creating an array using __new__:

\n\n
    \n
  1. If buffer is None, then only shape, dtype, and order\nare used.
  2. \n
  3. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
  4. \n
\n\n

No __init__ method is needed because the array is fully initialized\nafter the __new__ method.

\n\n
Examples
\n\n

These examples illustrate the low-level ndarray constructor. Refer\nto the See Also section above for easier ways of constructing an\nndarray.

\n\n

First mode, buffer is None:

\n\n
\n
>>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
\n
\n\n

Second mode:

\n\n
\n
>>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
\n
\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "

Gamma_5 hermitean conjugate

\n\n

Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.

\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "

Read hadrons ExternalLeg hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • result (Npr_matrix):\nread Cobs-matrix
  • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "

Read hadrons Bilinear hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict[Npr_matrix]):\nextracted Bilinears
  • \n
\n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "

Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the files to read
  • \n
  • filestem (str):\nnamestem of the files to read
  • \n
  • ens_id (str):\nname of the ensemble, required for internal bookkeeping
  • \n
  • idl (range):\nIf specified only configurations in the given range are read in.
  • \n
  • vertices (list):\nVertex functions to be extracted.
  • \n
\n\n
Returns
\n\n
    \n
  • result_dict (dict):\nextracted fourquark matrizes
  • \n
\n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "

\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "

Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
  • \n
  • description (str):\nOptional string that describes the contents of the json file.
  • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
  • \n
\n\n
Returns
\n\n
    \n
  • json_string (str):\nString for export to .json(.gz) file
  • \n
\n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "

Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.

\n\n
Parameters
\n\n
    \n
  • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
  • \n
  • fname (str):\nFilename of the output file.
  • \n
  • description (str):\nOptional string that describes the contents of the json file.
  • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
  • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
  • \n
\n\n
Returns
\n\n
    \n
  • Null
  • \n
\n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "

Reconstruct a list of Obs or structures containing Obs from a json string.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • json_string (str):\njson string containing the data.
  • \n
  • verbose (bool):\nPrint additional information that was written to the file.
  • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
  • \n
  • or
  • \n
  • result (Obs):\nonly one observable if the list only has one entry
  • \n
  • or
  • \n
  • result (dict):\nif full_output=True
  • \n
\n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "

Import a list of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
  • \n
  • verbose (bool):\nPrint additional information that was written to the file.
  • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
  • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nreconstructed list of observables from the json string
  • \n
  • or
  • \n
  • result (Obs):\nonly one observable if the list only has one entry
  • \n
  • or
  • \n
  • result (dict):\nif full_output=True
  • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "

Export a dict of Obs or structures containing Obs to a .json(.gz) file

\n\n
Parameters
\n\n
    \n
  • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
  • \n
  • fname (str):\nFilename of the output file.
  • \n
  • description (str):\nOptional string that describes the contents of the json file.
  • \n
  • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
  • \n
  • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
  • \n
  • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "

Import a dict of Obs or structures containing Obs from a .json(.gz) file.

\n\n

The following structures are supported: Obs, list, numpy.ndarray, Corr

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
  • \n
  • verbose (bool):\nPrint additional information that was written to the file.
  • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
  • \n
  • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
  • \n
  • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
  • \n
\n\n
Returns
\n\n
    \n
  • data (Obs / list / Corr):\nRead data
  • \n
  • or
  • \n
  • data (dict):\nRead data and meta-data
  • \n
\n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "

\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "

Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).

\n\n

It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.

\n\n

A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.

\n\n
Parameters
\n\n
    \n
  • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
  • \n
  • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
  • \n
\n\n
Returns
\n\n
    \n
  • root (Obs):\nThe root of the data series.
  • \n
\n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "

Read pbp format from given folder structure.

\n\n
Parameters
\n\n
    \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of observables read
  • \n
\n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "

\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "

Read rwms format from given folder structure. Returns a list of length nrw

\n\n
Parameters
\n\n
    \n
  • path (str):\npath that contains the data files
  • \n
  • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
  • \n
  • version (str):\nversion of openQCD, default 2.0
  • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum
  • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
  • \n
  • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
  • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
  • \n
  • print_err (bool):\nPrint additional information that is useful for debugging.
  • \n
\n\n
Returns
\n\n
    \n
  • rwms (Obs):\nReweighting factors read
  • \n
\n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "

Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.

\n\n

It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.

\n\n

It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
  • \n
  • prefix (str):\nEnsemble prefix
  • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
  • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
  • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
  • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
  • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
  • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
  • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
  • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
  • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
  • \n
\n\n
Returns
\n\n
    \n
  • t0 (Obs):\nExtracted t0
  • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "

Extract w0/a from given .ms.dat files. Returns w0 as Obs.

\n\n

It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt - (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.

\n\n

It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to .ms.dat files
  • \n
  • prefix (str):\nEnsemble prefix
  • \n
  • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
  • \n
  • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
  • \n
  • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
  • \n
  • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
  • \n
  • postfix (str):\nPostfix of measurement file (Default: ms)
  • \n
  • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
  • \n
  • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
  • \n
  • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
  • \n
  • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
  • \n
  • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
  • \n
  • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
  • \n
\n\n
Returns
\n\n
    \n
  • w0 (Obs):\nExtracted w0
  • \n
\n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "

Read the topologial charge based on openQCD gradient flow measurements.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
  • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
  • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
  • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
  • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
  • \n
  • version (str):\nEither openQCD or sfqcd, depending on the data.
  • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
  • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
  • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
  • \n
  • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
  • \n
\n\n
Returns
\n\n
    \n
  • result (Obs):\nRead topological charge
  • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "

Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.

\n\n

Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
  • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
  • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
  • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
  • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
  • \n
  • r_start (list):\nlist which contains the first config to be read for each replicum.
  • \n
  • r_stop (list):\nlist which contains the last config to be read for each replicum.
  • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
  • \n
  • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
  • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
  • \n
\n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "

Returns the projection to the topological charge sector defined by target.

\n\n
Parameters
\n\n
    \n
  • path (Obs):\nTopological charge.
  • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
  • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
  • \n
\n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "

Constructs reweighting factors to a specified topological sector.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath of the measurement files
  • \n
  • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
  • \n
  • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
  • \n
  • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
  • \n
  • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
  • \n
  • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
  • \n
  • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
  • \n
  • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
  • \n
  • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
  • \n
  • r_stop (list):\nlast configurations that need to be read (per replicum)
  • \n
  • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
  • \n
  • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
  • \n
\n\n
Returns
\n\n
    \n
  • reto (Obs):\nprojection to the topological charge sector defined by target
  • \n
\n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "

Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.

\n\n
Parameters
\n\n
    \n
  • path (str):\nThe directory to search for the files in.
  • \n
  • prefix (str):\nThe prefix to match the files against.
  • \n
  • qc (str):\nThe quark combination extension to match the files against.
  • \n
  • corr (str):\nThe correlator to extract data for.
  • \n
  • sep (str, optional):\nThe separator to use when parsing the replika names.
  • \n
  • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:

    \n\n
      \n
    • names (List[str]): A list of names to use for the replicas.
    • \n
    • files (List[str]): A list of files to read data from.
    • \n
    • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
    • \n
  • \n
\n\n
Returns
\n\n
    \n
  • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
  • \n
  • or
  • \n
  • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
  • \n
\n\n
Raises
\n\n
    \n
  • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
  • \n
  • IOError: If there is an error reading a file.
  • \n
  • struct.error: If there is an error unpacking binary data.
  • \n
\n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "

\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "

Write DataFrame including Obs or Corr valued columns to sqlite database.

\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be written to the database.
  • \n
  • table_name (str):\nName of the table in the database.
  • \n
  • db (str):\nPath to the sqlite database.
  • \n
  • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
  • \n
  • gz (bool):\nIf True the json strings are gzipped.
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "

Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.

\n\n
Parameters
\n\n
    \n
  • sql (str):\nSQL query to be executed.
  • \n
  • db (str):\nPath to the sqlite database.
  • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
  • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
  • \n
\n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "

Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.

\n\n

Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.

\n\n
Parameters
\n\n
    \n
  • df (pandas.DataFrame):\nDataframe to be dumped to a file.
  • \n
  • fname (str):\nFilename of the output file.
  • \n
  • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "

Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.

\n\n
Parameters
\n\n
    \n
  • fname (str):\nFilename of the input file.
  • \n
  • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
  • \n
  • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
  • \n
\n\n
Returns
\n\n
    \n
  • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
  • \n
\n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "

\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "

Read sfcf files from given folder structure.

\n\n
Parameters
\n\n
    \n
  • path (str):\nPath to the sfcf files.
  • \n
  • prefix (str):\nPrefix of the sfcf files.
  • \n
  • name (str):\nName of the correlation function to read.
  • \n
  • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
  • \n
  • corr_type (str):\nType of correlation function to read. Can be\n
      \n
    • 'bi' for boundary-inner
    • \n
    • 'bb' for boundary-boundary
    • \n
    • 'bib' for boundary-inner-boundary
    • \n
  • \n
  • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
  • \n
  • wf (int):\nID of wave function
  • \n
  • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
  • \n
  • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
  • \n
  • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
  • \n
  • ens_name (str):\nreplaces the name of the ensemble
  • \n
  • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
  • \n
  • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
  • \n
  • replica (list):\nlist of replica to be read, default is all
  • \n
  • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
  • \n
  • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
  • \n
\n\n
Returns
\n\n
    \n
  • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
  • \n
\n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "

\n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "

Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.

\n\n
Parameters
\n\n
    \n
  • ll (list):\nlist to sort
  • \n
\n\n
Returns
\n\n
    \n
  • ll (list):\nsorted list
  • \n
\n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "

Checks if list of configurations is contained in an idl

\n\n
Parameters
\n\n
    \n
  • idl (range or list):\nidl of the current replicum
  • \n
  • che (list):\nlist of configurations to be checked against
  • \n
\n\n
Returns
\n\n
    \n
  • miss_str (str):\nstring with integers of which idls are missing
  • \n
\n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "

\n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "

Performs a (one-dimensional) numeric integration of f(p, x) from a to b.

\n\n

The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.

\n\n
Parameters
\n\n
    \n
  • func (object):\nfunction to integrate, has to be of the form

    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(p, x):\n   return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
    \n
    \n\n

    where x is the integration variable.

  • \n
  • p (list of floats or Obs):\nparameters of the function func.
  • \n
  • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
  • \n
  • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
  • \n
  • All parameters of scipy.integrate.quad
  • \n
\n\n
Returns
\n\n
    \n
  • y (Obs):\nThe integral of func from a to b.
  • \n
  • abserr (float):\nAn estimate of the absolute error in the result.
  • \n
  • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
  • \n
  • message: A convergence message.
  • \n
  • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
  • \n
\n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "

\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "

Matrix multiply all operands.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
  • \n
  • This implementation is faster compared to standard multiplication via the @ operator.
  • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "

Matrix multiply both operands making use of the jackknife approximation.

\n\n
Parameters
\n\n
    \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
  • \n
  • For large matrices this is considerably faster compared to matmul.
  • \n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "

Wrapper for numpy.einsum

\n\n
Parameters
\n\n
    \n
  • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
  • \n
  • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
  • \n
\n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "

Inverse of Obs or CObs valued matrices.

\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "

Cholesky decomposition of Obs valued matrices.

\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "

Determinant of Obs valued matrices.

\n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "

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

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "

Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "

Computes the Moore-Penrose pseudoinverse of a matrix of Obs.

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "

Computes the singular value decomposition of a matrix of Obs.

\n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "

\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "

Print information about version of python, pyerrors and dependencies.

\n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "

pyerrors wrapper for the errorbars method of matplotlib

\n\n
Parameters
\n\n
    \n
  • x (list):\nA list of x-values which can be Obs.
  • \n
  • y (list):\nA list of y-values which can be Obs.
  • \n
  • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
  • \n
\n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "

Dump object into pickle file.

\n\n
Parameters
\n\n
    \n
  • obj (object):\nobject to be saved in the pickle file
  • \n
  • name (str):\nname of the file
  • \n
  • path (str):\nspecifies a custom path for the file (default '.')
  • \n
\n\n
Returns
\n\n
    \n
  • None
  • \n
\n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "

Load object from pickle file.

\n\n
Parameters
\n\n
    \n
  • path (str):\npath to the file
  • \n
\n\n
Returns
\n\n
    \n
  • object (Obs):\nLoaded Object
  • \n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "

Generate an Obs object with given value, dvalue and name for test purposes

\n\n
Parameters
\n\n
    \n
  • value (float):\ncentral value of the Obs to be generated.
  • \n
  • dvalue (float):\nerror of the Obs to be generated.
  • \n
  • name (str):\nname of the ensemble for which the Obs is to be generated.
  • \n
  • samples (int):\nnumber of samples for the Obs (default 1000).
  • \n
\n\n
Returns
\n\n
    \n
  • res (Obs):\nGenerated Observable
  • \n
\n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "

Generate observables with given covariance and autocorrelation times.

\n\n
Parameters
\n\n
    \n
  • means (list):\nlist containing the mean value of each observable.
  • \n
  • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
  • \n
  • name (str):\nensemble name for the data to be geneated.
  • \n
  • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
  • \n
  • samples (int):\nnumber of samples to be generated for each observable.
  • \n
\n\n
Returns
\n\n
    \n
  • corr_obs (list[Obs]):\nGenerated observable list
  • \n
\n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "

\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "

Matrix pencil method to extract k energy levels from data

\n\n

Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)

\n\n
Parameters
\n\n
    \n
  • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
  • \n
  • k (int):\nNumber of states to extract (default 1).
  • \n
  • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
  • \n
\n\n
Returns
\n\n
    \n
  • energy_levels (list[Obs]):\nExtracted energy levels
  • \n
\n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "

\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "

Class for a general observable.

\n\n

Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.

\n\n
Attributes
\n\n
    \n
  • S_global (float):\nStandard value for S (default 2.0)
  • \n
  • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
  • \n
  • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
  • \n
  • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
  • \n
  • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
  • \n
  • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
  • \n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "

Initialize Obs object.

\n\n
Parameters
\n\n
    \n
  • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
  • \n
  • names (list):\nlist of strings labeling the individual samples
  • \n
  • idl (list, optional):\nlist of ranges or lists on which the samples are defined
  • \n
\n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "

\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "

\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "

\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "

\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "

\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "

\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "

Estimate the error and related properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
  • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
  • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
  • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
  • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "

Estimate the error and related properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
  • \n
  • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
  • \n
  • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
  • \n
  • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
  • \n
\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "

Output detailed properties of the Obs.

\n\n
Parameters
\n\n
    \n
  • ens_content (bool):\nprint details about the ensembles and replica if true.
  • \n
\n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "

Reweight the obs with given rewighting factors.

\n\n
Parameters
\n\n
    \n
  • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
  • \n
  • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
  • \n
\n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "

Checks whether the observable is zero within 'sigma' standard errors.

\n\n
Parameters
\n\n
    \n
  • sigma (int):\nNumber of standard errors used for the check.
  • \n
  • Works only properly when the gamma method was run.
  • \n
\n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "

Checks whether the observable is zero within a given tolerance.

\n\n
Parameters
\n\n
    \n
  • atol (float):\nAbsolute tolerance (for details see numpy documentation).
  • \n
\n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "

Plot integrated autocorrelation time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
  • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "

Plot normalized autocorrelation function time for each ensemble.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
  • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "

Plot replica distribution for each ensemble with more than one replicum.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "

Plot derived Monte Carlo history for each ensemble

\n\n
Parameters
\n\n
    \n
  • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
  • \n
\n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "

Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.

\n\n
Parameters
\n\n
    \n
  • save (str):\nsaves the figure to a file named 'save' if.
  • \n
\n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "

Dump the Obs to a file 'name' of chosen format.

\n\n
Parameters
\n\n
    \n
  • filename (str):\nname of the file to be saved.
  • \n
  • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
  • \n
  • description (str):\nDescription for output file, only relevant for json.gz format.
  • \n
  • path (str):\nspecifies a custom path for the file (default '.')
  • \n
\n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "

Export jackknife samples from the Obs

\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
  • \n
\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "

Export bootstrap samples from the Obs

\n\n
Parameters
\n\n
    \n
  • samples (int):\nNumber of bootstrap samples to generate.
  • \n
  • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
  • \n
  • save_rng (str):\nSave the random numbers to a file if a path is specified.
  • \n
\n\n
Returns
\n\n
    \n
  • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
  • \n
\n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "

Class for a complex valued observable.

\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "

\n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "

\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "

Executes the gamma_method for the real and the imaginary part.

\n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "

Checks whether both real and imaginary part are zero within machine precision.

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "

\n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.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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