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)
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.
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.
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 +@@ -3103,14 +3176,14 @@ matrix at every timeslice. Other dependency (eg. spatial) are not supported.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
- 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.
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) +@@ -3211,16 +3284,16 @@ region indentified for this correlator.141 def gamma_method(self, **kwargs): +142 """Apply the gamma method to the content of the Corr.""" +143 for item in self.content: +144 if not (item is None): +145 if self.N == 1: +146 item[0].gamma_method(**kwargs) +147 else: +148 for i in range(self.N): +149 for j in range(self.N): +150 item[i, j].gamma_method(**kwargs)
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) +@@ -3240,44 +3313,44 @@ region indentified for this correlator.141 def gamma_method(self, **kwargs): +142 """Apply the gamma method to the content of the Corr.""" +143 for item in self.content: +144 if not (item is None): +145 if self.N == 1: +146 item[0].gamma_method(**kwargs) +147 else: +148 for i in range(self.N): +149 for j in range(self.N): +150 item[i, j].gamma_method(**kwargs)
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) +@@ -3301,20 +3374,20 @@ By default it will return the lowest source, which usually means unsmeared-unsme154 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)
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) +@@ -3343,19 +3416,19 @@ Second index to be picked.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)
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 +@@ -3378,26 +3451,26 @@ timeslice and the error on each timeslice.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
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) +@@ -3417,27 +3490,27 @@ timeslice and the error on each timeslice.222 def symmetric(self): +223 """ Symmetrize the correlator around x0=0.""" +224 if self.N != 1: +225 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') +226 if self.T % 2 != 0: +227 raise Exception("Can not symmetrize odd T") +228 +229 if self.content[0] is not None: +230 if np.argmax(np.abs([o[0].value if o is not None else 0 for o in self.content])) != 0: +231 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) +232 +233 newcontent = [self.content[0]] +234 for t in range(1, self.T): +235 if (self.content[t] is None) or (self.content[self.T - t] is None): +236 newcontent.append(None) +237 else: +238 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) +239 if (all([x is None for x in newcontent])): +240 raise Exception("Corr could not be symmetrized: No redundant values") +241 return Corr(newcontent, prange=self.prange)
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) +@@ -3457,20 +3530,20 @@ timeslice and the error on each timeslice.243 def anti_symmetric(self): +244 """Anti-symmetrize the correlator around x0=0.""" +245 if self.N != 1: +246 raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.') +247 if self.T % 2 != 0: +248 raise Exception("Can not symmetrize odd T") +249 +250 test = 1 * self +251 test.gamma_method() +252 if not all([o.is_zero_within_error(3) for o in test.content[0]]): +253 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) +254 +255 newcontent = [self.content[0]] +256 for t in range(1, self.T): +257 if (self.content[t] is None) or (self.content[self.T - t] is None): +258 newcontent.append(None) +259 else: +260 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) +261 if (all([x is None for x in newcontent])): +262 raise Exception("Corr could not be symmetrized: No redundant values") +263 return Corr(newcontent, prange=self.prange)
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 +@@ -3490,17 +3563,17 @@ timeslice and the error on each timeslice.265 def is_matrix_symmetric(self): +266 """Checks whether a correlator matrices is symmetric on every timeslice.""" +267 if self.N == 1: +268 raise TypeError("Only works for correlator matrices.") +269 for t in range(self.T): +270 if self[t] is None: +271 continue +272 for i in range(self.N): +273 for j in range(i + 1, self.N): +274 if self[t][i, j] is self[t][j, i]: +275 continue +276 if hash(self[t][i, j]) != hash(self[t][j, i]): +277 return False +278 return True
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) +@@ -3520,15 +3593,15 @@ timeslice and the error on each timeslice.280 def trace(self): +281 """Calculates the per-timeslice trace of a correlator matrix.""" +282 if self.N == 1: +283 raise ValueError("Only works for correlator matrices.") +284 newcontent = [] +285 for t in range(self.T): +286 if _check_for_none(self, self.content[t]): +287 newcontent.append(None) +288 else: +289 newcontent.append(np.trace(self.content[t])) +290 return Corr(newcontent)
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) +@@ -3548,84 +3621,84 @@ timeslice and the error on each timeslice.292 def matrix_symmetric(self): +293 """Symmetrizes the correlator matrices on every timeslice.""" +294 if self.N == 1: +295 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") +296 if self.is_matrix_symmetric(): +297 return 1.0 * self +298 else: +299 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] +300 return 0.5 * (Corr(transposed) + self)
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 +@@ -3678,18 +3751,18 @@ Returns only the vector(s) for a specified state. The lowest state is zero.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
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) +@@ -3717,46 +3790,46 @@ The state one is interested in ordered by energy. The lowest state is zero.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)
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) +@@ -3790,15 +3863,15 @@ determines whether the matrix is extended periodically394 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)
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))) + @@ -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]) + @@ -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) +@@ -3892,34 +3965,34 @@ Offset the equal spacing449 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)
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) +@@ -3948,28 +4021,28 @@ correlator or a Corr of same length.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)
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) +@@ -4001,35 +4074,35 @@ on the configurations in obs[i].idl.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)
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 +@@ -4040,7 +4113,7 @@ on the configurations in obs[i].idl.519 def T_symmetry(self, partner, parity=+1): +520 """Return the time symmetry average of the correlator and its partner +521 +522 Parameters +523 ---------- +524 partner : Corr +525 Time symmetry partner of the Corr +526 parity : int +527 Parity quantum number of the correlator, can be +1 or -1 +528 """ +529 if self.N != 1: +530 raise Exception("T_symmetry only implemented for one-dimensional correlators.") +531 if not isinstance(partner, Corr): +532 raise Exception("T partner has to be a Corr object.") +533 if parity not in [+1, -1]: +534 raise Exception("Parity has to be +1 or -1.") +535 T_partner = parity * partner.reverse() +536 +537 t_slices = [] +538 test = (self - T_partner) +539 test.gamma_method() +540 for x0, t_slice in enumerate(test.content): +541 if t_slice is not None: +542 if not t_slice[0].is_zero_within_error(5): +543 t_slices.append(x0) +544 if t_slices: +545 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) +546 +547 return (self + T_partner) / 2
- partner (Corr): Time symmetry partner of the Corr
-- partity (int): +
- parity (int): 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.") +@@ -4149,68 +4222,68 @@ Available choice: symmetric, forward, backward, improved, log, default: symmetri549 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.")
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.") +@@ -4246,89 +4319,89 @@ Available choice: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.")
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 +@@ -4339,8 +4412,8 @@ Available choice:677 def m_eff(self, variant='log', guess=1.0): +678 """Returns the effective mass of the correlator as correlator object +679 +680 Parameters +681 ---------- +682 variant : str +683 log : uses the standard effective mass log(C(t) / C(t+1)) +684 cosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. +685 sinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m. +686 See, e.g., arXiv:1205.5380 +687 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) +688 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 +689 guess : float +690 guess for the root finder, only relevant for the root variant +691 """ +692 if self.N != 1: +693 raise Exception('Correlator must be projected before getting m_eff') +694 if variant == 'log': +695 newcontent = [] +696 for t in range(self.T - 1): +697 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): +698 newcontent.append(None) +699 elif self.content[t][0].value / self.content[t + 1][0].value < 0: +700 newcontent.append(None) +701 else: +702 newcontent.append(self.content[t] / self.content[t + 1]) +703 if (all([x is None for x in newcontent])): +704 raise Exception('m_eff is undefined at all timeslices') 705 -706 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.')
- 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 +@@ -4428,42 +4501,42 @@ Decides whether output is printed to the standard output.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
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) +@@ -4497,17 +4570,17 @@ apply gamma_method with default parameters to the Corr. Defaults to None795 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)
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 +@@ -4527,130 +4600,130 @@ apply gamma_method with default parameters to the Corr. Defaults to None832 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
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='-') +@@ -4700,34 +4773,34 @@ Optional title of the figure.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.")
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') +@@ -4754,29 +4827,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.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()
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)) +@@ -4808,8 +4881,8 @@ specifies a custom path for the file (default '.')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))
1000 def print(self, print_range=None): -1001 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 + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) + @@ -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) +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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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)0&&t.push(e);for(var i in n)"docs"!==i&&"df"!==i&&this.expandToken(e+i,t,n[i]);return t},t.InvertedIndex.prototype.toJSON=function(){return{root:this.root}},t.Configuration=function(e,n){var e=e||"";if(void 0==n||null==n)throw new Error("fields should not be null");this.config={};var i;try{i=JSON.parse(e),this.buildUserConfig(i,n)}catch(o){t.utils.warn("user configuration parse failed, will use default 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;e 1;){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();o What is pyerrors?\n\n \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...).
\nMore detailed examples can found in the GitHub repository
\n\n.
If you use
\n\npyerrors
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.
\nand
\n\n\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.
\nwhere applicable.
\n\nThere exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
\n\nInstallation
\n\nInstall the most recent release using pip and pypi:
\n\n\n\n\n\npython -m pip install pyerrors # Fresh install\npython -m pip install -U pyerrors # Update\n
Install the most recent release using conda and conda-forge:
\n\n\n\n\n\nconda install -c conda-forge pyerrors # Fresh install\nconda update -c conda-forge pyerrors # Update\n
Install the current
\n\ndevelop
version:\n\n\n\npython -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
(Also works for any feature branch).
\n\nBasic example
\n\n\n\n\n\nimport 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
The
\n\nObs
class\n\n
pyerrors
introduces a new datatype,Obs
, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAnObs
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\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
Error propagation
\n\nWhen performing mathematical operations on
\n\nObs
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.The
\n\nObs
class is designed such that mathematical numpy functions can be used onObs
just as for regular floats.\n\n\n\nimport 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
Error estimation
\n\nThe error estimation within
\n\npyerrors
is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest thegamma_method
can be called as detailed in the following example.\n\n\n\nmy_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
The
\n\ngamma_method
is not automatically called after every intermediate step in order to prevent computational overhead.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
\n\ngamma_method
as parameter.\n\n\n\nmy_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
The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods
\n\npyerrors.obs.Obs.plot_tauint
andpyerrors.obs.Obs.plot_rho
.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\nExponential tails
\n\nSlow 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
\n\ngamma_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\nmy_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
For the full API see
\n\npyerrors.obs.Obs.gamma_method
.Multiple ensembles/replica
\n\nError propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their
\n\nname
.\n\n\n\nobs1 = 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
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\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\nobs1 = 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
Error estimation for multiple ensembles
\n\nIn 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\n\n\npe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
In case the
\n\ngamma_method
is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to thegamma_method
still dominates over the dictionaries.Irregular Monte Carlo chains
\n\n\n\n
Obs
objects defined on irregular Monte Carlo chains can be initialized with the parameteridl
.\n\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
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.Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g.
\n\npyerrors.obs.Obs.plot_rho
orpyerrors.obs.Obs.plot_tauint
.For the full API see
\n\npyerrors.obs.Obs
.Correlators
\n\nWhen one is not interested in single observables but correlation functions,
\n\npyerrors
offers theCorr
class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize aCorr
objects one needs to arrange the data as a list ofObs
\n\n\n\nmy_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
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\n\n\nmy_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
The individual entries of a correlator can be accessed via slicing
\n\n\n\n\n\nprint(my_corr[3])\n> 0.3227(33)\n
Error propagation with the
\n\nCorr
class works very similar toObs
objects. Mathematical operations are overloaded andCorr
objects can be computed together with otherCorr
objects,Obs
objects or real numbers and integers.\n\n\n\nmy_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
\n\n
pyerrors
provides the user with a set of regularly used methods for the manipulation of correlator objects:\n
\n\n- \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 asCorr
. Different discretizations of the numerical derivative are available.- \n
Corr.second_deriv
returns the second derivative of the correlator asCorr
. 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 anotherCorr
orObs
object.- \n
Corr.reweight
reweights the correlator.\n\n
pyerrors
can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (seepyerrors.correlators.Corr.GEVP
).For the full API see
\n\npyerrors.correlators.Corr
.Complex valued observables
\n\n\n\n
pyerrors
can handle complex valued observables via the classpyerrors.obs.CObs
.\nCObs
are initialized with a real and an imaginary part which both can beObs
valued.\n\n\n\nmy_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
Elementary mathematical operations are overloaded and samples are properly propagated as for the
\n\nObs
class.\n\n\n\nmy_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
The
\n\nCovobs
classIn 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
\n\nCovobs
class allows to define such quantities inpyerrors
. 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.This concept is built into the definition of
\n\nCovobs
. Inpyerrors
, 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 enterscov_Obs
, since the second argument of this function is the covariance matrix of theCovobs
.\n\n\n\nimport 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
The resulting object
\n\nmpi
is anObs
that contains aCovobs
. In the following, it may be handled as any otherObs
. The contribution of the covariance matrix to the error of anObs
is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of theObs
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.Correlated auxiliary data is defined similarly to above, e.g., via
\n\n\n\n\n\nRAP = 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
where
\n\nRAP
now is a list of twoObs
that contains the two correlated parameters.Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the
\n\nCovobs
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 anObs
o
with respect to a covariance matrix with the identifying stringk
may be accessed via\n\n\n\no.covobs[k].grad\n
Error propagation in iterative algorithms
\n\n\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.Least squares fits
\n\nStandard non-linear least square fits with errors on the dependent but not the independent variables can be performed with
\n\npyerrors.fits.least_squares
. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.Fit functions have to be of the following form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(a, x):\n return a[1] * anp.exp(-a[0] * x)\n
It is important that numerical functions refer to
\n\nautograd.numpy
instead ofnumpy
for the automatic differentiation in iterative algorithms to work properly.Fits can then be performed via
\n\n\n\n\n\nfit_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
where x is a
\n\nlist
ornumpy.array
offloats
and y is alist
ornumpy.array
ofObs
.Data stored in
\n\nCorr
objects can be fitted directly using theCorr.fit
method.\n\n\n\nmy_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
\n\nFor fit functions with multiple independent variables the fit function can be of the form
\n\n\n\n\n\ndef func(a, x):\n (x1, x2) = x\n return a[0] * x1 ** 2 + a[1] * x2\n
\n\n
pyerrors
also supports correlated fits which can be triggered via the parametercorrelated_fit=True
.\nDetails about how the required covariance matrix is estimated can be found inpyerrors.obs.covariance
.\nDirect visualizations of the performed fits can be triggered viaresplot=True
orqqplot=True
.For all available options including combined fits to multiple datasets see
\n\npyerrors.fits.least_squares
.Total least squares fits
\n\n\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, seepyerrors.fits.least_squares
. The syntax is identical to the standard least squares case, the only difference being thatx
also has to be alist
ornumpy.array
ofObs
.For the full API see
\n\npyerrors.fits
for fits andpyerrors.roots
for finding roots of functions.Matrix operations
\n\n\n\n
pyerrors
provides wrappers forObs
- andCObs
-valued matrix operations based onnumpy.linalg
. The supported functions include:\n
\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.For the full API see
\n\npyerrors.linalg
.Export data
\n\n\n\nThe preferred exported file format within
\n\npyerrors
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?
\nThis can be achieved by storing all information in one single file. The export routines of
\n\npyerrors
are written such that as much information as possible is written automatically as described in the following example\n\n\n\nmy_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
The format also allows to directly write out the content of
\n\nCorr
objects or lists and arrays ofObs
objects by passing the desired data topyerrors.input.json.dump_to_json
.json.gz format specification
\n\nThe first entries of the file provide optional auxiliary information:
\n\n\n
\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 inpyerrors
. 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.The only necessary entry of the file is the field\n-
\n\nobsdata
, an array that contains the actual data.Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of
\n\nObs
,list
,numpy.ndarray
,Corr
. AllObs
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 arrayobsdata
, are treated independently. Each entry of the arrayobsdata
has the following required entries:\n
\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. Thetag
of anObs
inpyerrors
is written here.- \n
reweighted
is a Bool that may be used to specify, whether theObs
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
inpyerrors
). We will define it below.The array
\n\ndata
contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:\n
\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.Each entry of
\n\nreplica
contains\nname
, a string that contains the name of the replica\ndeltas
, an array that contains the actual data.Each entry in
\n\ndeltas
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 eachObs
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.The array
\n\ncdata
contains information about the contribution of auxiliary observables, represented byCovobs
inpyerrors
, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:\n
\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 eachObs
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.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\nJulia 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\nEverything, 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\nThe 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\nParameters
\n\n\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": "- 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.
\nApply 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\nThe 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\nParameters
\n\n\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": "- i (int):\nFirst index to be picked.
\n- j (int):\nSecond index to be picked.
\nOutputs the correlator in a plotable format.
\n\nOutputs 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\nThe 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\n\n\nC.GEVP(t0=2)[0] # Ground state vector(s)\nC.GEVP(t0=2)[:3] # Vectors for the lowest three states\n
Parameters
\n\n\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\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 $t=t_s$.
\nOther Parameters
\n\n\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": "- state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
\nDetermines the eigenvalue of the GEVP by solving and projecting the correlator
\n\nParameters
\n\n\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": "- 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.
\nConstructs an NxN Hankel matrix
\n\nC(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\nParameters
\n\n\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": "- N (int):\nDimension of the Hankel matrix
\n- periodic (bool, optional):\ndetermines whether the matrix is extended periodically
\nPeriodically shift the correlator by dt timeslices
\n\nParameters
\n\n\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": "- dt (int):\nnumber of timeslices
\nReverse 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\nParameters
\n\n\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": "- spacing (int):\nKeep only every 'spacing'th entry of the correlator
\n- offset (int):\nOffset the equal spacing
\nCorrelate the correlator with another correlator or Obs
\n\nParameters
\n\n\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": "- 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.
\nReweight the correlator.
\n\nParameters
\n\n\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": "- 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.
\nReturn the time symmetry average of the correlator and its partner
\n\nParameters
\n\n\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": "- partner (Corr):\nTime symmetry partner of the Corr
\n- partity (int):\nParity quantum number of the correlator, can be +1 or -1
\nReturn the first derivative of the correlator with respect to x0.
\n\nParameters
\n\n\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": "- variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
\nReturn the second derivative of the correlator with respect to x0.
\n\nParameters
\n\n\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": "- 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 $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
\nReturns the effective mass of the correlator as correlator object
\n\nParameters
\n\n\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": "- 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
\nFits function to the data
\n\nParameters
\n\n\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": "- 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.\n
\nfitrange=[4, 6]
corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.- silent (bool):\nDecides whether output is printed to the standard output.
\nExtract a plateau value from a Corr object
\n\nParameters
\n\n\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": "- 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
\nSets 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\nParameters
\n\n\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": "- 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.
\nProduces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\nParameters
\n\n\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": "- logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
\nDumps the Corr into a file of chosen type
\n\nParameters
\n\n\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": "- 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 '.')
\nProject large correlation matrix to lowest states
\n\nThis 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\nParameters
\n\n\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.
\nNotes
\n\nWe 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\nParameters
\n\n\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": "- 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.
\nReturn 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\nBased on https://codegolf.stackexchange.com/a/160375
\n\nReturns
\n\n\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": "- elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
\nRank-4 epsilon tensor
\n\nExtension of https://codegolf.stackexchange.com/a/160375
\n\nReturns
\n\n\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": "- elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
\nReturns 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\nAttributes
\n\n\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": "- 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.
\nApply 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\nParameters
\n\n\n
\n\n- For an uncombined fit:
\n- x (list):\nlist of floats.
\n- y (list):\nlist of Obs.
\n- \n
func (object):\nfit function, has to be of the form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(a, x):\n return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
For multiple x values func can be of the form
\n\n\n\n\n\ndef func(a, x):\n (x1, x2) = x\n return a[0] * x1 ** 2 + a[1] * x2\n
It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
- OR For a combined fit:
\n- x (dict):\ndict of lists.
\n- y (dict):\ndict of lists of Obs.
\n- \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\ndef func_a(a, x):\n return a[1] * anp.exp(-a[0] * x)
\n\ndef func_b(a, x):\n return a[2] * anp.exp(-a[0] * x)
\n\nIt is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
- 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
\npyerrors.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).- 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).
\nReturns
\n\n\n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "- output (Fit_result):\nParameters and information on the fitted result.
\nPerforms a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\nParameters
\n\n\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- \n
func (object):\nfunc has to be of the form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(a, x):\n return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
For multiple x values func can be of the form
\n\n\n\n\n\ndef func(a, x):\n (x1, x2) = x\n return a[0] * x1 ** 2 + a[1] * x2\n
It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
- 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).
\nNotes
\n\nBased on the orthogonal distance regression module of scipy.
\n\nReturns
\n\n\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": "- output (Fit_result):\nParameters and information on the fitted result.
\nPerforms a linear fit to y = n + m * x and returns two Obs n, m.
\n\nParameters
\n\n\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.
\nReturns
\n\n\n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "- fit_parameters (list[Obs]):\nLIist of fitted observables.
\nGenerates 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\nReturns
\n\n\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": "- None
\nGenerates a plot which compares the fit to the data and displays the corresponding residuals
\n\nFor uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\nReturns
\n\n\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": "- None
\nCalculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\nReturns
\n\n\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": "- err (np.array(Obs)):\nError band for an array of sample values x
\nPerforms a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\nParameters
\n\n\n
\n\n- objects (list):\nList of fit results to include in the analysis (optional).
\nReturns
\n\n\n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "- None
\n\n\n
pyerrors
includes aninput
submodule in which input routines and parsers for the output of various numerical programs are contained.Jackknife samples
\n\nFor comparison with other analysis workflows
\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": "pyerrors
can also generate jackknife samples from anObs
object or import jackknife samples into anObs
object.\nSeepyerrors.obs.Obs.export_jackknife
andpyerrors.obs.import_jackknife
for details.Extract generic MCMC data from a bdio file
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\n
\n\n- file_path -- path to the bdio file
\n- bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
\nReturns
\n\n\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": "- data (List[Obs]):\nExtracted data
\nWrite Obs to a bdio file according to ADerrors conventions
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\n
\n\n- file_path -- path to the bdio file
\n- bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
\nReturns
\n\n\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": "- success (int):\nreturns 0 is successful
\nExtract mesons data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\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
\nReturns
\n\n\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": "- data (dict):\nExtracted meson data
\nExtract dSdm data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, kappa)
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\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": "- 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
\nExport a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- xml_str (str):\nXML formatted string of the input data
\nExport a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nImport a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- res (list[Obs]):\nImported data
\n- or
\n- res (dict):\nImported data and meta-data
\nImport a list of Obs from a string in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- res (list[Obs]):\nImported data
\n- or
\n- res (dict):\nImported data and meta-data
\nImport a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- res (list[Obs]):\nImported data
\n- or
\n- res (dict):\nImported data and meta-data
\nGenerate 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\nTags are not written or recovered automatically. The separator |is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- xml_str (str):\nXML string generated from the data
\nExport a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nRead hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- corr (Corr):\nCorrelator of the source sink combination in question.
\nRead hadrons FlowObservables hdf5 file and extract t0
\n\nParameters
\n\n\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": "- 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.
\nRead hadrons DistillationContraction hdf5 files in given directory structure
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result (dict):\nextracted DistillationContration data
\nndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)
\n\nAn 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\nArrays should be constructed using
\n\narray
,zeros
orempty
(refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)
) for instantiating an array.For more information, refer to the
\n\nnumpy
module and examine the\nmethods and attributes of an array.Parameters
\n\n\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.
\nAttributes
\n\n\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.,
\nx.flat = 3
(Seendarray.flat
for\nassignment examples; TODO).- 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.,
\nitemsize * size
.- 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
\n(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
).- 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
\nbase
\n(unless that array is also a view). Thebase
array is where the\narray data is actually stored.See Also
\n\n\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. itsdtype.type <numpy.dtype.type>
.Notes
\n\nThere are two modes of creating an array using
\n\n__new__
:\n
\n\n- If
\nbuffer
is None, then onlyshape
,dtype
, andorder
\nare used.- If
\nbuffer
is an object exposing the buffer interface, then\nall keywords are interpreted.No
\n\n__init__
method is needed because the array is fully initialized\nafter the__new__
method.Examples
\n\nThese examples illustrate the low-level
\n\nndarray
constructor. Refer\nto theSee Also
section above for easier ways of constructing an\nndarray.First mode,
\n\nbuffer
is None:\n\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
Second mode:
\n\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": "\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
Gamma_5 hermitean conjugate
\n\nUses 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\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result (Npr_matrix):\nread Cobs-matrix
\nRead hadrons Bilinear hdf5 file and output an array of CObs
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result_dict (dict[Npr_matrix]):\nextracted Bilinears
\nRead hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result_dict (dict):\nextracted fourquark matrizes
\nGenerate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- json_string (str):\nString for export to .json(.gz) file
\nExport 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\nParameters
\n\n\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.
\nReturns
\n\n\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": "- Null
\nReconstruct a list of Obs or structures containing Obs from a json string.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- 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
\nImport a list of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- 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
\nExport a dict of Obs or structures containing Obs to a .json(.gz) file
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nImport a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr
\n\nParameters
\n\n\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]+.
\nReturns
\n\n\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": "- data (Obs / list / Corr):\nRead data
\n- or
\n- data (dict):\nRead data and meta-data
\nCompute 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\nIt 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\nA linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
\n\nParameters
\n\n\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')
\nReturns
\n\n\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": "- root (Obs):\nThe root of the data series.
\nRead pbp format from given folder structure.
\n\nParameters
\n\n\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
\nReturns
\n\n\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": "- result (list[Obs]):\nlist of observables read
\nRead rwms format from given folder structure. Returns a list of length nrw
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- rwms (Obs):\nReweighting factors read
\nExtract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
\n\nIt is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2
\n\n- c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted. 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\nParameters
\n\n\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
\nReturns
\n\n\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": "- t0 (Obs):\nExtracted t0
\nExtract w0/a from given .ms.dat files. Returns w0 as Obs.
\n\nIt is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2
\n\n)/dt - (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted. 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\nParameters
\n\n\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
\nReturns
\n\n\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": "- w0 (Obs):\nExtracted w0
\nRead the topologial charge based on openQCD gradient flow measurements.
\n\nParameters
\n\n\n
\n\n- path (str):\npath of the measurement files
\n- prefix (str):\nprefix of the measurement files, e.g.
\n_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files. - 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.
\nReturns
\n\n\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": "- result (Obs):\nRead topological charge
\nRead the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
\n\nNote: 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\nParameters
\n\n\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": "- path (str):\npath of the measurement files
\n- prefix (str):\nprefix of the measurement files, e.g.
\n_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files. - 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.
\nReturns the projection to the topological charge sector defined by target.
\n\nParameters
\n\n\n
\n\n- path (Obs):\nTopological charge.
\n- target (int):\nSpecifies the topological sector to be reweighted to (default 0)
\nReturns
\n\n\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": "- reto (Obs):\nprojection to the topological charge sector defined by target
\nConstructs reweighting factors to a specified topological sector.
\n\nParameters
\n\n\n
\n\n- path (str):\npath of the measurement files
\n- prefix (str):\nprefix of the measurement files, e.g.
\n_id0_r0.ms.dat - 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.
\nReturns
\n\n\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": "- reto (Obs):\nprojection to the topological charge sector defined by target
\nRead data from files in the specified directory with the specified prefix and quark combination extension, and return a
\n\nCorr
object containing the data.Parameters
\n\n\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- \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.
\nReturns
\n\n\n
\n\n- Corr: A complex valued
\nCorr
object containing the data read from the files. In case of boudary to bulk correlators.- or
\n- CObs: A complex valued
\nCObs
object containing the data read from the files. In case of boudary to boundary correlators.Raises
\n\n\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": "- 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.
\nWrite DataFrame including Obs or Corr valued columns to sqlite database.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nExecute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
\nExports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
\n\nBefore making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nImports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
\nRead sfcf files from given folder structure.
\n\nParameters
\n\n\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\n
- 'bi' for boundary-inner
\n- 'bb' for boundary-boundary
\n- 'bib' for boundary-inner-boundary
\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
\nReturns
\n\n\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": "- result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
\nSorts a list of names of replika with searches for
\n\nr
andid
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.Parameters
\n\n\n
\n\n- ll (list):\nlist to sort
\nReturns
\n\n\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": "- ll (list):\nsorted list
\nChecks if list of configurations is contained in an idl
\n\nParameters
\n\n\n
\n\n- idl (range or list):\nidl of the current replicum
\n- che (list):\nlist of configurations to be checked against
\nReturns
\n\n\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": "- miss_str (str):\nstring with integers of which idls are missing
\nPerforms a (one-dimensional) numeric integration of f(p, x) from a to b.
\n\nThe 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\nParameters
\n\n\n
\n\n- \n
func (object):\nfunction to integrate, has to be of the form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(p, x):\n return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
where x is the integration variable.
- 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
\nReturns
\n\n\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": "- y (Obs):\nThe integral of func from
\na
tob
.- 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']
\nMatrix multiply all operands.
\n\nParameters
\n\n\n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "- 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.
\nMatrix multiply both operands making use of the jackknife approximation.
\n\nParameters
\n\n\n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "- 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.
\nWrapper for numpy.einsum
\n\nParameters
\n\n\n
\n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "- 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.
\nInverse 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\nParameters
\n\n\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": "- 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.
\nDump object into pickle file.
\n\nParameters
\n\n\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 '.')
\nReturns
\n\n\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": "- None
\nLoad object from pickle file.
\n\nParameters
\n\n\n
\n\n- path (str):\npath to the file
\nReturns
\n\n\n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "- object (Obs):\nLoaded Object
\nGenerate an Obs object with given value, dvalue and name for test purposes
\n\nParameters
\n\n\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).
\nReturns
\n\n\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": "- res (Obs):\nGenerated Observable
\nGenerate observables with given covariance and autocorrelation times.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- corr_obs (list[Obs]):\nGenerated observable list
\nMatrix pencil method to extract k energy levels from data
\n\nImplementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\nParameters
\n\n\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).
\nReturns
\n\n\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": "- energy_levels (list[Obs]):\nExtracted energy levels
\nClass for a general observable.
\n\nInstances 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\nAttributes
\n\n\n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "- 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.
\nInitialize Obs object.
\n\nParameters
\n\n\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": "- 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
\nEstimate the error and related properties of the Obs.
\n\nParameters
\n\n\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": "- 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)
\nEstimate the error and related properties of the Obs.
\n\nParameters
\n\n\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": "- 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)
\nOutput detailed properties of the Obs.
\n\nParameters
\n\n\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": "- ens_content (bool):\nprint details about the ensembles and replica if true.
\nReweight the obs with given rewighting factors.
\n\nParameters
\n\n\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": "- 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.
\nChecks whether the observable is zero within 'sigma' standard errors.
\n\nParameters
\n\n\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": "- sigma (int):\nNumber of standard errors used for the check.
\n- Works only properly when the gamma method was run.
\nChecks whether the observable is zero within a given tolerance.
\n\nParameters
\n\n\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": "- atol (float):\nAbsolute tolerance (for details see numpy documentation).
\nPlot integrated autocorrelation time for each ensemble.
\n\nParameters
\n\n\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": "- save (str):\nsaves the figure to a file named 'save' if.
\nPlot normalized autocorrelation function time for each ensemble.
\n\nParameters
\n\n\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": "- save (str):\nsaves the figure to a file named 'save' if.
\nPlot 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\nParameters
\n\n\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": "- expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
\nPlot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\nParameters
\n\n\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": "- save (str):\nsaves the figure to a file named 'save' if.
\nDump the Obs to a file 'name' of chosen format.
\n\nParameters
\n\n\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": "- 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 '.')
\nExport jackknife samples from the Obs
\n\nReturns
\n\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": "- 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).
\nExport bootstrap samples from the Obs
\n\nParameters
\n\n\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.
\nReturns
\n\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": "- 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).
\nClass 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\nParameters
\n\n\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.
\nNotes
\n\nFor simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\nnew_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\nParameters
\n\n\n
\n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "- 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.
\nCorrelate two observables.
\n\nParameters
\n\n\n
\n\n- obs_a (Obs):\nFirst observable
\n- obs_b (Obs):\nSecond observable
\nNotes
\n\nKeep 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\nWARNING: 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\nThe gamma method has to be applied first to all observables.
\n\nParameters
\n\n\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.
\nNotes
\n\nThe 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\nParameters
\n\n\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": "- 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.
\nImports bootstrap samples and returns an Obs
\n\nParameters
\n\n\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": "- 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.
\nCombine all observables in list_of_obs into one new observable
\n\nParameters
\n\n\n
\n\n- list_of_obs (list):\nlist of the Obs object to be combined
\nNotes
\n\nIt 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\nParameters
\n\n\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": "- 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.
\nFinds the root of the function func(x, d) where d is an
\n\nObs
.Parameters
\n\n\n
\n\n- d (Obs):\nObs passed to the function.
\n- \n
func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
\n\n\n\nimport autograd.numpy as anp\ndef root_func(x, d):\n return anp.exp(-x ** 2) - d\n
- \n
guess (float):\nInitial guess for the minimization.
Returns
\n\n\n
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\nObs
valued root of the function.What is pyerrors?
\n\n\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...).
\nMore detailed examples can found in the GitHub repository
\n\n.
If you use
\n\npyerrors
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.
\nand
\n\n\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.
\nwhere applicable.
\n\nThere exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
\n\nInstallation
\n\nInstall the most recent release using pip and pypi:
\n\n\n\n\n\npython -m pip install pyerrors # Fresh install\npython -m pip install -U pyerrors # Update\n
Install the most recent release using conda and conda-forge:
\n\n\n\n\n\nconda install -c conda-forge pyerrors # Fresh install\nconda update -c conda-forge pyerrors # Update\n
Install the current
\n\ndevelop
version:\n\n\n\npython -m pip install -U --no-deps --force-reinstall git+https://github.com/fjosw/pyerrors.git@develop\n
(Also works for any feature branch).
\n\nBasic example
\n\n\n\n\n\nimport 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
The
\n\nObs
class\n\n
pyerrors
introduces a new datatype,Obs
, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAnObs
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\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
Error propagation
\n\nWhen performing mathematical operations on
\n\nObs
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.The
\n\nObs
class is designed such that mathematical numpy functions can be used onObs
just as for regular floats.\n\n\n\nimport 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
Error estimation
\n\nThe error estimation within
\n\npyerrors
is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest thegamma_method
can be called as detailed in the following example.\n\n\n\nmy_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
The
\n\ngamma_method
is not automatically called after every intermediate step in order to prevent computational overhead.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
\n\ngamma_method
as parameter.\n\n\n\nmy_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
The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods
\n\npyerrors.obs.Obs.plot_tauint
andpyerrors.obs.Obs.plot_rho
.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\nExponential tails
\n\nSlow 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
\n\ngamma_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\nmy_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
For the full API see
\n\npyerrors.obs.Obs.gamma_method
.Multiple ensembles/replica
\n\nError propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their
\n\nname
.\n\n\n\nobs1 = 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
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\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\nobs1 = 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
Error estimation for multiple ensembles
\n\nIn 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\n\n\npe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
In case the
\n\ngamma_method
is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to thegamma_method
still dominates over the dictionaries.Irregular Monte Carlo chains
\n\n\n\n
Obs
objects defined on irregular Monte Carlo chains can be initialized with the parameteridl
.\n\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
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.Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g.
\n\npyerrors.obs.Obs.plot_rho
orpyerrors.obs.Obs.plot_tauint
.For the full API see
\n\npyerrors.obs.Obs
.Correlators
\n\nWhen one is not interested in single observables but correlation functions,
\n\npyerrors
offers theCorr
class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize aCorr
objects one needs to arrange the data as a list ofObs
\n\n\n\nmy_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
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\n\n\nmy_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
The individual entries of a correlator can be accessed via slicing
\n\n\n\n\n\nprint(my_corr[3])\n> 0.3227(33)\n
Error propagation with the
\n\nCorr
class works very similar toObs
objects. Mathematical operations are overloaded andCorr
objects can be computed together with otherCorr
objects,Obs
objects or real numbers and integers.\n\n\n\nmy_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
\n\n
pyerrors
provides the user with a set of regularly used methods for the manipulation of correlator objects:\n
\n\n- \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 asCorr
. Different discretizations of the numerical derivative are available.- \n
Corr.second_deriv
returns the second derivative of the correlator asCorr
. 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 anotherCorr
orObs
object.- \n
Corr.reweight
reweights the correlator.\n\n
pyerrors
can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (seepyerrors.correlators.Corr.GEVP
).For the full API see
\n\npyerrors.correlators.Corr
.Complex valued observables
\n\n\n\n
pyerrors
can handle complex valued observables via the classpyerrors.obs.CObs
.\nCObs
are initialized with a real and an imaginary part which both can beObs
valued.\n\n\n\nmy_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
Elementary mathematical operations are overloaded and samples are properly propagated as for the
\n\nObs
class.\n\n\n\nmy_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
The
\n\nCovobs
classIn 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
\n\nCovobs
class allows to define such quantities inpyerrors
. 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.This concept is built into the definition of
\n\nCovobs
. Inpyerrors
, 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 enterscov_Obs
, since the second argument of this function is the covariance matrix of theCovobs
.\n\n\n\nimport 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
The resulting object
\n\nmpi
is anObs
that contains aCovobs
. In the following, it may be handled as any otherObs
. The contribution of the covariance matrix to the error of anObs
is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of theObs
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.Correlated auxiliary data is defined similarly to above, e.g., via
\n\n\n\n\n\nRAP = 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
where
\n\nRAP
now is a list of twoObs
that contains the two correlated parameters.Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the
\n\nCovobs
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 anObs
o
with respect to a covariance matrix with the identifying stringk
may be accessed via\n\n\n\no.covobs[k].grad\n
Error propagation in iterative algorithms
\n\n\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.Least squares fits
\n\nStandard non-linear least square fits with errors on the dependent but not the independent variables can be performed with
\n\npyerrors.fits.least_squares
. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.Fit functions have to be of the following form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(a, x):\n return a[1] * anp.exp(-a[0] * x)\n
It is important that numerical functions refer to
\n\nautograd.numpy
instead ofnumpy
for the automatic differentiation in iterative algorithms to work properly.Fits can then be performed via
\n\n\n\n\n\nfit_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
where x is a
\n\nlist
ornumpy.array
offloats
and y is alist
ornumpy.array
ofObs
.Data stored in
\n\nCorr
objects can be fitted directly using theCorr.fit
method.\n\n\n\nmy_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
\n\nFor fit functions with multiple independent variables the fit function can be of the form
\n\n\n\n\n\ndef func(a, x):\n (x1, x2) = x\n return a[0] * x1 ** 2 + a[1] * x2\n
\n\n
pyerrors
also supports correlated fits which can be triggered via the parametercorrelated_fit=True
.\nDetails about how the required covariance matrix is estimated can be found inpyerrors.obs.covariance
.\nDirect visualizations of the performed fits can be triggered viaresplot=True
orqqplot=True
.For all available options including combined fits to multiple datasets see
\n\npyerrors.fits.least_squares
.Total least squares fits
\n\n\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, seepyerrors.fits.least_squares
. The syntax is identical to the standard least squares case, the only difference being thatx
also has to be alist
ornumpy.array
ofObs
.For the full API see
\n\npyerrors.fits
for fits andpyerrors.roots
for finding roots of functions.Matrix operations
\n\n\n\n
pyerrors
provides wrappers forObs
- andCObs
-valued matrix operations based onnumpy.linalg
. The supported functions include:\n
\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.For the full API see
\n\npyerrors.linalg
.Export data
\n\n\n\nThe preferred exported file format within
\n\npyerrors
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?
\nThis can be achieved by storing all information in one single file. The export routines of
\n\npyerrors
are written such that as much information as possible is written automatically as described in the following example\n\n\n\nmy_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
The format also allows to directly write out the content of
\n\nCorr
objects or lists and arrays ofObs
objects by passing the desired data topyerrors.input.json.dump_to_json
.json.gz format specification
\n\nThe first entries of the file provide optional auxiliary information:
\n\n\n
\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 inpyerrors
. 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.The only necessary entry of the file is the field\n-
\n\nobsdata
, an array that contains the actual data.Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of
\n\nObs
,list
,numpy.ndarray
,Corr
. AllObs
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 arrayobsdata
, are treated independently. Each entry of the arrayobsdata
has the following required entries:\n
\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. Thetag
of anObs
inpyerrors
is written here.- \n
reweighted
is a Bool that may be used to specify, whether theObs
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
inpyerrors
). We will define it below.The array
\n\ndata
contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:\n
\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.Each entry of
\n\nreplica
contains\nname
, a string that contains the name of the replica\ndeltas
, an array that contains the actual data.Each entry in
\n\ndeltas
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 eachObs
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.The array
\n\ncdata
contains information about the contribution of auxiliary observables, represented byCovobs
inpyerrors
, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:\n
\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 eachObs
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.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\nJulia 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\nEverything, 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\nThe 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\nThe Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the
\n\nNone
object.Initialization
\n\nA simple correlator can be initialized with a list or a one-dimensional array of
\n\nObs
orCobs
\n\n\n\ncorr11 = pe.Corr([obs1, obs2])\ncorr11 = pe.Corr(np.array([obs1, obs2]))\n
A matrix-valued correlator can either be initialized via a two-dimensional array of
\n\nCorr
objects\n\n\n\nmatrix_corr = pe.Corr(np.array([[corr11, corr12], [corr21, corr22]]))\n
or alternatively via a three-dimensional array of
\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "Obs
orCObs
of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.Initialize a Corr object.
\n\nParameters
\n\n\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": "- 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.
\nApply 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\nThe 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\nParameters
\n\n\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": "- i (int):\nFirst index to be picked.
\n- j (int):\nSecond index to be picked.
\nOutputs the correlator in a plotable format.
\n\nOutputs 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\nThe 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\n\n\nC.GEVP(t0=2)[0] # Ground state vector(s)\nC.GEVP(t0=2)[:3] # Vectors for the lowest three states\n
Parameters
\n\n\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\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 $t=t_s$.
\nOther Parameters
\n\n\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": "- state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
\nDetermines the eigenvalue of the GEVP by solving and projecting the correlator
\n\nParameters
\n\n\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": "- 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.
\nConstructs an NxN Hankel matrix
\n\nC(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\nParameters
\n\n\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": "- N (int):\nDimension of the Hankel matrix
\n- periodic (bool, optional):\ndetermines whether the matrix is extended periodically
\nPeriodically shift the correlator by dt timeslices
\n\nParameters
\n\n\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": "- dt (int):\nnumber of timeslices
\nReverse 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\nParameters
\n\n\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": "- spacing (int):\nKeep only every 'spacing'th entry of the correlator
\n- offset (int):\nOffset the equal spacing
\nCorrelate the correlator with another correlator or Obs
\n\nParameters
\n\n\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": "- 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.
\nReweight the correlator.
\n\nParameters
\n\n\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": "- 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.
\nReturn the time symmetry average of the correlator and its partner
\n\nParameters
\n\n\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": "- partner (Corr):\nTime symmetry partner of the Corr
\n- parity (int):\nParity quantum number of the correlator, can be +1 or -1
\nReturn the first derivative of the correlator with respect to x0.
\n\nParameters
\n\n\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": "- variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
\nReturn the second derivative of the correlator with respect to x0.
\n\nParameters
\n\n\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": "- 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 $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
\nReturns the effective mass of the correlator as correlator object
\n\nParameters
\n\n\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": "- 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
\nFits function to the data
\n\nParameters
\n\n\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": "- 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.\n
\nfitrange=[4, 6]
corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.- silent (bool):\nDecides whether output is printed to the standard output.
\nExtract a plateau value from a Corr object
\n\nParameters
\n\n\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": "- 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
\nSets 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\nParameters
\n\n\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": "- 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.
\nProduces a spaghetti plot of the correlator suited to monitor exceptional configurations.
\n\nParameters
\n\n\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": "- logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
\nDumps the Corr into a file of chosen type
\n\nParameters
\n\n\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": "- 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 '.')
\nProject large correlation matrix to lowest states
\n\nThis 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\nParameters
\n\n\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.
\nNotes
\n\nWe 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\nParameters
\n\n\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": "- 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.
\nReturn 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\nBased on https://codegolf.stackexchange.com/a/160375
\n\nReturns
\n\n\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": "- elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
\nRank-4 epsilon tensor
\n\nExtension of https://codegolf.stackexchange.com/a/160375
\n\nReturns
\n\n\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": "- elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
\nReturns 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\nAttributes
\n\n\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": "- 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.
\nApply 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\nParameters
\n\n\n
\n\n- For an uncombined fit:
\n- x (list):\nlist of floats.
\n- y (list):\nlist of Obs.
\n- \n
func (object):\nfit function, has to be of the form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(a, x):\n return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
For multiple x values func can be of the form
\n\n\n\n\n\ndef func(a, x):\n (x1, x2) = x\n return a[0] * x1 ** 2 + a[1] * x2\n
It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
- OR For a combined fit:
\n- x (dict):\ndict of lists.
\n- y (dict):\ndict of lists of Obs.
\n- \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\ndef func_a(a, x):\n return a[1] * anp.exp(-a[0] * x)
\n\ndef func_b(a, x):\n return a[2] * anp.exp(-a[0] * x)
\n\nIt is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
- 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
\npyerrors.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).- 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).
\nReturns
\n\n\n
\n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "- output (Fit_result):\nParameters and information on the fitted result.
\nPerforms a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
\n\nParameters
\n\n\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- \n
func (object):\nfunc has to be of the form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(a, x):\n return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
For multiple x values func can be of the form
\n\n\n\n\n\ndef func(a, x):\n (x1, x2) = x\n return a[0] * x1 ** 2 + a[1] * x2\n
It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
- 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).
\nNotes
\n\nBased on the orthogonal distance regression module of scipy.
\n\nReturns
\n\n\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": "- output (Fit_result):\nParameters and information on the fitted result.
\nPerforms a linear fit to y = n + m * x and returns two Obs n, m.
\n\nParameters
\n\n\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.
\nReturns
\n\n\n
\n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "- fit_parameters (list[Obs]):\nLIist of fitted observables.
\nGenerates 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\nReturns
\n\n\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": "- None
\nGenerates a plot which compares the fit to the data and displays the corresponding residuals
\n\nFor uncorrelated data the residuals are expected to be distributed ~N(0,1).
\n\nReturns
\n\n\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": "- None
\nCalculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
\n\nReturns
\n\n\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": "- err (np.array(Obs)):\nError band for an array of sample values x
\nPerforms a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
\n\nParameters
\n\n\n
\n\n- objects (list):\nList of fit results to include in the analysis (optional).
\nReturns
\n\n\n
\n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "- None
\n\n\n
pyerrors
includes aninput
submodule in which input routines and parsers for the output of various numerical programs are contained.Jackknife samples
\n\nFor comparison with other analysis workflows
\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": "pyerrors
can also generate jackknife samples from anObs
object or import jackknife samples into anObs
object.\nSeepyerrors.obs.Obs.export_jackknife
andpyerrors.obs.import_jackknife
for details.Extract generic MCMC data from a bdio file
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\n
\n\n- file_path -- path to the bdio file
\n- bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
\nReturns
\n\n\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": "- data (List[Obs]):\nExtracted data
\nWrite Obs to a bdio file according to ADerrors conventions
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\n
\n\n- file_path -- path to the bdio file
\n- bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
\nReturns
\n\n\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": "- success (int):\nreturns 0 is successful
\nExtract mesons data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\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
\nReturns
\n\n\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": "- data (dict):\nExtracted meson data
\nExtract dSdm data from a bdio file and return it as a dictionary
\n\nThe dictionary can be accessed with a tuple consisting of (type, kappa)
\n\nread_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\nall: bdio.o $(LIBDIR)\n gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
\n\nParameters
\n\n\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": "- 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
\nExport a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- xml_str (str):\nXML formatted string of the input data
\nExport a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nImport a list of Obs from an xml.gz file in the Zeuthen pobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- res (list[Obs]):\nImported data
\n- or
\n- res (dict):\nImported data and meta-data
\nImport a list of Obs from a string in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- res (list[Obs]):\nImported data
\n- or
\n- res (dict):\nImported data and meta-data
\nImport a list of Obs from an xml.gz file in the Zeuthen dobs format.
\n\nTags are not written or recovered automatically.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- res (list[Obs]):\nImported data
\n- or
\n- res (dict):\nImported data and meta-data
\nGenerate 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\nTags are not written or recovered automatically. The separator |is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- xml_str (str):\nXML string generated from the data
\nExport a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
\n\nTags are not written or recovered automatically. The separator | is removed from the replica names.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nRead hadrons meson hdf5 file and extract the meson labeled 'meson'
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- corr (Corr):\nCorrelator of the source sink combination in question.
\nRead hadrons FlowObservables hdf5 file and extract t0
\n\nParameters
\n\n\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": "- 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.
\nRead hadrons DistillationContraction hdf5 files in given directory structure
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result (dict):\nextracted DistillationContration data
\nndarray(shape, dtype=float, buffer=None, offset=0,\n strides=None, order=None)
\n\nAn 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\nArrays should be constructed using
\n\narray
,zeros
orempty
(refer\nto the See Also section below). The parameters given here refer to\na low-level method (ndarray(...)
) for instantiating an array.For more information, refer to the
\n\nnumpy
module and examine the\nmethods and attributes of an array.Parameters
\n\n\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.
\nAttributes
\n\n\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.,
\nx.flat = 3
(Seendarray.flat
for\nassignment examples; TODO).- 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.,
\nitemsize * size
.- 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
\n(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
).- 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
\nbase
\n(unless that array is also a view). Thebase
array is where the\narray data is actually stored.See Also
\n\n\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. itsdtype.type <numpy.dtype.type>
.Notes
\n\nThere are two modes of creating an array using
\n\n__new__
:\n
\n\n- If
\nbuffer
is None, then onlyshape
,dtype
, andorder
\nare used.- If
\nbuffer
is an object exposing the buffer interface, then\nall keywords are interpreted.No
\n\n__init__
method is needed because the array is fully initialized\nafter the__new__
method.Examples
\n\nThese examples illustrate the low-level
\n\nndarray
constructor. Refer\nto theSee Also
section above for easier ways of constructing an\nndarray.First mode,
\n\nbuffer
is None:\n\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
Second mode:
\n\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": "\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
Gamma_5 hermitean conjugate
\n\nUses 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\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result (Npr_matrix):\nread Cobs-matrix
\nRead hadrons Bilinear hdf5 file and output an array of CObs
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result_dict (dict[Npr_matrix]):\nextracted Bilinears
\nRead hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- result_dict (dict):\nextracted fourquark matrizes
\nGenerate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- json_string (str):\nString for export to .json(.gz) file
\nExport 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\nParameters
\n\n\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.
\nReturns
\n\n\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": "- Null
\nReconstruct a list of Obs or structures containing Obs from a json string.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- 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
\nImport a list of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- 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
\nExport a dict of Obs or structures containing Obs to a .json(.gz) file
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nImport a dict of Obs or structures containing Obs from a .json(.gz) file.
\n\nThe following structures are supported: Obs, list, numpy.ndarray, Corr
\n\nParameters
\n\n\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]+.
\nReturns
\n\n\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": "- data (Obs / list / Corr):\nRead data
\n- or
\n- data (dict):\nRead data and meta-data
\nCompute 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\nIt 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\nA linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
\n\nParameters
\n\n\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')
\nReturns
\n\n\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": "- root (Obs):\nThe root of the data series.
\nRead pbp format from given folder structure.
\n\nParameters
\n\n\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
\nReturns
\n\n\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": "- result (list[Obs]):\nlist of observables read
\nRead rwms format from given folder structure. Returns a list of length nrw
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- rwms (Obs):\nReweighting factors read
\nExtract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
\n\nIt is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2
\n\n- c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted. 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\nParameters
\n\n\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
\nReturns
\n\n\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": "- t0 (Obs):\nExtracted t0
\nExtract w0/a from given .ms.dat files. Returns w0 as Obs.
\n\nIt is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2
\n\n)/dt - (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted. 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\nParameters
\n\n\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
\nReturns
\n\n\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": "- w0 (Obs):\nExtracted w0
\nRead the topologial charge based on openQCD gradient flow measurements.
\n\nParameters
\n\n\n
\n\n- path (str):\npath of the measurement files
\n- prefix (str):\nprefix of the measurement files, e.g.
\n_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files. - 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.
\nReturns
\n\n\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": "- result (Obs):\nRead topological charge
\nRead the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
\n\nNote: 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\nParameters
\n\n\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": "- path (str):\npath of the measurement files
\n- prefix (str):\nprefix of the measurement files, e.g.
\n_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files. - 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.
\nReturns the projection to the topological charge sector defined by target.
\n\nParameters
\n\n\n
\n\n- path (Obs):\nTopological charge.
\n- target (int):\nSpecifies the topological sector to be reweighted to (default 0)
\nReturns
\n\n\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": "- reto (Obs):\nprojection to the topological charge sector defined by target
\nConstructs reweighting factors to a specified topological sector.
\n\nParameters
\n\n\n
\n\n- path (str):\npath of the measurement files
\n- prefix (str):\nprefix of the measurement files, e.g.
\n_id0_r0.ms.dat - 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.
\nReturns
\n\n\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": "- reto (Obs):\nprojection to the topological charge sector defined by target
\nRead data from files in the specified directory with the specified prefix and quark combination extension, and return a
\n\nCorr
object containing the data.Parameters
\n\n\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- \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.
\nReturns
\n\n\n
\n\n- Corr: A complex valued
\nCorr
object containing the data read from the files. In case of boudary to bulk correlators.- or
\n- CObs: A complex valued
\nCObs
object containing the data read from the files. In case of boudary to boundary correlators.Raises
\n\n\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": "- 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.
\nWrite DataFrame including Obs or Corr valued columns to sqlite database.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nExecute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
\nExports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
\n\nBefore making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- None
\nImports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
\nRead sfcf files from given folder structure.
\n\nParameters
\n\n\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\n
- 'bi' for boundary-inner
\n- 'bb' for boundary-boundary
\n- 'bib' for boundary-inner-boundary
\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
\nReturns
\n\n\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": "- result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
\nSorts a list of names of replika with searches for
\n\nr
andid
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.Parameters
\n\n\n
\n\n- ll (list):\nlist to sort
\nReturns
\n\n\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": "- ll (list):\nsorted list
\nChecks if list of configurations is contained in an idl
\n\nParameters
\n\n\n
\n\n- idl (range or list):\nidl of the current replicum
\n- che (list):\nlist of configurations to be checked against
\nReturns
\n\n\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": "- miss_str (str):\nstring with integers of which idls are missing
\nPerforms a (one-dimensional) numeric integration of f(p, x) from a to b.
\n\nThe 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\nParameters
\n\n\n
\n\n- \n
func (object):\nfunction to integrate, has to be of the form
\n\n\n\n\n\nimport autograd.numpy as anp\n\ndef func(p, x):\n return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
where x is the integration variable.
- 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
\nReturns
\n\n\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": "- y (Obs):\nThe integral of func from
\na
tob
.- 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']
\nMatrix multiply all operands.
\n\nParameters
\n\n\n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "- 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.
\nMatrix multiply both operands making use of the jackknife approximation.
\n\nParameters
\n\n\n
\n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "- 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.
\nWrapper for numpy.einsum
\n\nParameters
\n\n\n
\n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "- 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.
\nInverse 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\nParameters
\n\n\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": "- 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.
\nDump object into pickle file.
\n\nParameters
\n\n\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 '.')
\nReturns
\n\n\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": "- None
\nLoad object from pickle file.
\n\nParameters
\n\n\n
\n\n- path (str):\npath to the file
\nReturns
\n\n\n
\n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "- object (Obs):\nLoaded Object
\nGenerate an Obs object with given value, dvalue and name for test purposes
\n\nParameters
\n\n\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).
\nReturns
\n\n\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": "- res (Obs):\nGenerated Observable
\nGenerate observables with given covariance and autocorrelation times.
\n\nParameters
\n\n\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.
\nReturns
\n\n\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": "- corr_obs (list[Obs]):\nGenerated observable list
\nMatrix pencil method to extract k energy levels from data
\n\nImplementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
\n\nParameters
\n\n\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).
\nReturns
\n\n\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": "- energy_levels (list[Obs]):\nExtracted energy levels
\nClass for a general observable.
\n\nInstances 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\nAttributes
\n\n\n
\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "- 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.
\nInitialize Obs object.
\n\nParameters
\n\n\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": "- 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
\nEstimate the error and related properties of the Obs.
\n\nParameters
\n\n\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": "- 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)
\nEstimate the error and related properties of the Obs.
\n\nParameters
\n\n\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": "- 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)
\nOutput detailed properties of the Obs.
\n\nParameters
\n\n\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": "- ens_content (bool):\nprint details about the ensembles and replica if true.
\nReweight the obs with given rewighting factors.
\n\nParameters
\n\n\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": "- 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.
\nChecks whether the observable is zero within 'sigma' standard errors.
\n\nParameters
\n\n\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": "- sigma (int):\nNumber of standard errors used for the check.
\n- Works only properly when the gamma method was run.
\nChecks whether the observable is zero within a given tolerance.
\n\nParameters
\n\n\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": "- atol (float):\nAbsolute tolerance (for details see numpy documentation).
\nPlot integrated autocorrelation time for each ensemble.
\n\nParameters
\n\n\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": "- save (str):\nsaves the figure to a file named 'save' if.
\nPlot normalized autocorrelation function time for each ensemble.
\n\nParameters
\n\n\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": "- save (str):\nsaves the figure to a file named 'save' if.
\nPlot 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\nParameters
\n\n\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": "- expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
\nPlot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
\n\nParameters
\n\n\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": "- save (str):\nsaves the figure to a file named 'save' if.
\nDump the Obs to a file 'name' of chosen format.
\n\nParameters
\n\n\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": "- 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 '.')
\nExport jackknife samples from the Obs
\n\nReturns
\n\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": "- 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).
\nExport bootstrap samples from the Obs
\n\nParameters
\n\n\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.
\nReturns
\n\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": "- 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).
\nClass 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\nParameters
\n\n\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.
\nNotes
\n\nFor simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
\n\nnew_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\nParameters
\n\n\n
\n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "- 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.
\nCorrelate two observables.
\n\nParameters
\n\n\n
\n\n- obs_a (Obs):\nFirst observable
\n- obs_b (Obs):\nSecond observable
\nNotes
\n\nKeep 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\nWARNING: 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\nThe gamma method has to be applied first to all observables.
\n\nParameters
\n\n\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.
\nNotes
\n\nThe 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\nParameters
\n\n\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": "- 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.
\nImports bootstrap samples and returns an Obs
\n\nParameters
\n\n\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": "- 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.
\nCombine all observables in list_of_obs into one new observable
\n\nParameters
\n\n\n
\n\n- list_of_obs (list):\nlist of the Obs object to be combined
\nNotes
\n\nIt 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\nParameters
\n\n\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": "- 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.
\nFinds the root of the function func(x, d) where d is an
\n\nObs
.Parameters
\n\n\n
\n\n- d (Obs):\nObs passed to the function.
\n- \n
func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
\n\n\n\nimport autograd.numpy as anp\ndef root_func(x, d):\n return anp.exp(-x ** 2) - d\n
- \n
guess (float):\nInitial guess for the minimization.
Returns
\n\n\n
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"pyerrors.input.openQCD.read_qtop": {"tf": 1.4142135623730951}, "pyerrors.input.openQCD.read_gf_coupling": {"tf": 1.4142135623730951}, "pyerrors.input.openQCD.read_qtop_sector": {"tf": 1.4142135623730951}}, "df": 10}}}}}}}}}}, "pipeline": ["trimmer"], "_isPrebuiltIndex": true}; // mirrored in build-search-index.js (part 1) // Also split on html tags. this is a cheap heuristic, but good enough.- res (Obs):\n
\nObs
valued root of the function.