From c318a4a63683b86895617b5cbb6abaff58433989 Mon Sep 17 00:00:00 2001 From: fjosw Date: Fri, 13 Jan 2023 17:28:08 +0000 Subject: [PATCH] Documentation updated --- docs/pyerrors/correlators.html | 6426 ++++++++++++++++---------------- docs/pyerrors/fits.html | 2229 +++++------ docs/search.js | 2 +- 3 files changed, 4361 insertions(+), 4296 deletions(-) diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index b96c4856..c6aff27c 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -61,6 +61,9 @@
  • gamma_method
    • +
  • + gm +
  • projected
    • @@ -337,1194 +340,1196 @@ 124 for j in range(self.N): 125 item[i, j].gamma_method(**kwargs) 126 - 127 def projected(self, vector_l=None, vector_r=None, normalize=False): - 128 """We need to project the Correlator with a Vector to get a single value at each timeslice. - 129 - 130 The method can use one or two vectors. - 131 If two are specified it returns v1@G@v2 (the order might be very important.) - 132 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to - 133 """ - 134 if self.N == 1: - 135 raise Exception("Trying to project a Corr, that already has N=1.") - 136 - 137 if vector_l is None: - 138 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) - 139 elif (vector_r is None): - 140 vector_r = vector_l - 141 if isinstance(vector_l, list) and not isinstance(vector_r, list): - 142 if len(vector_l) != self.T: - 143 raise Exception("Length of vector list must be equal to T") - 144 vector_r = [vector_r] * self.T - 145 if isinstance(vector_r, list) and not isinstance(vector_l, list): - 146 if len(vector_r) != self.T: - 147 raise Exception("Length of vector list must be equal to T") - 148 vector_l = [vector_l] * self.T - 149 - 150 if not isinstance(vector_l, list): - 151 if not vector_l.shape == vector_r.shape == (self.N,): - 152 raise Exception("Vectors are of wrong shape!") - 153 if normalize: - 154 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) - 155 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] - 156 - 157 else: - 158 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. - 159 if normalize: - 160 for t in range(self.T): - 161 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]) - 162 - 163 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)] - 164 return Corr(newcontent) - 165 - 166 def item(self, i, j): - 167 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. - 168 - 169 Parameters - 170 ---------- - 171 i : int - 172 First index to be picked. - 173 j : int - 174 Second index to be picked. - 175 """ - 176 if self.N == 1: - 177 raise Exception("Trying to pick item from projected Corr") - 178 newcontent = [None if (item is None) else item[i, j] for item in self.content] - 179 return Corr(newcontent) - 180 - 181 def plottable(self): - 182 """Outputs the correlator in a plotable format. - 183 - 184 Outputs three lists containing the timeslice index, the value on each - 185 timeslice and the error on each timeslice. - 186 """ - 187 if self.N != 1: - 188 raise Exception("Can only make Corr[N=1] plottable") - 189 x_list = [x for x in range(self.T) if not self.content[x] is None] - 190 y_list = [y[0].value for y in self.content if y is not None] - 191 y_err_list = [y[0].dvalue for y in self.content if y is not None] - 192 - 193 return x_list, y_list, y_err_list + 127 gm = gamma_method + 128 + 129 def projected(self, vector_l=None, vector_r=None, normalize=False): + 130 """We need to project the Correlator with a Vector to get a single value at each timeslice. + 131 + 132 The method can use one or two vectors. + 133 If two are specified it returns v1@G@v2 (the order might be very important.) + 134 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to + 135 """ + 136 if self.N == 1: + 137 raise Exception("Trying to project a Corr, that already has N=1.") + 138 + 139 if vector_l is None: + 140 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) + 141 elif (vector_r is None): + 142 vector_r = vector_l + 143 if isinstance(vector_l, list) and not isinstance(vector_r, list): + 144 if len(vector_l) != self.T: + 145 raise Exception("Length of vector list must be equal to T") + 146 vector_r = [vector_r] * self.T + 147 if isinstance(vector_r, list) and not isinstance(vector_l, list): + 148 if len(vector_r) != self.T: + 149 raise Exception("Length of vector list must be equal to T") + 150 vector_l = [vector_l] * self.T + 151 + 152 if not isinstance(vector_l, list): + 153 if not vector_l.shape == vector_r.shape == (self.N,): + 154 raise Exception("Vectors are of wrong shape!") + 155 if normalize: + 156 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) + 157 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] + 158 + 159 else: + 160 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. + 161 if normalize: + 162 for t in range(self.T): + 163 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]) + 164 + 165 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)] + 166 return Corr(newcontent) + 167 + 168 def item(self, i, j): + 169 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. + 170 + 171 Parameters + 172 ---------- + 173 i : int + 174 First index to be picked. + 175 j : int + 176 Second index to be picked. + 177 """ + 178 if self.N == 1: + 179 raise Exception("Trying to pick item from projected Corr") + 180 newcontent = [None if (item is None) else item[i, j] for item in self.content] + 181 return Corr(newcontent) + 182 + 183 def plottable(self): + 184 """Outputs the correlator in a plotable format. + 185 + 186 Outputs three lists containing the timeslice index, the value on each + 187 timeslice and the error on each timeslice. + 188 """ + 189 if self.N != 1: + 190 raise Exception("Can only make Corr[N=1] plottable") + 191 x_list = [x for x in range(self.T) if not self.content[x] is None] + 192 y_list = [y[0].value for y in self.content if y is not None] + 193 y_err_list = [y[0].dvalue for y in self.content if y is not None] 194 - 195 def symmetric(self): - 196 """ Symmetrize the correlator around x0=0.""" - 197 if self.N != 1: - 198 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') - 199 if self.T % 2 != 0: - 200 raise Exception("Can not symmetrize odd T") - 201 - 202 if np.argmax(np.abs(self.content)) != 0: - 203 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) - 204 - 205 newcontent = [self.content[0]] - 206 for t in range(1, self.T): - 207 if (self.content[t] is None) or (self.content[self.T - t] is None): - 208 newcontent.append(None) - 209 else: - 210 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) - 211 if (all([x is None for x in newcontent])): - 212 raise Exception("Corr could not be symmetrized: No redundant values") - 213 return Corr(newcontent, prange=self.prange) - 214 - 215 def anti_symmetric(self): - 216 """Anti-symmetrize the correlator around x0=0.""" - 217 if self.N != 1: - 218 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') - 219 if self.T % 2 != 0: - 220 raise Exception("Can not symmetrize odd T") - 221 - 222 test = 1 * self - 223 test.gamma_method() - 224 if not all([o.is_zero_within_error(3) for o in test.content[0]]): - 225 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) - 226 - 227 newcontent = [self.content[0]] - 228 for t in range(1, self.T): - 229 if (self.content[t] is None) or (self.content[self.T - t] is None): - 230 newcontent.append(None) - 231 else: - 232 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) - 233 if (all([x is None for x in newcontent])): - 234 raise Exception("Corr could not be symmetrized: No redundant values") - 235 return Corr(newcontent, prange=self.prange) - 236 - 237 def is_matrix_symmetric(self): - 238 """Checks whether a correlator matrices is symmetric on every timeslice.""" - 239 if self.N == 1: - 240 raise Exception("Only works for correlator matrices.") - 241 for t in range(self.T): - 242 if self[t] is None: - 243 continue - 244 for i in range(self.N): - 245 for j in range(i + 1, self.N): - 246 if self[t][i, j] is self[t][j, i]: - 247 continue - 248 if hash(self[t][i, j]) != hash(self[t][j, i]): - 249 return False - 250 return True - 251 - 252 def matrix_symmetric(self): - 253 """Symmetrizes the correlator matrices on every timeslice.""" - 254 if self.N == 1: - 255 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 256 if self.is_matrix_symmetric(): - 257 return 1.0 * self - 258 else: - 259 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 260 return 0.5 * (Corr(transposed) + self) - 261 - 262 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 263 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 264 - 265 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 266 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 267 ```python - 268 C.GEVP(t0=2)[0] # Ground state vector(s) - 269 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 270 ``` - 271 - 272 Parameters - 273 ---------- - 274 t0 : int - 275 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 276 ts : int - 277 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 278 If sort="Eigenvector" it gives a reference point for the sorting method. - 279 sort : string - 280 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. - 281 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 282 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 283 The reference state is identified by its eigenvalue at $t=t_s$. - 284 - 285 Other Parameters - 286 ---------------- - 287 state : int - 288 Returns only the vector(s) for a specified state. The lowest state is zero. - 289 ''' - 290 - 291 if self.N == 1: - 292 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 293 if ts is not None: - 294 if (ts <= t0): - 295 raise Exception("ts has to be larger than t0.") - 296 - 297 if "sorted_list" in kwargs: - 298 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 299 sort = kwargs.get("sorted_list") - 300 - 301 if self.is_matrix_symmetric(): - 302 symmetric_corr = self - 303 else: - 304 symmetric_corr = self.matrix_symmetric() - 305 - 306 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) - 307 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. - 308 - 309 if sort is None: - 310 if (ts is None): - 311 raise Exception("ts is required if sort=None.") - 312 if (self.content[t0] is None) or (self.content[ts] is None): - 313 raise Exception("Corr not defined at t0/ts.") - 314 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) - 315 reordered_vecs = _GEVP_solver(Gt, G0) - 316 - 317 elif sort in ["Eigenvalue", "Eigenvector"]: - 318 if sort == "Eigenvalue" and ts is not None: - 319 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) - 320 all_vecs = [None] * (t0 + 1) - 321 for t in range(t0 + 1, self.T): - 322 try: - 323 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) - 324 all_vecs.append(_GEVP_solver(Gt, G0)) - 325 except Exception: - 326 all_vecs.append(None) - 327 if sort == "Eigenvector": - 328 if ts is None: - 329 raise Exception("ts is required for the Eigenvector sorting method.") - 330 all_vecs = _sort_vectors(all_vecs, ts) - 331 - 332 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 333 else: - 334 raise Exception("Unkown value for 'sort'.") - 335 - 336 if "state" in kwargs: - 337 return reordered_vecs[kwargs.get("state")] - 338 else: - 339 return reordered_vecs - 340 - 341 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 342 """Determines the eigenvalue of the GEVP by solving and projecting the correlator - 343 - 344 Parameters - 345 ---------- - 346 state : int - 347 The state one is interested in ordered by energy. The lowest state is zero. - 348 - 349 All other parameters are identical to the ones of Corr.GEVP. - 350 """ - 351 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 352 return self.projected(vec) - 353 - 354 def Hankel(self, N, periodic=False): - 355 """Constructs an NxN Hankel matrix - 356 - 357 C(t) c(t+1) ... c(t+n-1) - 358 C(t+1) c(t+2) ... c(t+n) - 359 ................. - 360 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) - 361 - 362 Parameters - 363 ---------- - 364 N : int - 365 Dimension of the Hankel matrix - 366 periodic : bool, optional - 367 determines whether the matrix is extended periodically - 368 """ - 369 - 370 if self.N != 1: - 371 raise Exception("Multi-operator Prony not implemented!") - 372 - 373 array = np.empty([N, N], dtype="object") - 374 new_content = [] - 375 for t in range(self.T): - 376 new_content.append(array.copy()) - 377 - 378 def wrap(i): - 379 while i >= self.T: - 380 i -= self.T - 381 return i - 382 - 383 for t in range(self.T): - 384 for i in range(N): - 385 for j in range(N): - 386 if periodic: - 387 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 388 elif (t + i + j) >= self.T: - 389 new_content[t] = None - 390 else: - 391 new_content[t][i, j] = self.content[t + i + j][0] - 392 - 393 return Corr(new_content) + 195 return x_list, y_list, y_err_list + 196 + 197 def symmetric(self): + 198 """ Symmetrize the correlator around x0=0.""" + 199 if self.N != 1: + 200 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') + 201 if self.T % 2 != 0: + 202 raise Exception("Can not symmetrize odd T") + 203 + 204 if np.argmax(np.abs(self.content)) != 0: + 205 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) + 206 + 207 newcontent = [self.content[0]] + 208 for t in range(1, self.T): + 209 if (self.content[t] is None) or (self.content[self.T - t] is None): + 210 newcontent.append(None) + 211 else: + 212 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) + 213 if (all([x is None for x in newcontent])): + 214 raise Exception("Corr could not be symmetrized: No redundant values") + 215 return Corr(newcontent, prange=self.prange) + 216 + 217 def anti_symmetric(self): + 218 """Anti-symmetrize the correlator around x0=0.""" + 219 if self.N != 1: + 220 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') + 221 if self.T % 2 != 0: + 222 raise Exception("Can not symmetrize odd T") + 223 + 224 test = 1 * self + 225 test.gamma_method() + 226 if not all([o.is_zero_within_error(3) for o in test.content[0]]): + 227 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) + 228 + 229 newcontent = [self.content[0]] + 230 for t in range(1, self.T): + 231 if (self.content[t] is None) or (self.content[self.T - t] is None): + 232 newcontent.append(None) + 233 else: + 234 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) + 235 if (all([x is None for x in newcontent])): + 236 raise Exception("Corr could not be symmetrized: No redundant values") + 237 return Corr(newcontent, prange=self.prange) + 238 + 239 def is_matrix_symmetric(self): + 240 """Checks whether a correlator matrices is symmetric on every timeslice.""" + 241 if self.N == 1: + 242 raise Exception("Only works for correlator matrices.") + 243 for t in range(self.T): + 244 if self[t] is None: + 245 continue + 246 for i in range(self.N): + 247 for j in range(i + 1, self.N): + 248 if self[t][i, j] is self[t][j, i]: + 249 continue + 250 if hash(self[t][i, j]) != hash(self[t][j, i]): + 251 return False + 252 return True + 253 + 254 def matrix_symmetric(self): + 255 """Symmetrizes the correlator matrices on every timeslice.""" + 256 if self.N == 1: + 257 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") + 258 if self.is_matrix_symmetric(): + 259 return 1.0 * self + 260 else: + 261 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] + 262 return 0.5 * (Corr(transposed) + self) + 263 + 264 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): + 265 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. + 266 + 267 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the + 268 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing + 269 ```python + 270 C.GEVP(t0=2)[0] # Ground state vector(s) + 271 C.GEVP(t0=2)[:3] # Vectors for the lowest three states + 272 ``` + 273 + 274 Parameters + 275 ---------- + 276 t0 : int + 277 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ + 278 ts : int + 279 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. + 280 If sort="Eigenvector" it gives a reference point for the sorting method. + 281 sort : string + 282 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. + 283 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. + 284 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. + 285 The reference state is identified by its eigenvalue at $t=t_s$. + 286 + 287 Other Parameters + 288 ---------------- + 289 state : int + 290 Returns only the vector(s) for a specified state. The lowest state is zero. + 291 ''' + 292 + 293 if self.N == 1: + 294 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") + 295 if ts is not None: + 296 if (ts <= t0): + 297 raise Exception("ts has to be larger than t0.") + 298 + 299 if "sorted_list" in kwargs: + 300 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) + 301 sort = kwargs.get("sorted_list") + 302 + 303 if self.is_matrix_symmetric(): + 304 symmetric_corr = self + 305 else: + 306 symmetric_corr = self.matrix_symmetric() + 307 + 308 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) + 309 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. + 310 + 311 if sort is None: + 312 if (ts is None): + 313 raise Exception("ts is required if sort=None.") + 314 if (self.content[t0] is None) or (self.content[ts] is None): + 315 raise Exception("Corr not defined at t0/ts.") + 316 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) + 317 reordered_vecs = _GEVP_solver(Gt, G0) + 318 + 319 elif sort in ["Eigenvalue", "Eigenvector"]: + 320 if sort == "Eigenvalue" and ts is not None: + 321 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) + 322 all_vecs = [None] * (t0 + 1) + 323 for t in range(t0 + 1, self.T): + 324 try: + 325 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) + 326 all_vecs.append(_GEVP_solver(Gt, G0)) + 327 except Exception: + 328 all_vecs.append(None) + 329 if sort == "Eigenvector": + 330 if ts is None: + 331 raise Exception("ts is required for the Eigenvector sorting method.") + 332 all_vecs = _sort_vectors(all_vecs, ts) + 333 + 334 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] + 335 else: + 336 raise Exception("Unkown value for 'sort'.") + 337 + 338 if "state" in kwargs: + 339 return reordered_vecs[kwargs.get("state")] + 340 else: + 341 return reordered_vecs + 342 + 343 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): + 344 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 345 + 346 Parameters + 347 ---------- + 348 state : int + 349 The state one is interested in ordered by energy. The lowest state is zero. + 350 + 351 All other parameters are identical to the ones of Corr.GEVP. + 352 """ + 353 vec = self.GEVP(t0, ts=ts, sort=sort)[state] + 354 return self.projected(vec) + 355 + 356 def Hankel(self, N, periodic=False): + 357 """Constructs an NxN Hankel matrix + 358 + 359 C(t) c(t+1) ... c(t+n-1) + 360 C(t+1) c(t+2) ... c(t+n) + 361 ................. + 362 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) + 363 + 364 Parameters + 365 ---------- + 366 N : int + 367 Dimension of the Hankel matrix + 368 periodic : bool, optional + 369 determines whether the matrix is extended periodically + 370 """ + 371 + 372 if self.N != 1: + 373 raise Exception("Multi-operator Prony not implemented!") + 374 + 375 array = np.empty([N, N], dtype="object") + 376 new_content = [] + 377 for t in range(self.T): + 378 new_content.append(array.copy()) + 379 + 380 def wrap(i): + 381 while i >= self.T: + 382 i -= self.T + 383 return i + 384 + 385 for t in range(self.T): + 386 for i in range(N): + 387 for j in range(N): + 388 if periodic: + 389 new_content[t][i, j] = self.content[wrap(t + i + j)][0] + 390 elif (t + i + j) >= self.T: + 391 new_content[t] = None + 392 else: + 393 new_content[t][i, j] = self.content[t + i + j][0] 394 - 395 def roll(self, dt): - 396 """Periodically shift the correlator by dt timeslices - 397 - 398 Parameters - 399 ---------- - 400 dt : int - 401 number of timeslices - 402 """ - 403 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) - 404 - 405 def reverse(self): - 406 """Reverse the time ordering of the Corr""" - 407 return Corr(self.content[:: -1]) - 408 - 409 def thin(self, spacing=2, offset=0): - 410 """Thin out a correlator to suppress correlations - 411 - 412 Parameters - 413 ---------- - 414 spacing : int - 415 Keep only every 'spacing'th entry of the correlator - 416 offset : int - 417 Offset the equal spacing - 418 """ - 419 new_content = [] - 420 for t in range(self.T): - 421 if (offset + t) % spacing != 0: - 422 new_content.append(None) - 423 else: - 424 new_content.append(self.content[t]) - 425 return Corr(new_content) - 426 - 427 def correlate(self, partner): - 428 """Correlate the correlator with another correlator or Obs - 429 - 430 Parameters - 431 ---------- - 432 partner : Obs or Corr - 433 partner to correlate the correlator with. - 434 Can either be an Obs which is correlated with all entries of the - 435 correlator or a Corr of same length. - 436 """ - 437 if self.N != 1: - 438 raise Exception("Only one-dimensional correlators can be safely correlated.") - 439 new_content = [] - 440 for x0, t_slice in enumerate(self.content): - 441 if _check_for_none(self, t_slice): - 442 new_content.append(None) - 443 else: - 444 if isinstance(partner, Corr): - 445 if _check_for_none(partner, partner.content[x0]): - 446 new_content.append(None) - 447 else: - 448 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 449 elif isinstance(partner, Obs): # Should this include CObs? - 450 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 451 else: - 452 raise Exception("Can only correlate with an Obs or a Corr.") - 453 - 454 return Corr(new_content) + 395 return Corr(new_content) + 396 + 397 def roll(self, dt): + 398 """Periodically shift the correlator by dt timeslices + 399 + 400 Parameters + 401 ---------- + 402 dt : int + 403 number of timeslices + 404 """ + 405 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) + 406 + 407 def reverse(self): + 408 """Reverse the time ordering of the Corr""" + 409 return Corr(self.content[:: -1]) + 410 + 411 def thin(self, spacing=2, offset=0): + 412 """Thin out a correlator to suppress correlations + 413 + 414 Parameters + 415 ---------- + 416 spacing : int + 417 Keep only every 'spacing'th entry of the correlator + 418 offset : int + 419 Offset the equal spacing + 420 """ + 421 new_content = [] + 422 for t in range(self.T): + 423 if (offset + t) % spacing != 0: + 424 new_content.append(None) + 425 else: + 426 new_content.append(self.content[t]) + 427 return Corr(new_content) + 428 + 429 def correlate(self, partner): + 430 """Correlate the correlator with another correlator or Obs + 431 + 432 Parameters + 433 ---------- + 434 partner : Obs or Corr + 435 partner to correlate the correlator with. + 436 Can either be an Obs which is correlated with all entries of the + 437 correlator or a Corr of same length. + 438 """ + 439 if self.N != 1: + 440 raise Exception("Only one-dimensional correlators can be safely correlated.") + 441 new_content = [] + 442 for x0, t_slice in enumerate(self.content): + 443 if _check_for_none(self, t_slice): + 444 new_content.append(None) + 445 else: + 446 if isinstance(partner, Corr): + 447 if _check_for_none(partner, partner.content[x0]): + 448 new_content.append(None) + 449 else: + 450 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) + 451 elif isinstance(partner, Obs): # Should this include CObs? + 452 new_content.append(np.array([correlate(o, partner) for o in t_slice])) + 453 else: + 454 raise Exception("Can only correlate with an Obs or a Corr.") 455 - 456 def reweight(self, weight, **kwargs): - 457 """Reweight the correlator. - 458 - 459 Parameters - 460 ---------- - 461 weight : Obs - 462 Reweighting factor. An Observable that has to be defined on a superset of the - 463 configurations in obs[i].idl for all i. - 464 all_configs : bool - 465 if True, the reweighted observables are normalized by the average of - 466 the reweighting factor on all configurations in weight.idl and not - 467 on the configurations in obs[i].idl. - 468 """ - 469 if self.N != 1: - 470 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 471 new_content = [] - 472 for t_slice in self.content: - 473 if _check_for_none(self, t_slice): - 474 new_content.append(None) - 475 else: - 476 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 477 return Corr(new_content) - 478 - 479 def T_symmetry(self, partner, parity=+1): - 480 """Return the time symmetry average of the correlator and its partner - 481 - 482 Parameters - 483 ---------- - 484 partner : Corr - 485 Time symmetry partner of the Corr - 486 partity : int - 487 Parity quantum number of the correlator, can be +1 or -1 - 488 """ - 489 if self.N != 1: - 490 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 491 if not isinstance(partner, Corr): - 492 raise Exception("T partner has to be a Corr object.") - 493 if parity not in [+1, -1]: - 494 raise Exception("Parity has to be +1 or -1.") - 495 T_partner = parity * partner.reverse() - 496 - 497 t_slices = [] - 498 test = (self - T_partner) - 499 test.gamma_method() - 500 for x0, t_slice in enumerate(test.content): - 501 if t_slice is not None: - 502 if not t_slice[0].is_zero_within_error(5): - 503 t_slices.append(x0) - 504 if t_slices: - 505 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) - 506 - 507 return (self + T_partner) / 2 + 456 return Corr(new_content) + 457 + 458 def reweight(self, weight, **kwargs): + 459 """Reweight the correlator. + 460 + 461 Parameters + 462 ---------- + 463 weight : Obs + 464 Reweighting factor. An Observable that has to be defined on a superset of the + 465 configurations in obs[i].idl for all i. + 466 all_configs : bool + 467 if True, the reweighted observables are normalized by the average of + 468 the reweighting factor on all configurations in weight.idl and not + 469 on the configurations in obs[i].idl. + 470 """ + 471 if self.N != 1: + 472 raise Exception("Reweighting only implemented for one-dimensional correlators.") + 473 new_content = [] + 474 for t_slice in self.content: + 475 if _check_for_none(self, t_slice): + 476 new_content.append(None) + 477 else: + 478 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) + 479 return Corr(new_content) + 480 + 481 def T_symmetry(self, partner, parity=+1): + 482 """Return the time symmetry average of the correlator and its partner + 483 + 484 Parameters + 485 ---------- + 486 partner : Corr + 487 Time symmetry partner of the Corr + 488 partity : int + 489 Parity quantum number of the correlator, can be +1 or -1 + 490 """ + 491 if self.N != 1: + 492 raise Exception("T_symmetry only implemented for one-dimensional correlators.") + 493 if not isinstance(partner, Corr): + 494 raise Exception("T partner has to be a Corr object.") + 495 if parity not in [+1, -1]: + 496 raise Exception("Parity has to be +1 or -1.") + 497 T_partner = parity * partner.reverse() + 498 + 499 t_slices = [] + 500 test = (self - T_partner) + 501 test.gamma_method() + 502 for x0, t_slice in enumerate(test.content): + 503 if t_slice is not None: + 504 if not t_slice[0].is_zero_within_error(5): + 505 t_slices.append(x0) + 506 if t_slices: + 507 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) 508 - 509 def deriv(self, variant="symmetric"): - 510 """Return the first derivative of the correlator with respect to x0. - 511 - 512 Parameters - 513 ---------- - 514 variant : str - 515 decides which definition of the finite differences derivative is used. - 516 Available choice: symmetric, forward, backward, improved, log, default: symmetric - 517 """ - 518 if self.N != 1: - 519 raise Exception("deriv only implemented for one-dimensional correlators.") - 520 if variant == "symmetric": - 521 newcontent = [] - 522 for t in range(1, self.T - 1): - 523 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 524 newcontent.append(None) - 525 else: - 526 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 527 if (all([x is None for x in newcontent])): - 528 raise Exception('Derivative is undefined at all timeslices') - 529 return Corr(newcontent, padding=[1, 1]) - 530 elif variant == "forward": - 531 newcontent = [] - 532 for t in range(self.T - 1): - 533 if (self.content[t] is None) or (self.content[t + 1] is None): - 534 newcontent.append(None) - 535 else: - 536 newcontent.append(self.content[t + 1] - self.content[t]) - 537 if (all([x is None for x in newcontent])): - 538 raise Exception("Derivative is undefined at all timeslices") - 539 return Corr(newcontent, padding=[0, 1]) - 540 elif variant == "backward": - 541 newcontent = [] - 542 for t in range(1, self.T): - 543 if (self.content[t - 1] is None) or (self.content[t] is None): - 544 newcontent.append(None) - 545 else: - 546 newcontent.append(self.content[t] - self.content[t - 1]) - 547 if (all([x is None for x in newcontent])): - 548 raise Exception("Derivative is undefined at all timeslices") - 549 return Corr(newcontent, padding=[1, 0]) - 550 elif variant == "improved": - 551 newcontent = [] - 552 for t in range(2, self.T - 2): - 553 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): - 554 newcontent.append(None) - 555 else: - 556 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 557 if (all([x is None for x in newcontent])): - 558 raise Exception('Derivative is undefined at all timeslices') - 559 return Corr(newcontent, padding=[2, 2]) - 560 elif variant == 'log': - 561 newcontent = [] - 562 for t in range(self.T): - 563 if (self.content[t] is None) or (self.content[t] <= 0): - 564 newcontent.append(None) - 565 else: - 566 newcontent.append(np.log(self.content[t])) - 567 if (all([x is None for x in newcontent])): - 568 raise Exception("Log is undefined at all timeslices") - 569 logcorr = Corr(newcontent) - 570 return self * logcorr.deriv('symmetric') - 571 else: - 572 raise Exception("Unknown variant.") - 573 - 574 def second_deriv(self, variant="symmetric"): - 575 """Return the second derivative of the correlator with respect to x0. - 576 - 577 Parameters - 578 ---------- - 579 variant : str - 580 decides which definition of the finite differences derivative is used. - 581 Available choice: symmetric, improved, log, default: symmetric - 582 """ - 583 if self.N != 1: - 584 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 585 if variant == "symmetric": - 586 newcontent = [] - 587 for t in range(1, self.T - 1): - 588 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 589 newcontent.append(None) - 590 else: - 591 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 592 if (all([x is None for x in newcontent])): - 593 raise Exception("Derivative is undefined at all timeslices") - 594 return Corr(newcontent, padding=[1, 1]) - 595 elif variant == "improved": - 596 newcontent = [] - 597 for t in range(2, self.T - 2): - 598 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): - 599 newcontent.append(None) - 600 else: - 601 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])) - 602 if (all([x is None for x in newcontent])): - 603 raise Exception("Derivative is undefined at all timeslices") - 604 return Corr(newcontent, padding=[2, 2]) - 605 elif variant == 'log': - 606 newcontent = [] - 607 for t in range(self.T): - 608 if (self.content[t] is None) or (self.content[t] <= 0): - 609 newcontent.append(None) - 610 else: - 611 newcontent.append(np.log(self.content[t])) - 612 if (all([x is None for x in newcontent])): - 613 raise Exception("Log is undefined at all timeslices") - 614 logcorr = Corr(newcontent) - 615 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) - 616 else: - 617 raise Exception("Unknown variant.") - 618 - 619 def m_eff(self, variant='log', guess=1.0): - 620 """Returns the effective mass of the correlator as correlator object - 621 - 622 Parameters - 623 ---------- - 624 variant : str - 625 log : uses the standard effective mass log(C(t) / C(t+1)) - 626 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. - 627 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. - 628 See, e.g., arXiv:1205.5380 - 629 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 630 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 - 631 guess : float - 632 guess for the root finder, only relevant for the root variant - 633 """ - 634 if self.N != 1: - 635 raise Exception('Correlator must be projected before getting m_eff') - 636 if variant == 'log': - 637 newcontent = [] - 638 for t in range(self.T - 1): - 639 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 640 newcontent.append(None) - 641 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 509 return (self + T_partner) / 2 + 510 + 511 def deriv(self, variant="symmetric"): + 512 """Return the first derivative of the correlator with respect to x0. + 513 + 514 Parameters + 515 ---------- + 516 variant : str + 517 decides which definition of the finite differences derivative is used. + 518 Available choice: symmetric, forward, backward, improved, log, default: symmetric + 519 """ + 520 if self.N != 1: + 521 raise Exception("deriv only implemented for one-dimensional correlators.") + 522 if variant == "symmetric": + 523 newcontent = [] + 524 for t in range(1, self.T - 1): + 525 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 526 newcontent.append(None) + 527 else: + 528 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) + 529 if (all([x is None for x in newcontent])): + 530 raise Exception('Derivative is undefined at all timeslices') + 531 return Corr(newcontent, padding=[1, 1]) + 532 elif variant == "forward": + 533 newcontent = [] + 534 for t in range(self.T - 1): + 535 if (self.content[t] is None) or (self.content[t + 1] is None): + 536 newcontent.append(None) + 537 else: + 538 newcontent.append(self.content[t + 1] - self.content[t]) + 539 if (all([x is None for x in newcontent])): + 540 raise Exception("Derivative is undefined at all timeslices") + 541 return Corr(newcontent, padding=[0, 1]) + 542 elif variant == "backward": + 543 newcontent = [] + 544 for t in range(1, self.T): + 545 if (self.content[t - 1] is None) or (self.content[t] is None): + 546 newcontent.append(None) + 547 else: + 548 newcontent.append(self.content[t] - self.content[t - 1]) + 549 if (all([x is None for x in newcontent])): + 550 raise Exception("Derivative is undefined at all timeslices") + 551 return Corr(newcontent, padding=[1, 0]) + 552 elif variant == "improved": + 553 newcontent = [] + 554 for t in range(2, self.T - 2): + 555 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): + 556 newcontent.append(None) + 557 else: + 558 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) + 559 if (all([x is None for x in newcontent])): + 560 raise Exception('Derivative is undefined at all timeslices') + 561 return Corr(newcontent, padding=[2, 2]) + 562 elif variant == 'log': + 563 newcontent = [] + 564 for t in range(self.T): + 565 if (self.content[t] is None) or (self.content[t] <= 0): + 566 newcontent.append(None) + 567 else: + 568 newcontent.append(np.log(self.content[t])) + 569 if (all([x is None for x in newcontent])): + 570 raise Exception("Log is undefined at all timeslices") + 571 logcorr = Corr(newcontent) + 572 return self * logcorr.deriv('symmetric') + 573 else: + 574 raise Exception("Unknown variant.") + 575 + 576 def second_deriv(self, variant="symmetric"): + 577 """Return the second derivative of the correlator with respect to x0. + 578 + 579 Parameters + 580 ---------- + 581 variant : str + 582 decides which definition of the finite differences derivative is used. + 583 Available choice: symmetric, improved, log, default: symmetric + 584 """ + 585 if self.N != 1: + 586 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 587 if variant == "symmetric": + 588 newcontent = [] + 589 for t in range(1, self.T - 1): + 590 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 591 newcontent.append(None) + 592 else: + 593 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 594 if (all([x is None for x in newcontent])): + 595 raise Exception("Derivative is undefined at all timeslices") + 596 return Corr(newcontent, padding=[1, 1]) + 597 elif variant == "improved": + 598 newcontent = [] + 599 for t in range(2, self.T - 2): + 600 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): + 601 newcontent.append(None) + 602 else: + 603 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])) + 604 if (all([x is None for x in newcontent])): + 605 raise Exception("Derivative is undefined at all timeslices") + 606 return Corr(newcontent, padding=[2, 2]) + 607 elif variant == 'log': + 608 newcontent = [] + 609 for t in range(self.T): + 610 if (self.content[t] is None) or (self.content[t] <= 0): + 611 newcontent.append(None) + 612 else: + 613 newcontent.append(np.log(self.content[t])) + 614 if (all([x is None for x in newcontent])): + 615 raise Exception("Log is undefined at all timeslices") + 616 logcorr = Corr(newcontent) + 617 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) + 618 else: + 619 raise Exception("Unknown variant.") + 620 + 621 def m_eff(self, variant='log', guess=1.0): + 622 """Returns the effective mass of the correlator as correlator object + 623 + 624 Parameters + 625 ---------- + 626 variant : str + 627 log : uses the standard effective mass log(C(t) / C(t+1)) + 628 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. + 629 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. + 630 See, e.g., arXiv:1205.5380 + 631 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 632 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 + 633 guess : float + 634 guess for the root finder, only relevant for the root variant + 635 """ + 636 if self.N != 1: + 637 raise Exception('Correlator must be projected before getting m_eff') + 638 if variant == 'log': + 639 newcontent = [] + 640 for t in range(self.T - 1): + 641 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 642 newcontent.append(None) - 643 else: - 644 newcontent.append(self.content[t] / self.content[t + 1]) - 645 if (all([x is None for x in newcontent])): - 646 raise Exception('m_eff is undefined at all timeslices') - 647 - 648 return np.log(Corr(newcontent, padding=[0, 1])) + 643 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 644 newcontent.append(None) + 645 else: + 646 newcontent.append(self.content[t] / self.content[t + 1]) + 647 if (all([x is None for x in newcontent])): + 648 raise Exception('m_eff is undefined at all timeslices') 649 - 650 elif variant == 'logsym': - 651 newcontent = [] - 652 for t in range(1, self.T - 1): - 653 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 654 newcontent.append(None) - 655 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: + 650 return np.log(Corr(newcontent, padding=[0, 1])) + 651 + 652 elif variant == 'logsym': + 653 newcontent = [] + 654 for t in range(1, self.T - 1): + 655 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 656 newcontent.append(None) - 657 else: - 658 newcontent.append(self.content[t - 1] / self.content[t + 1]) - 659 if (all([x is None for x in newcontent])): - 660 raise Exception('m_eff is undefined at all timeslices') - 661 - 662 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 657 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: + 658 newcontent.append(None) + 659 else: + 660 newcontent.append(self.content[t - 1] / self.content[t + 1]) + 661 if (all([x is None for x in newcontent])): + 662 raise Exception('m_eff is undefined at all timeslices') 663 - 664 elif variant in ['periodic', 'cosh', 'sinh']: - 665 if variant in ['periodic', 'cosh']: - 666 func = anp.cosh - 667 else: - 668 func = anp.sinh - 669 - 670 def root_function(x, d): - 671 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 672 - 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 # Fill the two timeslices in the middle of the lattice with their predecessors - 678 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 679 newcontent.append(newcontent[-1]) - 680 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 681 newcontent.append(None) - 682 else: - 683 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 684 if (all([x is None for x in newcontent])): - 685 raise Exception('m_eff is undefined at all timeslices') - 686 - 687 return Corr(newcontent, padding=[0, 1]) + 664 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 665 + 666 elif variant in ['periodic', 'cosh', 'sinh']: + 667 if variant in ['periodic', 'cosh']: + 668 func = anp.cosh + 669 else: + 670 func = anp.sinh + 671 + 672 def root_function(x, d): + 673 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 674 + 675 newcontent = [] + 676 for t in range(self.T - 1): + 677 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 678 newcontent.append(None) + 679 # Fill the two timeslices in the middle of the lattice with their predecessors + 680 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 681 newcontent.append(newcontent[-1]) + 682 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 683 newcontent.append(None) + 684 else: + 685 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) + 686 if (all([x is None for x in newcontent])): + 687 raise Exception('m_eff is undefined at all timeslices') 688 - 689 elif variant == 'arccosh': - 690 newcontent = [] - 691 for t in range(1, self.T - 1): - 692 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): - 693 newcontent.append(None) - 694 else: - 695 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) - 696 if (all([x is None for x in newcontent])): - 697 raise Exception("m_eff is undefined at all timeslices") - 698 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 699 - 700 else: - 701 raise Exception('Unknown variant.') - 702 - 703 def fit(self, function, fitrange=None, silent=False, **kwargs): - 704 r'''Fits function to the data - 705 - 706 Parameters - 707 ---------- - 708 function : obj - 709 function to fit to the data. See fits.least_squares for details. - 710 fitrange : list - 711 Two element list containing the timeslices on which the fit is supposed to start and stop. - 712 Caution: This range is inclusive as opposed to standard python indexing. - 713 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 714 If not specified, self.prange or all timeslices are used. - 715 silent : bool - 716 Decides whether output is printed to the standard output. - 717 ''' - 718 if self.N != 1: - 719 raise Exception("Correlator must be projected before fitting") - 720 - 721 if fitrange is None: - 722 if self.prange: - 723 fitrange = self.prange - 724 else: - 725 fitrange = [0, self.T - 1] - 726 else: - 727 if not isinstance(fitrange, list): - 728 raise Exception("fitrange has to be a list with two elements") - 729 if len(fitrange) != 2: - 730 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 731 - 732 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 733 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 734 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 735 return result - 736 - 737 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 738 """ Extract a plateau value from a Corr object - 739 - 740 Parameters - 741 ---------- - 742 plateau_range : list - 743 list with two entries, indicating the first and the last timeslice - 744 of the plateau region. - 745 method : str - 746 method to extract the plateau. - 747 'fit' fits a constant to the plateau region - 748 'avg', 'average' or 'mean' just average over the given timeslices. - 749 auto_gamma : bool - 750 apply gamma_method with default parameters to the Corr. Defaults to None - 751 """ - 752 if not plateau_range: - 753 if self.prange: - 754 plateau_range = self.prange - 755 else: - 756 raise Exception("no plateau range provided") - 757 if self.N != 1: - 758 raise Exception("Correlator must be projected before getting a plateau.") - 759 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 760 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 761 if auto_gamma: - 762 self.gamma_method() - 763 if method == "fit": - 764 def const_func(a, t): - 765 return a[0] - 766 return self.fit(const_func, plateau_range)[0] - 767 elif method in ["avg", "average", "mean"]: - 768 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 769 return returnvalue - 770 - 771 else: - 772 raise Exception("Unsupported plateau method: " + method) - 773 - 774 def set_prange(self, prange): - 775 """Sets the attribute prange of the Corr object.""" - 776 if not len(prange) == 2: - 777 raise Exception("prange must be a list or array with two values") - 778 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 779 raise Exception("Start and end point must be integers") - 780 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 781 raise Exception("Start and end point must define a range in the interval 0,T") - 782 - 783 self.prange = prange - 784 return - 785 - 786 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): - 787 """Plots the correlator using the tag of the correlator as label if available. - 788 - 789 Parameters - 790 ---------- - 791 x_range : list - 792 list of two values, determining the range of the x-axis e.g. [4, 8]. - 793 comp : Corr or list of Corr - 794 Correlator or list of correlators which are plotted for comparison. - 795 The tags of these correlators are used as labels if available. - 796 logscale : bool - 797 Sets y-axis to logscale. - 798 plateau : Obs - 799 Plateau value to be visualized in the figure. - 800 fit_res : Fit_result - 801 Fit_result object to be visualized. - 802 ylabel : str - 803 Label for the y-axis. - 804 save : str - 805 path to file in which the figure should be saved. - 806 auto_gamma : bool - 807 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 808 hide_sigma : float - 809 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 810 references : list - 811 List of floating point values that are displayed as horizontal lines for reference. - 812 title : string - 813 Optional title of the figure. - 814 """ - 815 if self.N != 1: - 816 raise Exception("Correlator must be projected before plotting") - 817 - 818 if auto_gamma: - 819 self.gamma_method() - 820 - 821 if x_range is None: - 822 x_range = [0, self.T - 1] - 823 - 824 fig = plt.figure() - 825 ax1 = fig.add_subplot(111) - 826 - 827 x, y, y_err = self.plottable() - 828 if hide_sigma: - 829 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 830 else: - 831 hide_from = None - 832 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 833 if logscale: - 834 ax1.set_yscale('log') - 835 else: - 836 if y_range is None: - 837 try: - 838 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)]) - 839 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)]) - 840 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 841 except Exception: - 842 pass - 843 else: - 844 ax1.set_ylim(y_range) - 845 if comp: - 846 if isinstance(comp, (Corr, list)): - 847 for corr in comp if isinstance(comp, list) else [comp]: - 848 if auto_gamma: - 849 corr.gamma_method() - 850 x, y, y_err = corr.plottable() - 851 if hide_sigma: - 852 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 853 else: - 854 hide_from = None - 855 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 856 else: - 857 raise Exception("'comp' must be a correlator or a list of correlators.") - 858 - 859 if plateau: - 860 if isinstance(plateau, Obs): - 861 if auto_gamma: - 862 plateau.gamma_method() - 863 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 864 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 865 else: - 866 raise Exception("'plateau' must be an Obs") - 867 - 868 if references: - 869 if isinstance(references, list): - 870 for ref in references: - 871 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 872 else: - 873 raise Exception("'references' must be a list of floating pint values.") - 874 - 875 if self.prange: - 876 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 877 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 878 - 879 if fit_res: - 880 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 881 ax1.plot(x_samples, - 882 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 883 ls='-', marker=',', lw=2) - 884 - 885 ax1.set_xlabel(r'$x_0 / a$') - 886 if ylabel: - 887 ax1.set_ylabel(ylabel) - 888 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 889 - 890 handles, labels = ax1.get_legend_handles_labels() - 891 if labels: - 892 ax1.legend() - 893 - 894 if title: - 895 plt.title(title) - 896 - 897 plt.draw() + 689 return Corr(newcontent, padding=[0, 1]) + 690 + 691 elif variant == 'arccosh': + 692 newcontent = [] + 693 for t in range(1, self.T - 1): + 694 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): + 695 newcontent.append(None) + 696 else: + 697 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 698 if (all([x is None for x in newcontent])): + 699 raise Exception("m_eff is undefined at all timeslices") + 700 return np.arccosh(Corr(newcontent, padding=[1, 1])) + 701 + 702 else: + 703 raise Exception('Unknown variant.') + 704 + 705 def fit(self, function, fitrange=None, silent=False, **kwargs): + 706 r'''Fits function to the data + 707 + 708 Parameters + 709 ---------- + 710 function : obj + 711 function to fit to the data. See fits.least_squares for details. + 712 fitrange : list + 713 Two element list containing the timeslices on which the fit is supposed to start and stop. + 714 Caution: This range is inclusive as opposed to standard python indexing. + 715 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 716 If not specified, self.prange or all timeslices are used. + 717 silent : bool + 718 Decides whether output is printed to the standard output. + 719 ''' + 720 if self.N != 1: + 721 raise Exception("Correlator must be projected before fitting") + 722 + 723 if fitrange is None: + 724 if self.prange: + 725 fitrange = self.prange + 726 else: + 727 fitrange = [0, self.T - 1] + 728 else: + 729 if not isinstance(fitrange, list): + 730 raise Exception("fitrange has to be a list with two elements") + 731 if len(fitrange) != 2: + 732 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 733 + 734 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 735 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 736 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 737 return result + 738 + 739 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 740 """ Extract a plateau value from a Corr object + 741 + 742 Parameters + 743 ---------- + 744 plateau_range : list + 745 list with two entries, indicating the first and the last timeslice + 746 of the plateau region. + 747 method : str + 748 method to extract the plateau. + 749 'fit' fits a constant to the plateau region + 750 'avg', 'average' or 'mean' just average over the given timeslices. + 751 auto_gamma : bool + 752 apply gamma_method with default parameters to the Corr. Defaults to None + 753 """ + 754 if not plateau_range: + 755 if self.prange: + 756 plateau_range = self.prange + 757 else: + 758 raise Exception("no plateau range provided") + 759 if self.N != 1: + 760 raise Exception("Correlator must be projected before getting a plateau.") + 761 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 762 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 763 if auto_gamma: + 764 self.gamma_method() + 765 if method == "fit": + 766 def const_func(a, t): + 767 return a[0] + 768 return self.fit(const_func, plateau_range)[0] + 769 elif method in ["avg", "average", "mean"]: + 770 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 771 return returnvalue + 772 + 773 else: + 774 raise Exception("Unsupported plateau method: " + method) + 775 + 776 def set_prange(self, prange): + 777 """Sets the attribute prange of the Corr object.""" + 778 if not len(prange) == 2: + 779 raise Exception("prange must be a list or array with two values") + 780 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 781 raise Exception("Start and end point must be integers") + 782 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 783 raise Exception("Start and end point must define a range in the interval 0,T") + 784 + 785 self.prange = prange + 786 return + 787 + 788 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): + 789 """Plots the correlator using the tag of the correlator as label if available. + 790 + 791 Parameters + 792 ---------- + 793 x_range : list + 794 list of two values, determining the range of the x-axis e.g. [4, 8]. + 795 comp : Corr or list of Corr + 796 Correlator or list of correlators which are plotted for comparison. + 797 The tags of these correlators are used as labels if available. + 798 logscale : bool + 799 Sets y-axis to logscale. + 800 plateau : Obs + 801 Plateau value to be visualized in the figure. + 802 fit_res : Fit_result + 803 Fit_result object to be visualized. + 804 ylabel : str + 805 Label for the y-axis. + 806 save : str + 807 path to file in which the figure should be saved. + 808 auto_gamma : bool + 809 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 810 hide_sigma : float + 811 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 812 references : list + 813 List of floating point values that are displayed as horizontal lines for reference. + 814 title : string + 815 Optional title of the figure. + 816 """ + 817 if self.N != 1: + 818 raise Exception("Correlator must be projected before plotting") + 819 + 820 if auto_gamma: + 821 self.gamma_method() + 822 + 823 if x_range is None: + 824 x_range = [0, self.T - 1] + 825 + 826 fig = plt.figure() + 827 ax1 = fig.add_subplot(111) + 828 + 829 x, y, y_err = self.plottable() + 830 if hide_sigma: + 831 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 832 else: + 833 hide_from = None + 834 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 835 if logscale: + 836 ax1.set_yscale('log') + 837 else: + 838 if y_range is None: + 839 try: + 840 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)]) + 841 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)]) + 842 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 843 except Exception: + 844 pass + 845 else: + 846 ax1.set_ylim(y_range) + 847 if comp: + 848 if isinstance(comp, (Corr, list)): + 849 for corr in comp if isinstance(comp, list) else [comp]: + 850 if auto_gamma: + 851 corr.gamma_method() + 852 x, y, y_err = corr.plottable() + 853 if hide_sigma: + 854 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 855 else: + 856 hide_from = None + 857 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 858 else: + 859 raise Exception("'comp' must be a correlator or a list of correlators.") + 860 + 861 if plateau: + 862 if isinstance(plateau, Obs): + 863 if auto_gamma: + 864 plateau.gamma_method() + 865 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 866 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 867 else: + 868 raise Exception("'plateau' must be an Obs") + 869 + 870 if references: + 871 if isinstance(references, list): + 872 for ref in references: + 873 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 874 else: + 875 raise Exception("'references' must be a list of floating pint values.") + 876 + 877 if self.prange: + 878 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 879 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') + 880 + 881 if fit_res: + 882 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 883 ax1.plot(x_samples, + 884 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 885 ls='-', marker=',', lw=2) + 886 + 887 ax1.set_xlabel(r'$x_0 / a$') + 888 if ylabel: + 889 ax1.set_ylabel(ylabel) + 890 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 891 + 892 handles, labels = ax1.get_legend_handles_labels() + 893 if labels: + 894 ax1.legend() + 895 + 896 if title: + 897 plt.title(title) 898 - 899 if save: - 900 if isinstance(save, str): - 901 fig.savefig(save, bbox_inches='tight') - 902 else: - 903 raise Exception("'save' has to be a string.") - 904 - 905 def spaghetti_plot(self, logscale=True): - 906 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 907 - 908 Parameters - 909 ---------- - 910 logscale : bool - 911 Determines whether the scale of the y-axis is logarithmic or standard. - 912 """ - 913 if self.N != 1: - 914 raise Exception("Correlator needs to be projected first.") - 915 - 916 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])) - 917 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 918 - 919 for name in mc_names: - 920 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T - 921 - 922 fig = plt.figure() - 923 ax = fig.add_subplot(111) - 924 for dat in data: - 925 ax.plot(x0_vals, dat, ls='-', marker='') - 926 - 927 if logscale is True: - 928 ax.set_yscale('log') - 929 - 930 ax.set_xlabel(r'$x_0 / a$') - 931 plt.title(name) - 932 plt.draw() - 933 - 934 def dump(self, filename, datatype="json.gz", **kwargs): - 935 """Dumps the Corr into a file of chosen type - 936 Parameters - 937 ---------- - 938 filename : str - 939 Name of the file to be saved. - 940 datatype : str - 941 Format of the exported file. Supported formats include - 942 "json.gz" and "pickle" - 943 path : str - 944 specifies a custom path for the file (default '.') - 945 """ - 946 if datatype == "json.gz": - 947 from .input.json import dump_to_json - 948 if 'path' in kwargs: - 949 file_name = kwargs.get('path') + '/' + filename - 950 else: - 951 file_name = filename - 952 dump_to_json(self, file_name) - 953 elif datatype == "pickle": - 954 dump_object(self, filename, **kwargs) - 955 else: - 956 raise Exception("Unknown datatype " + str(datatype)) - 957 - 958 def print(self, print_range=None): - 959 print(self.__repr__(print_range)) - 960 - 961 def __repr__(self, print_range=None): - 962 if print_range is None: - 963 print_range = [0, None] - 964 - 965 content_string = "" - 966 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 - 967 - 968 if self.tag is not None: - 969 content_string += "Description: " + self.tag + "\n" - 970 if self.N != 1: - 971 return content_string - 972 if isinstance(self[0], CObs): + 899 plt.draw() + 900 + 901 if save: + 902 if isinstance(save, str): + 903 fig.savefig(save, bbox_inches='tight') + 904 else: + 905 raise Exception("'save' has to be a string.") + 906 + 907 def spaghetti_plot(self, logscale=True): + 908 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 909 + 910 Parameters + 911 ---------- + 912 logscale : bool + 913 Determines whether the scale of the y-axis is logarithmic or standard. + 914 """ + 915 if self.N != 1: + 916 raise Exception("Correlator needs to be projected first.") + 917 + 918 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])) + 919 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 920 + 921 for name in mc_names: + 922 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 923 + 924 fig = plt.figure() + 925 ax = fig.add_subplot(111) + 926 for dat in data: + 927 ax.plot(x0_vals, dat, ls='-', marker='') + 928 + 929 if logscale is True: + 930 ax.set_yscale('log') + 931 + 932 ax.set_xlabel(r'$x_0 / a$') + 933 plt.title(name) + 934 plt.draw() + 935 + 936 def dump(self, filename, datatype="json.gz", **kwargs): + 937 """Dumps the Corr into a file of chosen type + 938 Parameters + 939 ---------- + 940 filename : str + 941 Name of the file to be saved. + 942 datatype : str + 943 Format of the exported file. Supported formats include + 944 "json.gz" and "pickle" + 945 path : str + 946 specifies a custom path for the file (default '.') + 947 """ + 948 if datatype == "json.gz": + 949 from .input.json import dump_to_json + 950 if 'path' in kwargs: + 951 file_name = kwargs.get('path') + '/' + filename + 952 else: + 953 file_name = filename + 954 dump_to_json(self, file_name) + 955 elif datatype == "pickle": + 956 dump_object(self, filename, **kwargs) + 957 else: + 958 raise Exception("Unknown datatype " + str(datatype)) + 959 + 960 def print(self, print_range=None): + 961 print(self.__repr__(print_range)) + 962 + 963 def __repr__(self, print_range=None): + 964 if print_range is None: + 965 print_range = [0, None] + 966 + 967 content_string = "" + 968 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 + 969 + 970 if self.tag is not None: + 971 content_string += "Description: " + self.tag + "\n" + 972 if self.N != 1: 973 return content_string - 974 - 975 if print_range[1]: - 976 print_range[1] += 1 - 977 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 978 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 979 if sub_corr is None: - 980 content_string += str(i + print_range[0]) + '\n' - 981 else: - 982 content_string += str(i + print_range[0]) - 983 for element in sub_corr: - 984 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 985 content_string += '\n' - 986 return content_string - 987 - 988 def __str__(self): - 989 return self.__repr__() - 990 - 991 # We define the basic operations, that can be performed with correlators. - 992 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 993 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 994 # One could try and tell Obs to check if the y in __mul__ is a Corr and - 995 - 996 def __add__(self, y): - 997 if isinstance(y, Corr): - 998 if ((self.N != y.N) or (self.T != y.T)): - 999 raise Exception("Addition of Corrs with different shape") -1000 newcontent = [] -1001 for t in range(self.T): -1002 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1003 newcontent.append(None) -1004 else: -1005 newcontent.append(self.content[t] + y.content[t]) -1006 return Corr(newcontent) -1007 -1008 elif isinstance(y, (Obs, int, float, CObs)): -1009 newcontent = [] -1010 for t in range(self.T): -1011 if _check_for_none(self, self.content[t]): -1012 newcontent.append(None) -1013 else: -1014 newcontent.append(self.content[t] + y) -1015 return Corr(newcontent, prange=self.prange) -1016 elif isinstance(y, np.ndarray): -1017 if y.shape == (self.T,): -1018 return Corr(list((np.array(self.content).T + y).T)) -1019 else: -1020 raise ValueError("operands could not be broadcast together") -1021 else: -1022 raise TypeError("Corr + wrong type") -1023 -1024 def __mul__(self, y): -1025 if isinstance(y, Corr): -1026 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1027 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1028 newcontent = [] -1029 for t in range(self.T): -1030 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1031 newcontent.append(None) -1032 else: -1033 newcontent.append(self.content[t] * y.content[t]) -1034 return Corr(newcontent) -1035 -1036 elif isinstance(y, (Obs, int, float, CObs)): -1037 newcontent = [] -1038 for t in range(self.T): -1039 if _check_for_none(self, self.content[t]): -1040 newcontent.append(None) -1041 else: -1042 newcontent.append(self.content[t] * y) -1043 return Corr(newcontent, prange=self.prange) -1044 elif isinstance(y, np.ndarray): -1045 if y.shape == (self.T,): -1046 return Corr(list((np.array(self.content).T * y).T)) -1047 else: -1048 raise ValueError("operands could not be broadcast together") -1049 else: -1050 raise TypeError("Corr * wrong type") -1051 -1052 def __truediv__(self, y): -1053 if isinstance(y, Corr): -1054 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1055 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1056 newcontent = [] -1057 for t in range(self.T): -1058 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1059 newcontent.append(None) -1060 else: -1061 newcontent.append(self.content[t] / y.content[t]) -1062 for t in range(self.T): -1063 if _check_for_none(self, newcontent[t]): -1064 continue -1065 if np.isnan(np.sum(newcontent[t]).value): -1066 newcontent[t] = None -1067 -1068 if all([item is None for item in newcontent]): -1069 raise Exception("Division returns completely undefined correlator") -1070 return Corr(newcontent) -1071 -1072 elif isinstance(y, (Obs, CObs)): -1073 if isinstance(y, Obs): -1074 if y.value == 0: -1075 raise Exception('Division by zero will return undefined correlator') -1076 if isinstance(y, CObs): -1077 if y.is_zero(): -1078 raise Exception('Division by zero will return undefined correlator') -1079 -1080 newcontent = [] -1081 for t in range(self.T): -1082 if _check_for_none(self, self.content[t]): -1083 newcontent.append(None) -1084 else: -1085 newcontent.append(self.content[t] / y) -1086 return Corr(newcontent, prange=self.prange) -1087 -1088 elif isinstance(y, (int, float)): -1089 if y == 0: -1090 raise Exception('Division by zero will return undefined correlator') -1091 newcontent = [] -1092 for t in range(self.T): -1093 if _check_for_none(self, self.content[t]): -1094 newcontent.append(None) -1095 else: -1096 newcontent.append(self.content[t] / y) -1097 return Corr(newcontent, prange=self.prange) -1098 elif isinstance(y, np.ndarray): -1099 if y.shape == (self.T,): -1100 return Corr(list((np.array(self.content).T / y).T)) -1101 else: -1102 raise ValueError("operands could not be broadcast together") -1103 else: -1104 raise TypeError('Corr / wrong type') -1105 -1106 def __neg__(self): -1107 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1108 return Corr(newcontent, prange=self.prange) -1109 -1110 def __sub__(self, y): -1111 return self + (-y) -1112 -1113 def __pow__(self, y): -1114 if isinstance(y, (Obs, int, float, CObs)): -1115 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1116 return Corr(newcontent, prange=self.prange) -1117 else: -1118 raise TypeError('Type of exponent not supported') -1119 -1120 def __abs__(self): -1121 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1122 return Corr(newcontent, prange=self.prange) -1123 -1124 # The numpy functions: -1125 def sqrt(self): -1126 return self ** 0.5 -1127 -1128 def log(self): -1129 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1130 return Corr(newcontent, prange=self.prange) -1131 -1132 def exp(self): -1133 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1134 return Corr(newcontent, prange=self.prange) -1135 -1136 def _apply_func_to_corr(self, func): -1137 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1138 for t in range(self.T): -1139 if _check_for_none(self, newcontent[t]): -1140 continue -1141 tmp_sum = np.sum(newcontent[t]) -1142 if hasattr(tmp_sum, "value"): -1143 if np.isnan(tmp_sum.value): -1144 newcontent[t] = None -1145 if all([item is None for item in newcontent]): -1146 raise Exception('Operation returns undefined correlator') -1147 return Corr(newcontent) -1148 -1149 def sin(self): -1150 return self._apply_func_to_corr(np.sin) -1151 -1152 def cos(self): -1153 return self._apply_func_to_corr(np.cos) -1154 -1155 def tan(self): -1156 return self._apply_func_to_corr(np.tan) -1157 -1158 def sinh(self): -1159 return self._apply_func_to_corr(np.sinh) -1160 -1161 def cosh(self): -1162 return self._apply_func_to_corr(np.cosh) -1163 -1164 def tanh(self): -1165 return self._apply_func_to_corr(np.tanh) -1166 -1167 def arcsin(self): -1168 return self._apply_func_to_corr(np.arcsin) -1169 -1170 def arccos(self): -1171 return self._apply_func_to_corr(np.arccos) -1172 -1173 def arctan(self): -1174 return self._apply_func_to_corr(np.arctan) -1175 -1176 def arcsinh(self): -1177 return self._apply_func_to_corr(np.arcsinh) -1178 -1179 def arccosh(self): -1180 return self._apply_func_to_corr(np.arccosh) -1181 -1182 def arctanh(self): -1183 return self._apply_func_to_corr(np.arctanh) -1184 -1185 # Right hand side operations (require tweak in main module to work) -1186 def __radd__(self, y): -1187 return self + y -1188 -1189 def __rsub__(self, y): -1190 return -self + y -1191 -1192 def __rmul__(self, y): -1193 return self * y -1194 -1195 def __rtruediv__(self, y): -1196 return (self / y) ** (-1) -1197 -1198 @property -1199 def real(self): -1200 def return_real(obs_OR_cobs): -1201 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1202 return np.vectorize(lambda x: x.real)(obs_OR_cobs) -1203 else: -1204 return obs_OR_cobs -1205 -1206 return self._apply_func_to_corr(return_real) + 974 if isinstance(self[0], CObs): + 975 return content_string + 976 + 977 if print_range[1]: + 978 print_range[1] += 1 + 979 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 980 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 981 if sub_corr is None: + 982 content_string += str(i + print_range[0]) + '\n' + 983 else: + 984 content_string += str(i + print_range[0]) + 985 for element in sub_corr: + 986 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 987 content_string += '\n' + 988 return content_string + 989 + 990 def __str__(self): + 991 return self.__repr__() + 992 + 993 # We define the basic operations, that can be performed with correlators. + 994 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. + 995 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. + 996 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 997 + 998 def __add__(self, y): + 999 if isinstance(y, Corr): +1000 if ((self.N != y.N) or (self.T != y.T)): +1001 raise Exception("Addition of Corrs with different shape") +1002 newcontent = [] +1003 for t in range(self.T): +1004 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1005 newcontent.append(None) +1006 else: +1007 newcontent.append(self.content[t] + y.content[t]) +1008 return Corr(newcontent) +1009 +1010 elif isinstance(y, (Obs, int, float, CObs)): +1011 newcontent = [] +1012 for t in range(self.T): +1013 if _check_for_none(self, self.content[t]): +1014 newcontent.append(None) +1015 else: +1016 newcontent.append(self.content[t] + y) +1017 return Corr(newcontent, prange=self.prange) +1018 elif isinstance(y, np.ndarray): +1019 if y.shape == (self.T,): +1020 return Corr(list((np.array(self.content).T + y).T)) +1021 else: +1022 raise ValueError("operands could not be broadcast together") +1023 else: +1024 raise TypeError("Corr + wrong type") +1025 +1026 def __mul__(self, y): +1027 if isinstance(y, Corr): +1028 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1029 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1030 newcontent = [] +1031 for t in range(self.T): +1032 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1033 newcontent.append(None) +1034 else: +1035 newcontent.append(self.content[t] * y.content[t]) +1036 return Corr(newcontent) +1037 +1038 elif isinstance(y, (Obs, int, float, CObs)): +1039 newcontent = [] +1040 for t in range(self.T): +1041 if _check_for_none(self, self.content[t]): +1042 newcontent.append(None) +1043 else: +1044 newcontent.append(self.content[t] * y) +1045 return Corr(newcontent, prange=self.prange) +1046 elif isinstance(y, np.ndarray): +1047 if y.shape == (self.T,): +1048 return Corr(list((np.array(self.content).T * y).T)) +1049 else: +1050 raise ValueError("operands could not be broadcast together") +1051 else: +1052 raise TypeError("Corr * wrong type") +1053 +1054 def __truediv__(self, y): +1055 if isinstance(y, Corr): +1056 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1057 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1058 newcontent = [] +1059 for t in range(self.T): +1060 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1061 newcontent.append(None) +1062 else: +1063 newcontent.append(self.content[t] / y.content[t]) +1064 for t in range(self.T): +1065 if _check_for_none(self, newcontent[t]): +1066 continue +1067 if np.isnan(np.sum(newcontent[t]).value): +1068 newcontent[t] = None +1069 +1070 if all([item is None for item in newcontent]): +1071 raise Exception("Division returns completely undefined correlator") +1072 return Corr(newcontent) +1073 +1074 elif isinstance(y, (Obs, CObs)): +1075 if isinstance(y, Obs): +1076 if y.value == 0: +1077 raise Exception('Division by zero will return undefined correlator') +1078 if isinstance(y, CObs): +1079 if y.is_zero(): +1080 raise Exception('Division by zero will return undefined correlator') +1081 +1082 newcontent = [] +1083 for t in range(self.T): +1084 if _check_for_none(self, self.content[t]): +1085 newcontent.append(None) +1086 else: +1087 newcontent.append(self.content[t] / y) +1088 return Corr(newcontent, prange=self.prange) +1089 +1090 elif isinstance(y, (int, float)): +1091 if y == 0: +1092 raise Exception('Division by zero will return undefined correlator') +1093 newcontent = [] +1094 for t in range(self.T): +1095 if _check_for_none(self, self.content[t]): +1096 newcontent.append(None) +1097 else: +1098 newcontent.append(self.content[t] / y) +1099 return Corr(newcontent, prange=self.prange) +1100 elif isinstance(y, np.ndarray): +1101 if y.shape == (self.T,): +1102 return Corr(list((np.array(self.content).T / y).T)) +1103 else: +1104 raise ValueError("operands could not be broadcast together") +1105 else: +1106 raise TypeError('Corr / wrong type') +1107 +1108 def __neg__(self): +1109 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1110 return Corr(newcontent, prange=self.prange) +1111 +1112 def __sub__(self, y): +1113 return self + (-y) +1114 +1115 def __pow__(self, y): +1116 if isinstance(y, (Obs, int, float, CObs)): +1117 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1118 return Corr(newcontent, prange=self.prange) +1119 else: +1120 raise TypeError('Type of exponent not supported') +1121 +1122 def __abs__(self): +1123 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1124 return Corr(newcontent, prange=self.prange) +1125 +1126 # The numpy functions: +1127 def sqrt(self): +1128 return self ** 0.5 +1129 +1130 def log(self): +1131 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1132 return Corr(newcontent, prange=self.prange) +1133 +1134 def exp(self): +1135 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1136 return Corr(newcontent, prange=self.prange) +1137 +1138 def _apply_func_to_corr(self, func): +1139 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1140 for t in range(self.T): +1141 if _check_for_none(self, newcontent[t]): +1142 continue +1143 tmp_sum = np.sum(newcontent[t]) +1144 if hasattr(tmp_sum, "value"): +1145 if np.isnan(tmp_sum.value): +1146 newcontent[t] = None +1147 if all([item is None for item in newcontent]): +1148 raise Exception('Operation returns undefined correlator') +1149 return Corr(newcontent) +1150 +1151 def sin(self): +1152 return self._apply_func_to_corr(np.sin) +1153 +1154 def cos(self): +1155 return self._apply_func_to_corr(np.cos) +1156 +1157 def tan(self): +1158 return self._apply_func_to_corr(np.tan) +1159 +1160 def sinh(self): +1161 return self._apply_func_to_corr(np.sinh) +1162 +1163 def cosh(self): +1164 return self._apply_func_to_corr(np.cosh) +1165 +1166 def tanh(self): +1167 return self._apply_func_to_corr(np.tanh) +1168 +1169 def arcsin(self): +1170 return self._apply_func_to_corr(np.arcsin) +1171 +1172 def arccos(self): +1173 return self._apply_func_to_corr(np.arccos) +1174 +1175 def arctan(self): +1176 return self._apply_func_to_corr(np.arctan) +1177 +1178 def arcsinh(self): +1179 return self._apply_func_to_corr(np.arcsinh) +1180 +1181 def arccosh(self): +1182 return self._apply_func_to_corr(np.arccosh) +1183 +1184 def arctanh(self): +1185 return self._apply_func_to_corr(np.arctanh) +1186 +1187 # Right hand side operations (require tweak in main module to work) +1188 def __radd__(self, y): +1189 return self + y +1190 +1191 def __rsub__(self, y): +1192 return -self + y +1193 +1194 def __rmul__(self, y): +1195 return self * y +1196 +1197 def __rtruediv__(self, y): +1198 return (self / y) ** (-1) +1199 +1200 @property +1201 def real(self): +1202 def return_real(obs_OR_cobs): +1203 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1204 return np.vectorize(lambda x: x.real)(obs_OR_cobs) +1205 else: +1206 return obs_OR_cobs 1207 -1208 @property -1209 def imag(self): -1210 def return_imag(obs_OR_cobs): -1211 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1212 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) -1213 else: -1214 return obs_OR_cobs * 0 # So it stays the right type -1215 -1216 return self._apply_func_to_corr(return_imag) +1208 return self._apply_func_to_corr(return_real) +1209 +1210 @property +1211 def imag(self): +1212 def return_imag(obs_OR_cobs): +1213 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1214 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) +1215 else: +1216 return obs_OR_cobs * 0 # So it stays the right type 1217 -1218 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1219 r''' Project large correlation matrix to lowest states -1220 -1221 This method can be used to reduce the size of an (N x N) correlation matrix -1222 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1223 is still small. -1224 -1225 Parameters -1226 ---------- -1227 Ntrunc: int -1228 Rank of the target matrix. -1229 tproj: int -1230 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1231 The default value is 3. -1232 t0proj: int -1233 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1234 discouraged for O(a) improved theories, since the correctness of the procedure -1235 cannot be granted in this case. The default value is 2. -1236 basematrix : Corr -1237 Correlation matrix that is used to determine the eigenvectors of the -1238 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1239 is is not specified. -1240 -1241 Notes -1242 ----- -1243 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1244 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1245 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1246 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1247 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1248 correlation matrix and to remove some noise that is added by irrelevant operators. -1249 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1250 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1251 ''' -1252 -1253 if self.N == 1: -1254 raise Exception('Method cannot be applied to one-dimensional correlators.') -1255 if basematrix is None: -1256 basematrix = self -1257 if Ntrunc >= basematrix.N: -1258 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1259 if basematrix.N != self.N: -1260 raise Exception('basematrix and targetmatrix have to be of the same size.') -1261 -1262 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1218 return self._apply_func_to_corr(return_imag) +1219 +1220 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1221 r''' Project large correlation matrix to lowest states +1222 +1223 This method can be used to reduce the size of an (N x N) correlation matrix +1224 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1225 is still small. +1226 +1227 Parameters +1228 ---------- +1229 Ntrunc: int +1230 Rank of the target matrix. +1231 tproj: int +1232 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1233 The default value is 3. +1234 t0proj: int +1235 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1236 discouraged for O(a) improved theories, since the correctness of the procedure +1237 cannot be granted in this case. The default value is 2. +1238 basematrix : Corr +1239 Correlation matrix that is used to determine the eigenvectors of the +1240 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1241 is is not specified. +1242 +1243 Notes +1244 ----- +1245 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1246 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1247 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1248 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1249 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1250 correlation matrix and to remove some noise that is added by irrelevant operators. +1251 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1252 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1253 ''' +1254 +1255 if self.N == 1: +1256 raise Exception('Method cannot be applied to one-dimensional correlators.') +1257 if basematrix is None: +1258 basematrix = self +1259 if Ntrunc >= basematrix.N: +1260 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1261 if basematrix.N != self.N: +1262 raise Exception('basematrix and targetmatrix have to be of the same size.') 1263 -1264 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1265 rmat = [] -1266 for t in range(basematrix.T): -1267 for i in range(Ntrunc): -1268 for j in range(Ntrunc): -1269 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1270 rmat.append(np.copy(tmpmat)) -1271 -1272 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1273 return Corr(newcontent) -1274 -1275 -1276def _sort_vectors(vec_set, ts): -1277 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" -1278 reference_sorting = np.array(vec_set[ts]) -1279 N = reference_sorting.shape[0] -1280 sorted_vec_set = [] -1281 for t in range(len(vec_set)): -1282 if vec_set[t] is None: -1283 sorted_vec_set.append(None) -1284 elif not t == ts: -1285 perms = [list(o) for o in permutations([i for i in range(N)], N)] -1286 best_score = 0 -1287 for perm in perms: -1288 current_score = 1 -1289 for k in range(N): -1290 new_sorting = reference_sorting.copy() -1291 new_sorting[perm[k], :] = vec_set[t][k] -1292 current_score *= abs(np.linalg.det(new_sorting)) -1293 if current_score > best_score: -1294 best_score = current_score -1295 best_perm = perm -1296 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) -1297 else: -1298 sorted_vec_set.append(vec_set[t]) -1299 -1300 return sorted_vec_set +1264 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1265 +1266 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1267 rmat = [] +1268 for t in range(basematrix.T): +1269 for i in range(Ntrunc): +1270 for j in range(Ntrunc): +1271 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1272 rmat.append(np.copy(tmpmat)) +1273 +1274 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1275 return Corr(newcontent) +1276 +1277 +1278def _sort_vectors(vec_set, ts): +1279 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" +1280 reference_sorting = np.array(vec_set[ts]) +1281 N = reference_sorting.shape[0] +1282 sorted_vec_set = [] +1283 for t in range(len(vec_set)): +1284 if vec_set[t] is None: +1285 sorted_vec_set.append(None) +1286 elif not t == ts: +1287 perms = [list(o) for o in permutations([i for i in range(N)], N)] +1288 best_score = 0 +1289 for perm in perms: +1290 current_score = 1 +1291 for k in range(N): +1292 new_sorting = reference_sorting.copy() +1293 new_sorting[perm[k], :] = vec_set[t][k] +1294 current_score *= abs(np.linalg.det(new_sorting)) +1295 if current_score > best_score: +1296 best_score = current_score +1297 best_perm = perm +1298 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) +1299 else: +1300 sorted_vec_set.append(vec_set[t]) 1301 -1302 -1303def _check_for_none(corr, entry): -1304 """Checks if entry for correlator corr is None""" -1305 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 -1306 -1307 -1308def _GEVP_solver(Gt, G0): -1309 """Helper function for solving the GEVP and sorting the eigenvectors. -1310 -1311 The helper function assumes that both provided matrices are symmetric and -1312 only processes the lower triangular part of both matrices. In case the matrices -1313 are not symmetric the upper triangular parts are effectively discarded.""" -1314 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] +1302 return sorted_vec_set +1303 +1304 +1305def _check_for_none(corr, entry): +1306 """Checks if entry for correlator corr is None""" +1307 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1308 +1309 +1310def _GEVP_solver(Gt, G0): +1311 """Helper function for solving the GEVP and sorting the eigenvectors. +1312 +1313 The helper function assumes that both provided matrices are symmetric and +1314 only processes the lower triangular part of both matrices. In case the matrices +1315 are not symmetric the upper triangular parts are effectively discarded.""" +1316 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] @@ -1654,1153 +1659,1155 @@ 125 for j in range(self.N): 126 item[i, j].gamma_method(**kwargs) 127 - 128 def projected(self, vector_l=None, vector_r=None, normalize=False): - 129 """We need to project the Correlator with a Vector to get a single value at each timeslice. - 130 - 131 The method can use one or two vectors. - 132 If two are specified it returns v1@G@v2 (the order might be very important.) - 133 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to - 134 """ - 135 if self.N == 1: - 136 raise Exception("Trying to project a Corr, that already has N=1.") - 137 - 138 if vector_l is None: - 139 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) - 140 elif (vector_r is None): - 141 vector_r = vector_l - 142 if isinstance(vector_l, list) and not isinstance(vector_r, list): - 143 if len(vector_l) != self.T: - 144 raise Exception("Length of vector list must be equal to T") - 145 vector_r = [vector_r] * self.T - 146 if isinstance(vector_r, list) and not isinstance(vector_l, list): - 147 if len(vector_r) != self.T: - 148 raise Exception("Length of vector list must be equal to T") - 149 vector_l = [vector_l] * self.T - 150 - 151 if not isinstance(vector_l, list): - 152 if not vector_l.shape == vector_r.shape == (self.N,): - 153 raise Exception("Vectors are of wrong shape!") - 154 if normalize: - 155 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) - 156 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] - 157 - 158 else: - 159 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. - 160 if normalize: - 161 for t in range(self.T): - 162 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]) - 163 - 164 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)] - 165 return Corr(newcontent) - 166 - 167 def item(self, i, j): - 168 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. - 169 - 170 Parameters - 171 ---------- - 172 i : int - 173 First index to be picked. - 174 j : int - 175 Second index to be picked. - 176 """ - 177 if self.N == 1: - 178 raise Exception("Trying to pick item from projected Corr") - 179 newcontent = [None if (item is None) else item[i, j] for item in self.content] - 180 return Corr(newcontent) - 181 - 182 def plottable(self): - 183 """Outputs the correlator in a plotable format. - 184 - 185 Outputs three lists containing the timeslice index, the value on each - 186 timeslice and the error on each timeslice. - 187 """ - 188 if self.N != 1: - 189 raise Exception("Can only make Corr[N=1] plottable") - 190 x_list = [x for x in range(self.T) if not self.content[x] is None] - 191 y_list = [y[0].value for y in self.content if y is not None] - 192 y_err_list = [y[0].dvalue for y in self.content if y is not None] - 193 - 194 return x_list, y_list, y_err_list + 128 gm = gamma_method + 129 + 130 def projected(self, vector_l=None, vector_r=None, normalize=False): + 131 """We need to project the Correlator with a Vector to get a single value at each timeslice. + 132 + 133 The method can use one or two vectors. + 134 If two are specified it returns v1@G@v2 (the order might be very important.) + 135 By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to + 136 """ + 137 if self.N == 1: + 138 raise Exception("Trying to project a Corr, that already has N=1.") + 139 + 140 if vector_l is None: + 141 vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.]) + 142 elif (vector_r is None): + 143 vector_r = vector_l + 144 if isinstance(vector_l, list) and not isinstance(vector_r, list): + 145 if len(vector_l) != self.T: + 146 raise Exception("Length of vector list must be equal to T") + 147 vector_r = [vector_r] * self.T + 148 if isinstance(vector_r, list) and not isinstance(vector_l, list): + 149 if len(vector_r) != self.T: + 150 raise Exception("Length of vector list must be equal to T") + 151 vector_l = [vector_l] * self.T + 152 + 153 if not isinstance(vector_l, list): + 154 if not vector_l.shape == vector_r.shape == (self.N,): + 155 raise Exception("Vectors are of wrong shape!") + 156 if normalize: + 157 vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r) + 158 newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content] + 159 + 160 else: + 161 # There are no checks here yet. There are so many possible scenarios, where this can go wrong. + 162 if normalize: + 163 for t in range(self.T): + 164 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]) + 165 + 166 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)] + 167 return Corr(newcontent) + 168 + 169 def item(self, i, j): + 170 """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice. + 171 + 172 Parameters + 173 ---------- + 174 i : int + 175 First index to be picked. + 176 j : int + 177 Second index to be picked. + 178 """ + 179 if self.N == 1: + 180 raise Exception("Trying to pick item from projected Corr") + 181 newcontent = [None if (item is None) else item[i, j] for item in self.content] + 182 return Corr(newcontent) + 183 + 184 def plottable(self): + 185 """Outputs the correlator in a plotable format. + 186 + 187 Outputs three lists containing the timeslice index, the value on each + 188 timeslice and the error on each timeslice. + 189 """ + 190 if self.N != 1: + 191 raise Exception("Can only make Corr[N=1] plottable") + 192 x_list = [x for x in range(self.T) if not self.content[x] is None] + 193 y_list = [y[0].value for y in self.content if y is not None] + 194 y_err_list = [y[0].dvalue for y in self.content if y is not None] 195 - 196 def symmetric(self): - 197 """ Symmetrize the correlator around x0=0.""" - 198 if self.N != 1: - 199 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') - 200 if self.T % 2 != 0: - 201 raise Exception("Can not symmetrize odd T") - 202 - 203 if np.argmax(np.abs(self.content)) != 0: - 204 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) - 205 - 206 newcontent = [self.content[0]] - 207 for t in range(1, self.T): - 208 if (self.content[t] is None) or (self.content[self.T - t] is None): - 209 newcontent.append(None) - 210 else: - 211 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) - 212 if (all([x is None for x in newcontent])): - 213 raise Exception("Corr could not be symmetrized: No redundant values") - 214 return Corr(newcontent, prange=self.prange) - 215 - 216 def anti_symmetric(self): - 217 """Anti-symmetrize the correlator around x0=0.""" - 218 if self.N != 1: - 219 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') - 220 if self.T % 2 != 0: - 221 raise Exception("Can not symmetrize odd T") - 222 - 223 test = 1 * self - 224 test.gamma_method() - 225 if not all([o.is_zero_within_error(3) for o in test.content[0]]): - 226 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) - 227 - 228 newcontent = [self.content[0]] - 229 for t in range(1, self.T): - 230 if (self.content[t] is None) or (self.content[self.T - t] is None): - 231 newcontent.append(None) - 232 else: - 233 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) - 234 if (all([x is None for x in newcontent])): - 235 raise Exception("Corr could not be symmetrized: No redundant values") - 236 return Corr(newcontent, prange=self.prange) - 237 - 238 def is_matrix_symmetric(self): - 239 """Checks whether a correlator matrices is symmetric on every timeslice.""" - 240 if self.N == 1: - 241 raise Exception("Only works for correlator matrices.") - 242 for t in range(self.T): - 243 if self[t] is None: - 244 continue - 245 for i in range(self.N): - 246 for j in range(i + 1, self.N): - 247 if self[t][i, j] is self[t][j, i]: - 248 continue - 249 if hash(self[t][i, j]) != hash(self[t][j, i]): - 250 return False - 251 return True - 252 - 253 def matrix_symmetric(self): - 254 """Symmetrizes the correlator matrices on every timeslice.""" - 255 if self.N == 1: - 256 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 257 if self.is_matrix_symmetric(): - 258 return 1.0 * self - 259 else: - 260 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 261 return 0.5 * (Corr(transposed) + self) - 262 - 263 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 264 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 265 - 266 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 267 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 268 ```python - 269 C.GEVP(t0=2)[0] # Ground state vector(s) - 270 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 271 ``` - 272 - 273 Parameters - 274 ---------- - 275 t0 : int - 276 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 277 ts : int - 278 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 279 If sort="Eigenvector" it gives a reference point for the sorting method. - 280 sort : string - 281 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. - 282 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 283 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 284 The reference state is identified by its eigenvalue at $t=t_s$. - 285 - 286 Other Parameters - 287 ---------------- - 288 state : int - 289 Returns only the vector(s) for a specified state. The lowest state is zero. - 290 ''' - 291 - 292 if self.N == 1: - 293 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 294 if ts is not None: - 295 if (ts <= t0): - 296 raise Exception("ts has to be larger than t0.") - 297 - 298 if "sorted_list" in kwargs: - 299 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 300 sort = kwargs.get("sorted_list") - 301 - 302 if self.is_matrix_symmetric(): - 303 symmetric_corr = self - 304 else: - 305 symmetric_corr = self.matrix_symmetric() - 306 - 307 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) - 308 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. - 309 - 310 if sort is None: - 311 if (ts is None): - 312 raise Exception("ts is required if sort=None.") - 313 if (self.content[t0] is None) or (self.content[ts] is None): - 314 raise Exception("Corr not defined at t0/ts.") - 315 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) - 316 reordered_vecs = _GEVP_solver(Gt, G0) - 317 - 318 elif sort in ["Eigenvalue", "Eigenvector"]: - 319 if sort == "Eigenvalue" and ts is not None: - 320 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) - 321 all_vecs = [None] * (t0 + 1) - 322 for t in range(t0 + 1, self.T): - 323 try: - 324 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) - 325 all_vecs.append(_GEVP_solver(Gt, G0)) - 326 except Exception: - 327 all_vecs.append(None) - 328 if sort == "Eigenvector": - 329 if ts is None: - 330 raise Exception("ts is required for the Eigenvector sorting method.") - 331 all_vecs = _sort_vectors(all_vecs, ts) - 332 - 333 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 334 else: - 335 raise Exception("Unkown value for 'sort'.") - 336 - 337 if "state" in kwargs: - 338 return reordered_vecs[kwargs.get("state")] - 339 else: - 340 return reordered_vecs - 341 - 342 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 343 """Determines the eigenvalue of the GEVP by solving and projecting the correlator - 344 - 345 Parameters - 346 ---------- - 347 state : int - 348 The state one is interested in ordered by energy. The lowest state is zero. - 349 - 350 All other parameters are identical to the ones of Corr.GEVP. - 351 """ - 352 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 353 return self.projected(vec) - 354 - 355 def Hankel(self, N, periodic=False): - 356 """Constructs an NxN Hankel matrix - 357 - 358 C(t) c(t+1) ... c(t+n-1) - 359 C(t+1) c(t+2) ... c(t+n) - 360 ................. - 361 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) - 362 - 363 Parameters - 364 ---------- - 365 N : int - 366 Dimension of the Hankel matrix - 367 periodic : bool, optional - 368 determines whether the matrix is extended periodically - 369 """ - 370 - 371 if self.N != 1: - 372 raise Exception("Multi-operator Prony not implemented!") - 373 - 374 array = np.empty([N, N], dtype="object") - 375 new_content = [] - 376 for t in range(self.T): - 377 new_content.append(array.copy()) - 378 - 379 def wrap(i): - 380 while i >= self.T: - 381 i -= self.T - 382 return i - 383 - 384 for t in range(self.T): - 385 for i in range(N): - 386 for j in range(N): - 387 if periodic: - 388 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 389 elif (t + i + j) >= self.T: - 390 new_content[t] = None - 391 else: - 392 new_content[t][i, j] = self.content[t + i + j][0] - 393 - 394 return Corr(new_content) + 196 return x_list, y_list, y_err_list + 197 + 198 def symmetric(self): + 199 """ Symmetrize the correlator around x0=0.""" + 200 if self.N != 1: + 201 raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.') + 202 if self.T % 2 != 0: + 203 raise Exception("Can not symmetrize odd T") + 204 + 205 if np.argmax(np.abs(self.content)) != 0: + 206 warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning) + 207 + 208 newcontent = [self.content[0]] + 209 for t in range(1, self.T): + 210 if (self.content[t] is None) or (self.content[self.T - t] is None): + 211 newcontent.append(None) + 212 else: + 213 newcontent.append(0.5 * (self.content[t] + self.content[self.T - t])) + 214 if (all([x is None for x in newcontent])): + 215 raise Exception("Corr could not be symmetrized: No redundant values") + 216 return Corr(newcontent, prange=self.prange) + 217 + 218 def anti_symmetric(self): + 219 """Anti-symmetrize the correlator around x0=0.""" + 220 if self.N != 1: + 221 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') + 222 if self.T % 2 != 0: + 223 raise Exception("Can not symmetrize odd T") + 224 + 225 test = 1 * self + 226 test.gamma_method() + 227 if not all([o.is_zero_within_error(3) for o in test.content[0]]): + 228 warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning) + 229 + 230 newcontent = [self.content[0]] + 231 for t in range(1, self.T): + 232 if (self.content[t] is None) or (self.content[self.T - t] is None): + 233 newcontent.append(None) + 234 else: + 235 newcontent.append(0.5 * (self.content[t] - self.content[self.T - t])) + 236 if (all([x is None for x in newcontent])): + 237 raise Exception("Corr could not be symmetrized: No redundant values") + 238 return Corr(newcontent, prange=self.prange) + 239 + 240 def is_matrix_symmetric(self): + 241 """Checks whether a correlator matrices is symmetric on every timeslice.""" + 242 if self.N == 1: + 243 raise Exception("Only works for correlator matrices.") + 244 for t in range(self.T): + 245 if self[t] is None: + 246 continue + 247 for i in range(self.N): + 248 for j in range(i + 1, self.N): + 249 if self[t][i, j] is self[t][j, i]: + 250 continue + 251 if hash(self[t][i, j]) != hash(self[t][j, i]): + 252 return False + 253 return True + 254 + 255 def matrix_symmetric(self): + 256 """Symmetrizes the correlator matrices on every timeslice.""" + 257 if self.N == 1: + 258 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") + 259 if self.is_matrix_symmetric(): + 260 return 1.0 * self + 261 else: + 262 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] + 263 return 0.5 * (Corr(transposed) + self) + 264 + 265 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): + 266 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. + 267 + 268 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the + 269 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing + 270 ```python + 271 C.GEVP(t0=2)[0] # Ground state vector(s) + 272 C.GEVP(t0=2)[:3] # Vectors for the lowest three states + 273 ``` + 274 + 275 Parameters + 276 ---------- + 277 t0 : int + 278 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ + 279 ts : int + 280 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. + 281 If sort="Eigenvector" it gives a reference point for the sorting method. + 282 sort : string + 283 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. + 284 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. + 285 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. + 286 The reference state is identified by its eigenvalue at $t=t_s$. + 287 + 288 Other Parameters + 289 ---------------- + 290 state : int + 291 Returns only the vector(s) for a specified state. The lowest state is zero. + 292 ''' + 293 + 294 if self.N == 1: + 295 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") + 296 if ts is not None: + 297 if (ts <= t0): + 298 raise Exception("ts has to be larger than t0.") + 299 + 300 if "sorted_list" in kwargs: + 301 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) + 302 sort = kwargs.get("sorted_list") + 303 + 304 if self.is_matrix_symmetric(): + 305 symmetric_corr = self + 306 else: + 307 symmetric_corr = self.matrix_symmetric() + 308 + 309 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) + 310 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. + 311 + 312 if sort is None: + 313 if (ts is None): + 314 raise Exception("ts is required if sort=None.") + 315 if (self.content[t0] is None) or (self.content[ts] is None): + 316 raise Exception("Corr not defined at t0/ts.") + 317 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) + 318 reordered_vecs = _GEVP_solver(Gt, G0) + 319 + 320 elif sort in ["Eigenvalue", "Eigenvector"]: + 321 if sort == "Eigenvalue" and ts is not None: + 322 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) + 323 all_vecs = [None] * (t0 + 1) + 324 for t in range(t0 + 1, self.T): + 325 try: + 326 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) + 327 all_vecs.append(_GEVP_solver(Gt, G0)) + 328 except Exception: + 329 all_vecs.append(None) + 330 if sort == "Eigenvector": + 331 if ts is None: + 332 raise Exception("ts is required for the Eigenvector sorting method.") + 333 all_vecs = _sort_vectors(all_vecs, ts) + 334 + 335 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] + 336 else: + 337 raise Exception("Unkown value for 'sort'.") + 338 + 339 if "state" in kwargs: + 340 return reordered_vecs[kwargs.get("state")] + 341 else: + 342 return reordered_vecs + 343 + 344 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): + 345 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 346 + 347 Parameters + 348 ---------- + 349 state : int + 350 The state one is interested in ordered by energy. The lowest state is zero. + 351 + 352 All other parameters are identical to the ones of Corr.GEVP. + 353 """ + 354 vec = self.GEVP(t0, ts=ts, sort=sort)[state] + 355 return self.projected(vec) + 356 + 357 def Hankel(self, N, periodic=False): + 358 """Constructs an NxN Hankel matrix + 359 + 360 C(t) c(t+1) ... c(t+n-1) + 361 C(t+1) c(t+2) ... c(t+n) + 362 ................. + 363 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) + 364 + 365 Parameters + 366 ---------- + 367 N : int + 368 Dimension of the Hankel matrix + 369 periodic : bool, optional + 370 determines whether the matrix is extended periodically + 371 """ + 372 + 373 if self.N != 1: + 374 raise Exception("Multi-operator Prony not implemented!") + 375 + 376 array = np.empty([N, N], dtype="object") + 377 new_content = [] + 378 for t in range(self.T): + 379 new_content.append(array.copy()) + 380 + 381 def wrap(i): + 382 while i >= self.T: + 383 i -= self.T + 384 return i + 385 + 386 for t in range(self.T): + 387 for i in range(N): + 388 for j in range(N): + 389 if periodic: + 390 new_content[t][i, j] = self.content[wrap(t + i + j)][0] + 391 elif (t + i + j) >= self.T: + 392 new_content[t] = None + 393 else: + 394 new_content[t][i, j] = self.content[t + i + j][0] 395 - 396 def roll(self, dt): - 397 """Periodically shift the correlator by dt timeslices - 398 - 399 Parameters - 400 ---------- - 401 dt : int - 402 number of timeslices - 403 """ - 404 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) - 405 - 406 def reverse(self): - 407 """Reverse the time ordering of the Corr""" - 408 return Corr(self.content[:: -1]) - 409 - 410 def thin(self, spacing=2, offset=0): - 411 """Thin out a correlator to suppress correlations - 412 - 413 Parameters - 414 ---------- - 415 spacing : int - 416 Keep only every 'spacing'th entry of the correlator - 417 offset : int - 418 Offset the equal spacing - 419 """ - 420 new_content = [] - 421 for t in range(self.T): - 422 if (offset + t) % spacing != 0: - 423 new_content.append(None) - 424 else: - 425 new_content.append(self.content[t]) - 426 return Corr(new_content) - 427 - 428 def correlate(self, partner): - 429 """Correlate the correlator with another correlator or Obs - 430 - 431 Parameters - 432 ---------- - 433 partner : Obs or Corr - 434 partner to correlate the correlator with. - 435 Can either be an Obs which is correlated with all entries of the - 436 correlator or a Corr of same length. - 437 """ - 438 if self.N != 1: - 439 raise Exception("Only one-dimensional correlators can be safely correlated.") - 440 new_content = [] - 441 for x0, t_slice in enumerate(self.content): - 442 if _check_for_none(self, t_slice): - 443 new_content.append(None) - 444 else: - 445 if isinstance(partner, Corr): - 446 if _check_for_none(partner, partner.content[x0]): - 447 new_content.append(None) - 448 else: - 449 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 450 elif isinstance(partner, Obs): # Should this include CObs? - 451 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 452 else: - 453 raise Exception("Can only correlate with an Obs or a Corr.") - 454 - 455 return Corr(new_content) + 396 return Corr(new_content) + 397 + 398 def roll(self, dt): + 399 """Periodically shift the correlator by dt timeslices + 400 + 401 Parameters + 402 ---------- + 403 dt : int + 404 number of timeslices + 405 """ + 406 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) + 407 + 408 def reverse(self): + 409 """Reverse the time ordering of the Corr""" + 410 return Corr(self.content[:: -1]) + 411 + 412 def thin(self, spacing=2, offset=0): + 413 """Thin out a correlator to suppress correlations + 414 + 415 Parameters + 416 ---------- + 417 spacing : int + 418 Keep only every 'spacing'th entry of the correlator + 419 offset : int + 420 Offset the equal spacing + 421 """ + 422 new_content = [] + 423 for t in range(self.T): + 424 if (offset + t) % spacing != 0: + 425 new_content.append(None) + 426 else: + 427 new_content.append(self.content[t]) + 428 return Corr(new_content) + 429 + 430 def correlate(self, partner): + 431 """Correlate the correlator with another correlator or Obs + 432 + 433 Parameters + 434 ---------- + 435 partner : Obs or Corr + 436 partner to correlate the correlator with. + 437 Can either be an Obs which is correlated with all entries of the + 438 correlator or a Corr of same length. + 439 """ + 440 if self.N != 1: + 441 raise Exception("Only one-dimensional correlators can be safely correlated.") + 442 new_content = [] + 443 for x0, t_slice in enumerate(self.content): + 444 if _check_for_none(self, t_slice): + 445 new_content.append(None) + 446 else: + 447 if isinstance(partner, Corr): + 448 if _check_for_none(partner, partner.content[x0]): + 449 new_content.append(None) + 450 else: + 451 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) + 452 elif isinstance(partner, Obs): # Should this include CObs? + 453 new_content.append(np.array([correlate(o, partner) for o in t_slice])) + 454 else: + 455 raise Exception("Can only correlate with an Obs or a Corr.") 456 - 457 def reweight(self, weight, **kwargs): - 458 """Reweight the correlator. - 459 - 460 Parameters - 461 ---------- - 462 weight : Obs - 463 Reweighting factor. An Observable that has to be defined on a superset of the - 464 configurations in obs[i].idl for all i. - 465 all_configs : bool - 466 if True, the reweighted observables are normalized by the average of - 467 the reweighting factor on all configurations in weight.idl and not - 468 on the configurations in obs[i].idl. - 469 """ - 470 if self.N != 1: - 471 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 472 new_content = [] - 473 for t_slice in self.content: - 474 if _check_for_none(self, t_slice): - 475 new_content.append(None) - 476 else: - 477 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 478 return Corr(new_content) - 479 - 480 def T_symmetry(self, partner, parity=+1): - 481 """Return the time symmetry average of the correlator and its partner - 482 - 483 Parameters - 484 ---------- - 485 partner : Corr - 486 Time symmetry partner of the Corr - 487 partity : int - 488 Parity quantum number of the correlator, can be +1 or -1 - 489 """ - 490 if self.N != 1: - 491 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 492 if not isinstance(partner, Corr): - 493 raise Exception("T partner has to be a Corr object.") - 494 if parity not in [+1, -1]: - 495 raise Exception("Parity has to be +1 or -1.") - 496 T_partner = parity * partner.reverse() - 497 - 498 t_slices = [] - 499 test = (self - T_partner) - 500 test.gamma_method() - 501 for x0, t_slice in enumerate(test.content): - 502 if t_slice is not None: - 503 if not t_slice[0].is_zero_within_error(5): - 504 t_slices.append(x0) - 505 if t_slices: - 506 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) - 507 - 508 return (self + T_partner) / 2 + 457 return Corr(new_content) + 458 + 459 def reweight(self, weight, **kwargs): + 460 """Reweight the correlator. + 461 + 462 Parameters + 463 ---------- + 464 weight : Obs + 465 Reweighting factor. An Observable that has to be defined on a superset of the + 466 configurations in obs[i].idl for all i. + 467 all_configs : bool + 468 if True, the reweighted observables are normalized by the average of + 469 the reweighting factor on all configurations in weight.idl and not + 470 on the configurations in obs[i].idl. + 471 """ + 472 if self.N != 1: + 473 raise Exception("Reweighting only implemented for one-dimensional correlators.") + 474 new_content = [] + 475 for t_slice in self.content: + 476 if _check_for_none(self, t_slice): + 477 new_content.append(None) + 478 else: + 479 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) + 480 return Corr(new_content) + 481 + 482 def T_symmetry(self, partner, parity=+1): + 483 """Return the time symmetry average of the correlator and its partner + 484 + 485 Parameters + 486 ---------- + 487 partner : Corr + 488 Time symmetry partner of the Corr + 489 partity : int + 490 Parity quantum number of the correlator, can be +1 or -1 + 491 """ + 492 if self.N != 1: + 493 raise Exception("T_symmetry only implemented for one-dimensional correlators.") + 494 if not isinstance(partner, Corr): + 495 raise Exception("T partner has to be a Corr object.") + 496 if parity not in [+1, -1]: + 497 raise Exception("Parity has to be +1 or -1.") + 498 T_partner = parity * partner.reverse() + 499 + 500 t_slices = [] + 501 test = (self - T_partner) + 502 test.gamma_method() + 503 for x0, t_slice in enumerate(test.content): + 504 if t_slice is not None: + 505 if not t_slice[0].is_zero_within_error(5): + 506 t_slices.append(x0) + 507 if t_slices: + 508 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) 509 - 510 def deriv(self, variant="symmetric"): - 511 """Return the first derivative of the correlator with respect to x0. - 512 - 513 Parameters - 514 ---------- - 515 variant : str - 516 decides which definition of the finite differences derivative is used. - 517 Available choice: symmetric, forward, backward, improved, log, default: symmetric - 518 """ - 519 if self.N != 1: - 520 raise Exception("deriv only implemented for one-dimensional correlators.") - 521 if variant == "symmetric": - 522 newcontent = [] - 523 for t in range(1, self.T - 1): - 524 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 525 newcontent.append(None) - 526 else: - 527 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 528 if (all([x is None for x in newcontent])): - 529 raise Exception('Derivative is undefined at all timeslices') - 530 return Corr(newcontent, padding=[1, 1]) - 531 elif variant == "forward": - 532 newcontent = [] - 533 for t in range(self.T - 1): - 534 if (self.content[t] is None) or (self.content[t + 1] is None): - 535 newcontent.append(None) - 536 else: - 537 newcontent.append(self.content[t + 1] - self.content[t]) - 538 if (all([x is None for x in newcontent])): - 539 raise Exception("Derivative is undefined at all timeslices") - 540 return Corr(newcontent, padding=[0, 1]) - 541 elif variant == "backward": - 542 newcontent = [] - 543 for t in range(1, self.T): - 544 if (self.content[t - 1] is None) or (self.content[t] is None): - 545 newcontent.append(None) - 546 else: - 547 newcontent.append(self.content[t] - self.content[t - 1]) - 548 if (all([x is None for x in newcontent])): - 549 raise Exception("Derivative is undefined at all timeslices") - 550 return Corr(newcontent, padding=[1, 0]) - 551 elif variant == "improved": - 552 newcontent = [] - 553 for t in range(2, self.T - 2): - 554 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): - 555 newcontent.append(None) - 556 else: - 557 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 558 if (all([x is None for x in newcontent])): - 559 raise Exception('Derivative is undefined at all timeslices') - 560 return Corr(newcontent, padding=[2, 2]) - 561 elif variant == 'log': - 562 newcontent = [] - 563 for t in range(self.T): - 564 if (self.content[t] is None) or (self.content[t] <= 0): - 565 newcontent.append(None) - 566 else: - 567 newcontent.append(np.log(self.content[t])) - 568 if (all([x is None for x in newcontent])): - 569 raise Exception("Log is undefined at all timeslices") - 570 logcorr = Corr(newcontent) - 571 return self * logcorr.deriv('symmetric') - 572 else: - 573 raise Exception("Unknown variant.") - 574 - 575 def second_deriv(self, variant="symmetric"): - 576 """Return the second derivative of the correlator with respect to x0. - 577 - 578 Parameters - 579 ---------- - 580 variant : str - 581 decides which definition of the finite differences derivative is used. - 582 Available choice: symmetric, improved, log, default: symmetric - 583 """ - 584 if self.N != 1: - 585 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 586 if variant == "symmetric": - 587 newcontent = [] - 588 for t in range(1, self.T - 1): - 589 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 590 newcontent.append(None) - 591 else: - 592 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 593 if (all([x is None for x in newcontent])): - 594 raise Exception("Derivative is undefined at all timeslices") - 595 return Corr(newcontent, padding=[1, 1]) - 596 elif variant == "improved": - 597 newcontent = [] - 598 for t in range(2, self.T - 2): - 599 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): - 600 newcontent.append(None) - 601 else: - 602 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])) - 603 if (all([x is None for x in newcontent])): - 604 raise Exception("Derivative is undefined at all timeslices") - 605 return Corr(newcontent, padding=[2, 2]) - 606 elif variant == 'log': - 607 newcontent = [] - 608 for t in range(self.T): - 609 if (self.content[t] is None) or (self.content[t] <= 0): - 610 newcontent.append(None) - 611 else: - 612 newcontent.append(np.log(self.content[t])) - 613 if (all([x is None for x in newcontent])): - 614 raise Exception("Log is undefined at all timeslices") - 615 logcorr = Corr(newcontent) - 616 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) - 617 else: - 618 raise Exception("Unknown variant.") - 619 - 620 def m_eff(self, variant='log', guess=1.0): - 621 """Returns the effective mass of the correlator as correlator object - 622 - 623 Parameters - 624 ---------- - 625 variant : str - 626 log : uses the standard effective mass log(C(t) / C(t+1)) - 627 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. - 628 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. - 629 See, e.g., arXiv:1205.5380 - 630 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 631 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 - 632 guess : float - 633 guess for the root finder, only relevant for the root variant - 634 """ - 635 if self.N != 1: - 636 raise Exception('Correlator must be projected before getting m_eff') - 637 if variant == 'log': - 638 newcontent = [] - 639 for t in range(self.T - 1): - 640 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 641 newcontent.append(None) - 642 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 510 return (self + T_partner) / 2 + 511 + 512 def deriv(self, variant="symmetric"): + 513 """Return the first derivative of the correlator with respect to x0. + 514 + 515 Parameters + 516 ---------- + 517 variant : str + 518 decides which definition of the finite differences derivative is used. + 519 Available choice: symmetric, forward, backward, improved, log, default: symmetric + 520 """ + 521 if self.N != 1: + 522 raise Exception("deriv only implemented for one-dimensional correlators.") + 523 if variant == "symmetric": + 524 newcontent = [] + 525 for t in range(1, self.T - 1): + 526 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 527 newcontent.append(None) + 528 else: + 529 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) + 530 if (all([x is None for x in newcontent])): + 531 raise Exception('Derivative is undefined at all timeslices') + 532 return Corr(newcontent, padding=[1, 1]) + 533 elif variant == "forward": + 534 newcontent = [] + 535 for t in range(self.T - 1): + 536 if (self.content[t] is None) or (self.content[t + 1] is None): + 537 newcontent.append(None) + 538 else: + 539 newcontent.append(self.content[t + 1] - self.content[t]) + 540 if (all([x is None for x in newcontent])): + 541 raise Exception("Derivative is undefined at all timeslices") + 542 return Corr(newcontent, padding=[0, 1]) + 543 elif variant == "backward": + 544 newcontent = [] + 545 for t in range(1, self.T): + 546 if (self.content[t - 1] is None) or (self.content[t] is None): + 547 newcontent.append(None) + 548 else: + 549 newcontent.append(self.content[t] - self.content[t - 1]) + 550 if (all([x is None for x in newcontent])): + 551 raise Exception("Derivative is undefined at all timeslices") + 552 return Corr(newcontent, padding=[1, 0]) + 553 elif variant == "improved": + 554 newcontent = [] + 555 for t in range(2, self.T - 2): + 556 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): + 557 newcontent.append(None) + 558 else: + 559 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) + 560 if (all([x is None for x in newcontent])): + 561 raise Exception('Derivative is undefined at all timeslices') + 562 return Corr(newcontent, padding=[2, 2]) + 563 elif variant == 'log': + 564 newcontent = [] + 565 for t in range(self.T): + 566 if (self.content[t] is None) or (self.content[t] <= 0): + 567 newcontent.append(None) + 568 else: + 569 newcontent.append(np.log(self.content[t])) + 570 if (all([x is None for x in newcontent])): + 571 raise Exception("Log is undefined at all timeslices") + 572 logcorr = Corr(newcontent) + 573 return self * logcorr.deriv('symmetric') + 574 else: + 575 raise Exception("Unknown variant.") + 576 + 577 def second_deriv(self, variant="symmetric"): + 578 """Return the second derivative of the correlator with respect to x0. + 579 + 580 Parameters + 581 ---------- + 582 variant : str + 583 decides which definition of the finite differences derivative is used. + 584 Available choice: symmetric, improved, log, default: symmetric + 585 """ + 586 if self.N != 1: + 587 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 588 if variant == "symmetric": + 589 newcontent = [] + 590 for t in range(1, self.T - 1): + 591 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 592 newcontent.append(None) + 593 else: + 594 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 595 if (all([x is None for x in newcontent])): + 596 raise Exception("Derivative is undefined at all timeslices") + 597 return Corr(newcontent, padding=[1, 1]) + 598 elif variant == "improved": + 599 newcontent = [] + 600 for t in range(2, self.T - 2): + 601 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): + 602 newcontent.append(None) + 603 else: + 604 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])) + 605 if (all([x is None for x in newcontent])): + 606 raise Exception("Derivative is undefined at all timeslices") + 607 return Corr(newcontent, padding=[2, 2]) + 608 elif variant == 'log': + 609 newcontent = [] + 610 for t in range(self.T): + 611 if (self.content[t] is None) or (self.content[t] <= 0): + 612 newcontent.append(None) + 613 else: + 614 newcontent.append(np.log(self.content[t])) + 615 if (all([x is None for x in newcontent])): + 616 raise Exception("Log is undefined at all timeslices") + 617 logcorr = Corr(newcontent) + 618 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) + 619 else: + 620 raise Exception("Unknown variant.") + 621 + 622 def m_eff(self, variant='log', guess=1.0): + 623 """Returns the effective mass of the correlator as correlator object + 624 + 625 Parameters + 626 ---------- + 627 variant : str + 628 log : uses the standard effective mass log(C(t) / C(t+1)) + 629 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. + 630 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. + 631 See, e.g., arXiv:1205.5380 + 632 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 633 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 + 634 guess : float + 635 guess for the root finder, only relevant for the root variant + 636 """ + 637 if self.N != 1: + 638 raise Exception('Correlator must be projected before getting m_eff') + 639 if variant == 'log': + 640 newcontent = [] + 641 for t in range(self.T - 1): + 642 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 643 newcontent.append(None) - 644 else: - 645 newcontent.append(self.content[t] / self.content[t + 1]) - 646 if (all([x is None for x in newcontent])): - 647 raise Exception('m_eff is undefined at all timeslices') - 648 - 649 return np.log(Corr(newcontent, padding=[0, 1])) + 644 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 645 newcontent.append(None) + 646 else: + 647 newcontent.append(self.content[t] / self.content[t + 1]) + 648 if (all([x is None for x in newcontent])): + 649 raise Exception('m_eff is undefined at all timeslices') 650 - 651 elif variant == 'logsym': - 652 newcontent = [] - 653 for t in range(1, self.T - 1): - 654 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 655 newcontent.append(None) - 656 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: + 651 return np.log(Corr(newcontent, padding=[0, 1])) + 652 + 653 elif variant == 'logsym': + 654 newcontent = [] + 655 for t in range(1, self.T - 1): + 656 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): 657 newcontent.append(None) - 658 else: - 659 newcontent.append(self.content[t - 1] / self.content[t + 1]) - 660 if (all([x is None for x in newcontent])): - 661 raise Exception('m_eff is undefined at all timeslices') - 662 - 663 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 658 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: + 659 newcontent.append(None) + 660 else: + 661 newcontent.append(self.content[t - 1] / self.content[t + 1]) + 662 if (all([x is None for x in newcontent])): + 663 raise Exception('m_eff is undefined at all timeslices') 664 - 665 elif variant in ['periodic', 'cosh', 'sinh']: - 666 if variant in ['periodic', 'cosh']: - 667 func = anp.cosh - 668 else: - 669 func = anp.sinh - 670 - 671 def root_function(x, d): - 672 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 673 - 674 newcontent = [] - 675 for t in range(self.T - 1): - 676 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 677 newcontent.append(None) - 678 # Fill the two timeslices in the middle of the lattice with their predecessors - 679 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 680 newcontent.append(newcontent[-1]) - 681 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 682 newcontent.append(None) - 683 else: - 684 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 685 if (all([x is None for x in newcontent])): - 686 raise Exception('m_eff is undefined at all timeslices') - 687 - 688 return Corr(newcontent, padding=[0, 1]) + 665 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 666 + 667 elif variant in ['periodic', 'cosh', 'sinh']: + 668 if variant in ['periodic', 'cosh']: + 669 func = anp.cosh + 670 else: + 671 func = anp.sinh + 672 + 673 def root_function(x, d): + 674 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 675 + 676 newcontent = [] + 677 for t in range(self.T - 1): + 678 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 679 newcontent.append(None) + 680 # Fill the two timeslices in the middle of the lattice with their predecessors + 681 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 682 newcontent.append(newcontent[-1]) + 683 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 684 newcontent.append(None) + 685 else: + 686 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) + 687 if (all([x is None for x in newcontent])): + 688 raise Exception('m_eff is undefined at all timeslices') 689 - 690 elif variant == 'arccosh': - 691 newcontent = [] - 692 for t in range(1, self.T - 1): - 693 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): - 694 newcontent.append(None) - 695 else: - 696 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) - 697 if (all([x is None for x in newcontent])): - 698 raise Exception("m_eff is undefined at all timeslices") - 699 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 700 - 701 else: - 702 raise Exception('Unknown variant.') - 703 - 704 def fit(self, function, fitrange=None, silent=False, **kwargs): - 705 r'''Fits function to the data - 706 - 707 Parameters - 708 ---------- - 709 function : obj - 710 function to fit to the data. See fits.least_squares for details. - 711 fitrange : list - 712 Two element list containing the timeslices on which the fit is supposed to start and stop. - 713 Caution: This range is inclusive as opposed to standard python indexing. - 714 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 715 If not specified, self.prange or all timeslices are used. - 716 silent : bool - 717 Decides whether output is printed to the standard output. - 718 ''' - 719 if self.N != 1: - 720 raise Exception("Correlator must be projected before fitting") - 721 - 722 if fitrange is None: - 723 if self.prange: - 724 fitrange = self.prange - 725 else: - 726 fitrange = [0, self.T - 1] - 727 else: - 728 if not isinstance(fitrange, list): - 729 raise Exception("fitrange has to be a list with two elements") - 730 if len(fitrange) != 2: - 731 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 732 - 733 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 734 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 735 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 736 return result - 737 - 738 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 739 """ Extract a plateau value from a Corr object - 740 - 741 Parameters - 742 ---------- - 743 plateau_range : list - 744 list with two entries, indicating the first and the last timeslice - 745 of the plateau region. - 746 method : str - 747 method to extract the plateau. - 748 'fit' fits a constant to the plateau region - 749 'avg', 'average' or 'mean' just average over the given timeslices. - 750 auto_gamma : bool - 751 apply gamma_method with default parameters to the Corr. Defaults to None - 752 """ - 753 if not plateau_range: - 754 if self.prange: - 755 plateau_range = self.prange - 756 else: - 757 raise Exception("no plateau range provided") - 758 if self.N != 1: - 759 raise Exception("Correlator must be projected before getting a plateau.") - 760 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 761 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 762 if auto_gamma: - 763 self.gamma_method() - 764 if method == "fit": - 765 def const_func(a, t): - 766 return a[0] - 767 return self.fit(const_func, plateau_range)[0] - 768 elif method in ["avg", "average", "mean"]: - 769 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 770 return returnvalue - 771 - 772 else: - 773 raise Exception("Unsupported plateau method: " + method) - 774 - 775 def set_prange(self, prange): - 776 """Sets the attribute prange of the Corr object.""" - 777 if not len(prange) == 2: - 778 raise Exception("prange must be a list or array with two values") - 779 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 780 raise Exception("Start and end point must be integers") - 781 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 782 raise Exception("Start and end point must define a range in the interval 0,T") - 783 - 784 self.prange = prange - 785 return - 786 - 787 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): - 788 """Plots the correlator using the tag of the correlator as label if available. - 789 - 790 Parameters - 791 ---------- - 792 x_range : list - 793 list of two values, determining the range of the x-axis e.g. [4, 8]. - 794 comp : Corr or list of Corr - 795 Correlator or list of correlators which are plotted for comparison. - 796 The tags of these correlators are used as labels if available. - 797 logscale : bool - 798 Sets y-axis to logscale. - 799 plateau : Obs - 800 Plateau value to be visualized in the figure. - 801 fit_res : Fit_result - 802 Fit_result object to be visualized. - 803 ylabel : str - 804 Label for the y-axis. - 805 save : str - 806 path to file in which the figure should be saved. - 807 auto_gamma : bool - 808 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 809 hide_sigma : float - 810 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 811 references : list - 812 List of floating point values that are displayed as horizontal lines for reference. - 813 title : string - 814 Optional title of the figure. - 815 """ - 816 if self.N != 1: - 817 raise Exception("Correlator must be projected before plotting") - 818 - 819 if auto_gamma: - 820 self.gamma_method() - 821 - 822 if x_range is None: - 823 x_range = [0, self.T - 1] - 824 - 825 fig = plt.figure() - 826 ax1 = fig.add_subplot(111) - 827 - 828 x, y, y_err = self.plottable() - 829 if hide_sigma: - 830 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 831 else: - 832 hide_from = None - 833 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 834 if logscale: - 835 ax1.set_yscale('log') - 836 else: - 837 if y_range is None: - 838 try: - 839 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)]) - 840 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)]) - 841 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 842 except Exception: - 843 pass - 844 else: - 845 ax1.set_ylim(y_range) - 846 if comp: - 847 if isinstance(comp, (Corr, list)): - 848 for corr in comp if isinstance(comp, list) else [comp]: - 849 if auto_gamma: - 850 corr.gamma_method() - 851 x, y, y_err = corr.plottable() - 852 if hide_sigma: - 853 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 854 else: - 855 hide_from = None - 856 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 857 else: - 858 raise Exception("'comp' must be a correlator or a list of correlators.") - 859 - 860 if plateau: - 861 if isinstance(plateau, Obs): - 862 if auto_gamma: - 863 plateau.gamma_method() - 864 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 865 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 866 else: - 867 raise Exception("'plateau' must be an Obs") - 868 - 869 if references: - 870 if isinstance(references, list): - 871 for ref in references: - 872 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 873 else: - 874 raise Exception("'references' must be a list of floating pint values.") - 875 - 876 if self.prange: - 877 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 878 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 879 - 880 if fit_res: - 881 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 882 ax1.plot(x_samples, - 883 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 884 ls='-', marker=',', lw=2) - 885 - 886 ax1.set_xlabel(r'$x_0 / a$') - 887 if ylabel: - 888 ax1.set_ylabel(ylabel) - 889 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 890 - 891 handles, labels = ax1.get_legend_handles_labels() - 892 if labels: - 893 ax1.legend() - 894 - 895 if title: - 896 plt.title(title) - 897 - 898 plt.draw() + 690 return Corr(newcontent, padding=[0, 1]) + 691 + 692 elif variant == 'arccosh': + 693 newcontent = [] + 694 for t in range(1, self.T - 1): + 695 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): + 696 newcontent.append(None) + 697 else: + 698 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 699 if (all([x is None for x in newcontent])): + 700 raise Exception("m_eff is undefined at all timeslices") + 701 return np.arccosh(Corr(newcontent, padding=[1, 1])) + 702 + 703 else: + 704 raise Exception('Unknown variant.') + 705 + 706 def fit(self, function, fitrange=None, silent=False, **kwargs): + 707 r'''Fits function to the data + 708 + 709 Parameters + 710 ---------- + 711 function : obj + 712 function to fit to the data. See fits.least_squares for details. + 713 fitrange : list + 714 Two element list containing the timeslices on which the fit is supposed to start and stop. + 715 Caution: This range is inclusive as opposed to standard python indexing. + 716 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 717 If not specified, self.prange or all timeslices are used. + 718 silent : bool + 719 Decides whether output is printed to the standard output. + 720 ''' + 721 if self.N != 1: + 722 raise Exception("Correlator must be projected before fitting") + 723 + 724 if fitrange is None: + 725 if self.prange: + 726 fitrange = self.prange + 727 else: + 728 fitrange = [0, self.T - 1] + 729 else: + 730 if not isinstance(fitrange, list): + 731 raise Exception("fitrange has to be a list with two elements") + 732 if len(fitrange) != 2: + 733 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 734 + 735 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 736 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 737 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 738 return result + 739 + 740 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 741 """ Extract a plateau value from a Corr object + 742 + 743 Parameters + 744 ---------- + 745 plateau_range : list + 746 list with two entries, indicating the first and the last timeslice + 747 of the plateau region. + 748 method : str + 749 method to extract the plateau. + 750 'fit' fits a constant to the plateau region + 751 'avg', 'average' or 'mean' just average over the given timeslices. + 752 auto_gamma : bool + 753 apply gamma_method with default parameters to the Corr. Defaults to None + 754 """ + 755 if not plateau_range: + 756 if self.prange: + 757 plateau_range = self.prange + 758 else: + 759 raise Exception("no plateau range provided") + 760 if self.N != 1: + 761 raise Exception("Correlator must be projected before getting a plateau.") + 762 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 763 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 764 if auto_gamma: + 765 self.gamma_method() + 766 if method == "fit": + 767 def const_func(a, t): + 768 return a[0] + 769 return self.fit(const_func, plateau_range)[0] + 770 elif method in ["avg", "average", "mean"]: + 771 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 772 return returnvalue + 773 + 774 else: + 775 raise Exception("Unsupported plateau method: " + method) + 776 + 777 def set_prange(self, prange): + 778 """Sets the attribute prange of the Corr object.""" + 779 if not len(prange) == 2: + 780 raise Exception("prange must be a list or array with two values") + 781 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 782 raise Exception("Start and end point must be integers") + 783 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 784 raise Exception("Start and end point must define a range in the interval 0,T") + 785 + 786 self.prange = prange + 787 return + 788 + 789 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): + 790 """Plots the correlator using the tag of the correlator as label if available. + 791 + 792 Parameters + 793 ---------- + 794 x_range : list + 795 list of two values, determining the range of the x-axis e.g. [4, 8]. + 796 comp : Corr or list of Corr + 797 Correlator or list of correlators which are plotted for comparison. + 798 The tags of these correlators are used as labels if available. + 799 logscale : bool + 800 Sets y-axis to logscale. + 801 plateau : Obs + 802 Plateau value to be visualized in the figure. + 803 fit_res : Fit_result + 804 Fit_result object to be visualized. + 805 ylabel : str + 806 Label for the y-axis. + 807 save : str + 808 path to file in which the figure should be saved. + 809 auto_gamma : bool + 810 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 811 hide_sigma : float + 812 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 813 references : list + 814 List of floating point values that are displayed as horizontal lines for reference. + 815 title : string + 816 Optional title of the figure. + 817 """ + 818 if self.N != 1: + 819 raise Exception("Correlator must be projected before plotting") + 820 + 821 if auto_gamma: + 822 self.gamma_method() + 823 + 824 if x_range is None: + 825 x_range = [0, self.T - 1] + 826 + 827 fig = plt.figure() + 828 ax1 = fig.add_subplot(111) + 829 + 830 x, y, y_err = self.plottable() + 831 if hide_sigma: + 832 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 833 else: + 834 hide_from = None + 835 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 836 if logscale: + 837 ax1.set_yscale('log') + 838 else: + 839 if y_range is None: + 840 try: + 841 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)]) + 842 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)]) + 843 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 844 except Exception: + 845 pass + 846 else: + 847 ax1.set_ylim(y_range) + 848 if comp: + 849 if isinstance(comp, (Corr, list)): + 850 for corr in comp if isinstance(comp, list) else [comp]: + 851 if auto_gamma: + 852 corr.gamma_method() + 853 x, y, y_err = corr.plottable() + 854 if hide_sigma: + 855 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 856 else: + 857 hide_from = None + 858 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 859 else: + 860 raise Exception("'comp' must be a correlator or a list of correlators.") + 861 + 862 if plateau: + 863 if isinstance(plateau, Obs): + 864 if auto_gamma: + 865 plateau.gamma_method() + 866 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 867 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 868 else: + 869 raise Exception("'plateau' must be an Obs") + 870 + 871 if references: + 872 if isinstance(references, list): + 873 for ref in references: + 874 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 875 else: + 876 raise Exception("'references' must be a list of floating pint values.") + 877 + 878 if self.prange: + 879 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 880 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') + 881 + 882 if fit_res: + 883 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 884 ax1.plot(x_samples, + 885 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 886 ls='-', marker=',', lw=2) + 887 + 888 ax1.set_xlabel(r'$x_0 / a$') + 889 if ylabel: + 890 ax1.set_ylabel(ylabel) + 891 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 892 + 893 handles, labels = ax1.get_legend_handles_labels() + 894 if labels: + 895 ax1.legend() + 896 + 897 if title: + 898 plt.title(title) 899 - 900 if save: - 901 if isinstance(save, str): - 902 fig.savefig(save, bbox_inches='tight') - 903 else: - 904 raise Exception("'save' has to be a string.") - 905 - 906 def spaghetti_plot(self, logscale=True): - 907 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 908 - 909 Parameters - 910 ---------- - 911 logscale : bool - 912 Determines whether the scale of the y-axis is logarithmic or standard. - 913 """ - 914 if self.N != 1: - 915 raise Exception("Correlator needs to be projected first.") - 916 - 917 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])) - 918 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 919 - 920 for name in mc_names: - 921 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T - 922 - 923 fig = plt.figure() - 924 ax = fig.add_subplot(111) - 925 for dat in data: - 926 ax.plot(x0_vals, dat, ls='-', marker='') - 927 - 928 if logscale is True: - 929 ax.set_yscale('log') - 930 - 931 ax.set_xlabel(r'$x_0 / a$') - 932 plt.title(name) - 933 plt.draw() - 934 - 935 def dump(self, filename, datatype="json.gz", **kwargs): - 936 """Dumps the Corr into a file of chosen type - 937 Parameters - 938 ---------- - 939 filename : str - 940 Name of the file to be saved. - 941 datatype : str - 942 Format of the exported file. Supported formats include - 943 "json.gz" and "pickle" - 944 path : str - 945 specifies a custom path for the file (default '.') - 946 """ - 947 if datatype == "json.gz": - 948 from .input.json import dump_to_json - 949 if 'path' in kwargs: - 950 file_name = kwargs.get('path') + '/' + filename - 951 else: - 952 file_name = filename - 953 dump_to_json(self, file_name) - 954 elif datatype == "pickle": - 955 dump_object(self, filename, **kwargs) - 956 else: - 957 raise Exception("Unknown datatype " + str(datatype)) - 958 - 959 def print(self, print_range=None): - 960 print(self.__repr__(print_range)) - 961 - 962 def __repr__(self, print_range=None): - 963 if print_range is None: - 964 print_range = [0, None] - 965 - 966 content_string = "" - 967 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 - 968 - 969 if self.tag is not None: - 970 content_string += "Description: " + self.tag + "\n" - 971 if self.N != 1: - 972 return content_string - 973 if isinstance(self[0], CObs): + 900 plt.draw() + 901 + 902 if save: + 903 if isinstance(save, str): + 904 fig.savefig(save, bbox_inches='tight') + 905 else: + 906 raise Exception("'save' has to be a string.") + 907 + 908 def spaghetti_plot(self, logscale=True): + 909 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 910 + 911 Parameters + 912 ---------- + 913 logscale : bool + 914 Determines whether the scale of the y-axis is logarithmic or standard. + 915 """ + 916 if self.N != 1: + 917 raise Exception("Correlator needs to be projected first.") + 918 + 919 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])) + 920 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 921 + 922 for name in mc_names: + 923 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 924 + 925 fig = plt.figure() + 926 ax = fig.add_subplot(111) + 927 for dat in data: + 928 ax.plot(x0_vals, dat, ls='-', marker='') + 929 + 930 if logscale is True: + 931 ax.set_yscale('log') + 932 + 933 ax.set_xlabel(r'$x_0 / a$') + 934 plt.title(name) + 935 plt.draw() + 936 + 937 def dump(self, filename, datatype="json.gz", **kwargs): + 938 """Dumps the Corr into a file of chosen type + 939 Parameters + 940 ---------- + 941 filename : str + 942 Name of the file to be saved. + 943 datatype : str + 944 Format of the exported file. Supported formats include + 945 "json.gz" and "pickle" + 946 path : str + 947 specifies a custom path for the file (default '.') + 948 """ + 949 if datatype == "json.gz": + 950 from .input.json import dump_to_json + 951 if 'path' in kwargs: + 952 file_name = kwargs.get('path') + '/' + filename + 953 else: + 954 file_name = filename + 955 dump_to_json(self, file_name) + 956 elif datatype == "pickle": + 957 dump_object(self, filename, **kwargs) + 958 else: + 959 raise Exception("Unknown datatype " + str(datatype)) + 960 + 961 def print(self, print_range=None): + 962 print(self.__repr__(print_range)) + 963 + 964 def __repr__(self, print_range=None): + 965 if print_range is None: + 966 print_range = [0, None] + 967 + 968 content_string = "" + 969 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 + 970 + 971 if self.tag is not None: + 972 content_string += "Description: " + self.tag + "\n" + 973 if self.N != 1: 974 return content_string - 975 - 976 if print_range[1]: - 977 print_range[1] += 1 - 978 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 979 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 980 if sub_corr is None: - 981 content_string += str(i + print_range[0]) + '\n' - 982 else: - 983 content_string += str(i + print_range[0]) - 984 for element in sub_corr: - 985 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 986 content_string += '\n' - 987 return content_string - 988 - 989 def __str__(self): - 990 return self.__repr__() - 991 - 992 # We define the basic operations, that can be performed with correlators. - 993 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 994 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 995 # One could try and tell Obs to check if the y in __mul__ is a Corr and - 996 - 997 def __add__(self, y): - 998 if isinstance(y, Corr): - 999 if ((self.N != y.N) or (self.T != y.T)): -1000 raise Exception("Addition of Corrs with different shape") -1001 newcontent = [] -1002 for t in range(self.T): -1003 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1004 newcontent.append(None) -1005 else: -1006 newcontent.append(self.content[t] + y.content[t]) -1007 return Corr(newcontent) -1008 -1009 elif isinstance(y, (Obs, int, float, CObs)): -1010 newcontent = [] -1011 for t in range(self.T): -1012 if _check_for_none(self, self.content[t]): -1013 newcontent.append(None) -1014 else: -1015 newcontent.append(self.content[t] + y) -1016 return Corr(newcontent, prange=self.prange) -1017 elif isinstance(y, np.ndarray): -1018 if y.shape == (self.T,): -1019 return Corr(list((np.array(self.content).T + y).T)) -1020 else: -1021 raise ValueError("operands could not be broadcast together") -1022 else: -1023 raise TypeError("Corr + wrong type") -1024 -1025 def __mul__(self, y): -1026 if isinstance(y, Corr): -1027 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1028 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1029 newcontent = [] -1030 for t in range(self.T): -1031 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1032 newcontent.append(None) -1033 else: -1034 newcontent.append(self.content[t] * y.content[t]) -1035 return Corr(newcontent) -1036 -1037 elif isinstance(y, (Obs, int, float, CObs)): -1038 newcontent = [] -1039 for t in range(self.T): -1040 if _check_for_none(self, self.content[t]): -1041 newcontent.append(None) -1042 else: -1043 newcontent.append(self.content[t] * y) -1044 return Corr(newcontent, prange=self.prange) -1045 elif isinstance(y, np.ndarray): -1046 if y.shape == (self.T,): -1047 return Corr(list((np.array(self.content).T * y).T)) -1048 else: -1049 raise ValueError("operands could not be broadcast together") -1050 else: -1051 raise TypeError("Corr * wrong type") -1052 -1053 def __truediv__(self, y): -1054 if isinstance(y, Corr): -1055 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1056 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1057 newcontent = [] -1058 for t in range(self.T): -1059 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1060 newcontent.append(None) -1061 else: -1062 newcontent.append(self.content[t] / y.content[t]) -1063 for t in range(self.T): -1064 if _check_for_none(self, newcontent[t]): -1065 continue -1066 if np.isnan(np.sum(newcontent[t]).value): -1067 newcontent[t] = None -1068 -1069 if all([item is None for item in newcontent]): -1070 raise Exception("Division returns completely undefined correlator") -1071 return Corr(newcontent) -1072 -1073 elif isinstance(y, (Obs, CObs)): -1074 if isinstance(y, Obs): -1075 if y.value == 0: -1076 raise Exception('Division by zero will return undefined correlator') -1077 if isinstance(y, CObs): -1078 if y.is_zero(): -1079 raise Exception('Division by zero will return undefined correlator') -1080 -1081 newcontent = [] -1082 for t in range(self.T): -1083 if _check_for_none(self, self.content[t]): -1084 newcontent.append(None) -1085 else: -1086 newcontent.append(self.content[t] / y) -1087 return Corr(newcontent, prange=self.prange) -1088 -1089 elif isinstance(y, (int, float)): -1090 if y == 0: -1091 raise Exception('Division by zero will return undefined correlator') -1092 newcontent = [] -1093 for t in range(self.T): -1094 if _check_for_none(self, self.content[t]): -1095 newcontent.append(None) -1096 else: -1097 newcontent.append(self.content[t] / y) -1098 return Corr(newcontent, prange=self.prange) -1099 elif isinstance(y, np.ndarray): -1100 if y.shape == (self.T,): -1101 return Corr(list((np.array(self.content).T / y).T)) -1102 else: -1103 raise ValueError("operands could not be broadcast together") -1104 else: -1105 raise TypeError('Corr / wrong type') -1106 -1107 def __neg__(self): -1108 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1109 return Corr(newcontent, prange=self.prange) -1110 -1111 def __sub__(self, y): -1112 return self + (-y) -1113 -1114 def __pow__(self, y): -1115 if isinstance(y, (Obs, int, float, CObs)): -1116 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1117 return Corr(newcontent, prange=self.prange) -1118 else: -1119 raise TypeError('Type of exponent not supported') -1120 -1121 def __abs__(self): -1122 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1123 return Corr(newcontent, prange=self.prange) -1124 -1125 # The numpy functions: -1126 def sqrt(self): -1127 return self ** 0.5 -1128 -1129 def log(self): -1130 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1131 return Corr(newcontent, prange=self.prange) -1132 -1133 def exp(self): -1134 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1135 return Corr(newcontent, prange=self.prange) -1136 -1137 def _apply_func_to_corr(self, func): -1138 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1139 for t in range(self.T): -1140 if _check_for_none(self, newcontent[t]): -1141 continue -1142 tmp_sum = np.sum(newcontent[t]) -1143 if hasattr(tmp_sum, "value"): -1144 if np.isnan(tmp_sum.value): -1145 newcontent[t] = None -1146 if all([item is None for item in newcontent]): -1147 raise Exception('Operation returns undefined correlator') -1148 return Corr(newcontent) -1149 -1150 def sin(self): -1151 return self._apply_func_to_corr(np.sin) -1152 -1153 def cos(self): -1154 return self._apply_func_to_corr(np.cos) -1155 -1156 def tan(self): -1157 return self._apply_func_to_corr(np.tan) -1158 -1159 def sinh(self): -1160 return self._apply_func_to_corr(np.sinh) -1161 -1162 def cosh(self): -1163 return self._apply_func_to_corr(np.cosh) -1164 -1165 def tanh(self): -1166 return self._apply_func_to_corr(np.tanh) -1167 -1168 def arcsin(self): -1169 return self._apply_func_to_corr(np.arcsin) -1170 -1171 def arccos(self): -1172 return self._apply_func_to_corr(np.arccos) -1173 -1174 def arctan(self): -1175 return self._apply_func_to_corr(np.arctan) -1176 -1177 def arcsinh(self): -1178 return self._apply_func_to_corr(np.arcsinh) -1179 -1180 def arccosh(self): -1181 return self._apply_func_to_corr(np.arccosh) -1182 -1183 def arctanh(self): -1184 return self._apply_func_to_corr(np.arctanh) -1185 -1186 # Right hand side operations (require tweak in main module to work) -1187 def __radd__(self, y): -1188 return self + y -1189 -1190 def __rsub__(self, y): -1191 return -self + y -1192 -1193 def __rmul__(self, y): -1194 return self * y -1195 -1196 def __rtruediv__(self, y): -1197 return (self / y) ** (-1) -1198 -1199 @property -1200 def real(self): -1201 def return_real(obs_OR_cobs): -1202 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1203 return np.vectorize(lambda x: x.real)(obs_OR_cobs) -1204 else: -1205 return obs_OR_cobs -1206 -1207 return self._apply_func_to_corr(return_real) + 975 if isinstance(self[0], CObs): + 976 return content_string + 977 + 978 if print_range[1]: + 979 print_range[1] += 1 + 980 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 981 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 982 if sub_corr is None: + 983 content_string += str(i + print_range[0]) + '\n' + 984 else: + 985 content_string += str(i + print_range[0]) + 986 for element in sub_corr: + 987 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 988 content_string += '\n' + 989 return content_string + 990 + 991 def __str__(self): + 992 return self.__repr__() + 993 + 994 # We define the basic operations, that can be performed with correlators. + 995 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. + 996 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. + 997 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 998 + 999 def __add__(self, y): +1000 if isinstance(y, Corr): +1001 if ((self.N != y.N) or (self.T != y.T)): +1002 raise Exception("Addition of Corrs with different shape") +1003 newcontent = [] +1004 for t in range(self.T): +1005 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1006 newcontent.append(None) +1007 else: +1008 newcontent.append(self.content[t] + y.content[t]) +1009 return Corr(newcontent) +1010 +1011 elif isinstance(y, (Obs, int, float, CObs)): +1012 newcontent = [] +1013 for t in range(self.T): +1014 if _check_for_none(self, self.content[t]): +1015 newcontent.append(None) +1016 else: +1017 newcontent.append(self.content[t] + y) +1018 return Corr(newcontent, prange=self.prange) +1019 elif isinstance(y, np.ndarray): +1020 if y.shape == (self.T,): +1021 return Corr(list((np.array(self.content).T + y).T)) +1022 else: +1023 raise ValueError("operands could not be broadcast together") +1024 else: +1025 raise TypeError("Corr + wrong type") +1026 +1027 def __mul__(self, y): +1028 if isinstance(y, Corr): +1029 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1030 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1031 newcontent = [] +1032 for t in range(self.T): +1033 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1034 newcontent.append(None) +1035 else: +1036 newcontent.append(self.content[t] * y.content[t]) +1037 return Corr(newcontent) +1038 +1039 elif isinstance(y, (Obs, int, float, CObs)): +1040 newcontent = [] +1041 for t in range(self.T): +1042 if _check_for_none(self, self.content[t]): +1043 newcontent.append(None) +1044 else: +1045 newcontent.append(self.content[t] * y) +1046 return Corr(newcontent, prange=self.prange) +1047 elif isinstance(y, np.ndarray): +1048 if y.shape == (self.T,): +1049 return Corr(list((np.array(self.content).T * y).T)) +1050 else: +1051 raise ValueError("operands could not be broadcast together") +1052 else: +1053 raise TypeError("Corr * wrong type") +1054 +1055 def __truediv__(self, y): +1056 if isinstance(y, Corr): +1057 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1058 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1059 newcontent = [] +1060 for t in range(self.T): +1061 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1062 newcontent.append(None) +1063 else: +1064 newcontent.append(self.content[t] / y.content[t]) +1065 for t in range(self.T): +1066 if _check_for_none(self, newcontent[t]): +1067 continue +1068 if np.isnan(np.sum(newcontent[t]).value): +1069 newcontent[t] = None +1070 +1071 if all([item is None for item in newcontent]): +1072 raise Exception("Division returns completely undefined correlator") +1073 return Corr(newcontent) +1074 +1075 elif isinstance(y, (Obs, CObs)): +1076 if isinstance(y, Obs): +1077 if y.value == 0: +1078 raise Exception('Division by zero will return undefined correlator') +1079 if isinstance(y, CObs): +1080 if y.is_zero(): +1081 raise Exception('Division by zero will return undefined correlator') +1082 +1083 newcontent = [] +1084 for t in range(self.T): +1085 if _check_for_none(self, self.content[t]): +1086 newcontent.append(None) +1087 else: +1088 newcontent.append(self.content[t] / y) +1089 return Corr(newcontent, prange=self.prange) +1090 +1091 elif isinstance(y, (int, float)): +1092 if y == 0: +1093 raise Exception('Division by zero will return undefined correlator') +1094 newcontent = [] +1095 for t in range(self.T): +1096 if _check_for_none(self, self.content[t]): +1097 newcontent.append(None) +1098 else: +1099 newcontent.append(self.content[t] / y) +1100 return Corr(newcontent, prange=self.prange) +1101 elif isinstance(y, np.ndarray): +1102 if y.shape == (self.T,): +1103 return Corr(list((np.array(self.content).T / y).T)) +1104 else: +1105 raise ValueError("operands could not be broadcast together") +1106 else: +1107 raise TypeError('Corr / wrong type') +1108 +1109 def __neg__(self): +1110 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1111 return Corr(newcontent, prange=self.prange) +1112 +1113 def __sub__(self, y): +1114 return self + (-y) +1115 +1116 def __pow__(self, y): +1117 if isinstance(y, (Obs, int, float, CObs)): +1118 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1119 return Corr(newcontent, prange=self.prange) +1120 else: +1121 raise TypeError('Type of exponent not supported') +1122 +1123 def __abs__(self): +1124 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1125 return Corr(newcontent, prange=self.prange) +1126 +1127 # The numpy functions: +1128 def sqrt(self): +1129 return self ** 0.5 +1130 +1131 def log(self): +1132 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1133 return Corr(newcontent, prange=self.prange) +1134 +1135 def exp(self): +1136 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1137 return Corr(newcontent, prange=self.prange) +1138 +1139 def _apply_func_to_corr(self, func): +1140 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1141 for t in range(self.T): +1142 if _check_for_none(self, newcontent[t]): +1143 continue +1144 tmp_sum = np.sum(newcontent[t]) +1145 if hasattr(tmp_sum, "value"): +1146 if np.isnan(tmp_sum.value): +1147 newcontent[t] = None +1148 if all([item is None for item in newcontent]): +1149 raise Exception('Operation returns undefined correlator') +1150 return Corr(newcontent) +1151 +1152 def sin(self): +1153 return self._apply_func_to_corr(np.sin) +1154 +1155 def cos(self): +1156 return self._apply_func_to_corr(np.cos) +1157 +1158 def tan(self): +1159 return self._apply_func_to_corr(np.tan) +1160 +1161 def sinh(self): +1162 return self._apply_func_to_corr(np.sinh) +1163 +1164 def cosh(self): +1165 return self._apply_func_to_corr(np.cosh) +1166 +1167 def tanh(self): +1168 return self._apply_func_to_corr(np.tanh) +1169 +1170 def arcsin(self): +1171 return self._apply_func_to_corr(np.arcsin) +1172 +1173 def arccos(self): +1174 return self._apply_func_to_corr(np.arccos) +1175 +1176 def arctan(self): +1177 return self._apply_func_to_corr(np.arctan) +1178 +1179 def arcsinh(self): +1180 return self._apply_func_to_corr(np.arcsinh) +1181 +1182 def arccosh(self): +1183 return self._apply_func_to_corr(np.arccosh) +1184 +1185 def arctanh(self): +1186 return self._apply_func_to_corr(np.arctanh) +1187 +1188 # Right hand side operations (require tweak in main module to work) +1189 def __radd__(self, y): +1190 return self + y +1191 +1192 def __rsub__(self, y): +1193 return -self + y +1194 +1195 def __rmul__(self, y): +1196 return self * y +1197 +1198 def __rtruediv__(self, y): +1199 return (self / y) ** (-1) +1200 +1201 @property +1202 def real(self): +1203 def return_real(obs_OR_cobs): +1204 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1205 return np.vectorize(lambda x: x.real)(obs_OR_cobs) +1206 else: +1207 return obs_OR_cobs 1208 -1209 @property -1210 def imag(self): -1211 def return_imag(obs_OR_cobs): -1212 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1213 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) -1214 else: -1215 return obs_OR_cobs * 0 # So it stays the right type -1216 -1217 return self._apply_func_to_corr(return_imag) +1209 return self._apply_func_to_corr(return_real) +1210 +1211 @property +1212 def imag(self): +1213 def return_imag(obs_OR_cobs): +1214 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1215 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) +1216 else: +1217 return obs_OR_cobs * 0 # So it stays the right type 1218 -1219 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1220 r''' Project large correlation matrix to lowest states -1221 -1222 This method can be used to reduce the size of an (N x N) correlation matrix -1223 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1224 is still small. -1225 -1226 Parameters -1227 ---------- -1228 Ntrunc: int -1229 Rank of the target matrix. -1230 tproj: int -1231 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1232 The default value is 3. -1233 t0proj: int -1234 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1235 discouraged for O(a) improved theories, since the correctness of the procedure -1236 cannot be granted in this case. The default value is 2. -1237 basematrix : Corr -1238 Correlation matrix that is used to determine the eigenvectors of the -1239 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1240 is is not specified. -1241 -1242 Notes -1243 ----- -1244 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1245 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1246 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1247 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1248 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1249 correlation matrix and to remove some noise that is added by irrelevant operators. -1250 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1251 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1252 ''' -1253 -1254 if self.N == 1: -1255 raise Exception('Method cannot be applied to one-dimensional correlators.') -1256 if basematrix is None: -1257 basematrix = self -1258 if Ntrunc >= basematrix.N: -1259 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1260 if basematrix.N != self.N: -1261 raise Exception('basematrix and targetmatrix have to be of the same size.') -1262 -1263 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1219 return self._apply_func_to_corr(return_imag) +1220 +1221 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1222 r''' Project large correlation matrix to lowest states +1223 +1224 This method can be used to reduce the size of an (N x N) correlation matrix +1225 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1226 is still small. +1227 +1228 Parameters +1229 ---------- +1230 Ntrunc: int +1231 Rank of the target matrix. +1232 tproj: int +1233 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1234 The default value is 3. +1235 t0proj: int +1236 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1237 discouraged for O(a) improved theories, since the correctness of the procedure +1238 cannot be granted in this case. The default value is 2. +1239 basematrix : Corr +1240 Correlation matrix that is used to determine the eigenvectors of the +1241 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1242 is is not specified. +1243 +1244 Notes +1245 ----- +1246 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1247 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1248 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1249 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1250 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1251 correlation matrix and to remove some noise that is added by irrelevant operators. +1252 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1253 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1254 ''' +1255 +1256 if self.N == 1: +1257 raise Exception('Method cannot be applied to one-dimensional correlators.') +1258 if basematrix is None: +1259 basematrix = self +1260 if Ntrunc >= basematrix.N: +1261 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1262 if basematrix.N != self.N: +1263 raise Exception('basematrix and targetmatrix have to be of the same size.') 1264 -1265 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1266 rmat = [] -1267 for t in range(basematrix.T): -1268 for i in range(Ntrunc): -1269 for j in range(Ntrunc): -1270 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1271 rmat.append(np.copy(tmpmat)) -1272 -1273 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1274 return Corr(newcontent) +1265 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1266 +1267 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1268 rmat = [] +1269 for t in range(basematrix.T): +1270 for i in range(Ntrunc): +1271 for j in range(Ntrunc): +1272 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1273 rmat.append(np.copy(tmpmat)) +1274 +1275 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1276 return Corr(newcontent) @@ -2942,6 +2949,35 @@ region indentified for this correlator. +

    Apply the gamma method to the content of the Corr.

    +
    + + + +
    + +
    + + def + gm(self, **kwargs): + + + +
    + + 
    117    def gamma_method(self, **kwargs):
+118        """Apply the gamma method to the content of the Corr."""
+119        for item in self.content:
+120            if not (item is None):
+121                if self.N == 1:
+122                    item[0].gamma_method(**kwargs)
+123                else:
+124                    for i in range(self.N):
+125                        for j in range(self.N):
+126                            item[i, j].gamma_method(**kwargs)
+
    + +

    Apply the gamma method to the content of the Corr.

    @@ -2958,44 +2994,44 @@ region indentified for this correlator.
    - 
    128    def projected(self, vector_l=None, vector_r=None, normalize=False):
-129        """We need to project the Correlator with a Vector to get a single value at each timeslice.
-130
-131        The method can use one or two vectors.
-132        If two are specified it returns v1@G@v2 (the order might be very important.)
-133        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
-134        """
-135        if self.N == 1:
-136            raise Exception("Trying to project a Corr, that already has N=1.")
-137
-138        if vector_l is None:
-139            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
-140        elif (vector_r is None):
-141            vector_r = vector_l
-142        if isinstance(vector_l, list) and not isinstance(vector_r, list):
-143            if len(vector_l) != self.T:
-144                raise Exception("Length of vector list must be equal to T")
-145            vector_r = [vector_r] * self.T
-146        if isinstance(vector_r, list) and not isinstance(vector_l, list):
-147            if len(vector_r) != self.T:
-148                raise Exception("Length of vector list must be equal to T")
-149            vector_l = [vector_l] * self.T
-150
-151        if not isinstance(vector_l, list):
-152            if not vector_l.shape == vector_r.shape == (self.N,):
-153                raise Exception("Vectors are of wrong shape!")
-154            if normalize:
-155                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
-156            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
-157
-158        else:
-159            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
-160            if normalize:
-161                for t in range(self.T):
-162                    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])
-163
-164            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)]
-165        return Corr(newcontent)
+            
    130    def projected(self, vector_l=None, vector_r=None, normalize=False):
+131        """We need to project the Correlator with a Vector to get a single value at each timeslice.
+132
+133        The method can use one or two vectors.
+134        If two are specified it returns v1@G@v2 (the order might be very important.)
+135        By default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
+136        """
+137        if self.N == 1:
+138            raise Exception("Trying to project a Corr, that already has N=1.")
+139
+140        if vector_l is None:
+141            vector_l, vector_r = np.asarray([1.] + (self.N - 1) * [0.]), np.asarray([1.] + (self.N - 1) * [0.])
+142        elif (vector_r is None):
+143            vector_r = vector_l
+144        if isinstance(vector_l, list) and not isinstance(vector_r, list):
+145            if len(vector_l) != self.T:
+146                raise Exception("Length of vector list must be equal to T")
+147            vector_r = [vector_r] * self.T
+148        if isinstance(vector_r, list) and not isinstance(vector_l, list):
+149            if len(vector_r) != self.T:
+150                raise Exception("Length of vector list must be equal to T")
+151            vector_l = [vector_l] * self.T
+152
+153        if not isinstance(vector_l, list):
+154            if not vector_l.shape == vector_r.shape == (self.N,):
+155                raise Exception("Vectors are of wrong shape!")
+156            if normalize:
+157                vector_l, vector_r = vector_l / np.sqrt((vector_l @ vector_l)), vector_r / np.sqrt(vector_r @ vector_r)
+158            newcontent = [None if _check_for_none(self, item) else np.asarray([vector_l.T @ item @ vector_r]) for item in self.content]
+159
+160        else:
+161            # There are no checks here yet. There are so many possible scenarios, where this can go wrong.
+162            if normalize:
+163                for t in range(self.T):
+164                    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])
+165
+166            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)]
+167        return Corr(newcontent)
 
    
 
 
@@ -3019,20 +3055,20 @@ By default it will return the lowest source, which usually means unsmeared-unsme
    - 
    167    def item(self, i, j):
-168        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
-169
-170        Parameters
-171        ----------
-172        i : int
-173            First index to be picked.
-174        j : int
-175            Second index to be picked.
-176        """
-177        if self.N == 1:
-178            raise Exception("Trying to pick item from projected Corr")
-179        newcontent = [None if (item is None) else item[i, j] for item in self.content]
-180        return Corr(newcontent)
+            
    169    def item(self, i, j):
+170        """Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
+171
+172        Parameters
+173        ----------
+174        i : int
+175            First index to be picked.
+176        j : int
+177            Second index to be picked.
+178        """
+179        if self.N == 1:
+180            raise Exception("Trying to pick item from projected Corr")
+181        newcontent = [None if (item is None) else item[i, j] for item in self.content]
+182        return Corr(newcontent)
 
    
 
 
@@ -3061,19 +3097,19 @@ Second index to be picked.
    - 
    182    def plottable(self):
-183        """Outputs the correlator in a plotable format.
-184
-185        Outputs three lists containing the timeslice index, the value on each
-186        timeslice and the error on each timeslice.
-187        """
-188        if self.N != 1:
-189            raise Exception("Can only make Corr[N=1] plottable")
-190        x_list = [x for x in range(self.T) if not self.content[x] is None]
-191        y_list = [y[0].value for y in self.content if y is not None]
-192        y_err_list = [y[0].dvalue for y in self.content if y is not None]
-193
-194        return x_list, y_list, y_err_list
+            
    184    def plottable(self):
+185        """Outputs the correlator in a plotable format.
+186
+187        Outputs three lists containing the timeslice index, the value on each
+188        timeslice and the error on each timeslice.
+189        """
+190        if self.N != 1:
+191            raise Exception("Can only make Corr[N=1] plottable")
+192        x_list = [x for x in range(self.T) if not self.content[x] is None]
+193        y_list = [y[0].value for y in self.content if y is not None]
+194        y_err_list = [y[0].dvalue for y in self.content if y is not None]
+195
+196        return x_list, y_list, y_err_list
 
    
 
 
@@ -3096,25 +3132,25 @@ timeslice and the error on each timeslice.
    - 
    196    def symmetric(self):
-197        """ Symmetrize the correlator around x0=0."""
-198        if self.N != 1:
-199            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
-200        if self.T % 2 != 0:
-201            raise Exception("Can not symmetrize odd T")
-202
-203        if np.argmax(np.abs(self.content)) != 0:
-204            warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
-205
-206        newcontent = [self.content[0]]
-207        for t in range(1, self.T):
-208            if (self.content[t] is None) or (self.content[self.T - t] is None):
-209                newcontent.append(None)
-210            else:
-211                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
-212        if (all([x is None for x in newcontent])):
-213            raise Exception("Corr could not be symmetrized: No redundant values")
-214        return Corr(newcontent, prange=self.prange)
+            
    198    def symmetric(self):
+199        """ Symmetrize the correlator around x0=0."""
+200        if self.N != 1:
+201            raise Exception('symmetric cannot be safely applied to multi-dimensional correlators.')
+202        if self.T % 2 != 0:
+203            raise Exception("Can not symmetrize odd T")
+204
+205        if np.argmax(np.abs(self.content)) != 0:
+206            warnings.warn("Correlator does not seem to be symmetric around x0=0.", RuntimeWarning)
+207
+208        newcontent = [self.content[0]]
+209        for t in range(1, self.T):
+210            if (self.content[t] is None) or (self.content[self.T - t] is None):
+211                newcontent.append(None)
+212            else:
+213                newcontent.append(0.5 * (self.content[t] + self.content[self.T - t]))
+214        if (all([x is None for x in newcontent])):
+215            raise Exception("Corr could not be symmetrized: No redundant values")
+216        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -3134,27 +3170,27 @@ timeslice and the error on each timeslice.
    - 
    216    def anti_symmetric(self):
-217        """Anti-symmetrize the correlator around x0=0."""
-218        if self.N != 1:
-219            raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
-220        if self.T % 2 != 0:
-221            raise Exception("Can not symmetrize odd T")
-222
-223        test = 1 * self
-224        test.gamma_method()
-225        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
-226            warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)
-227
-228        newcontent = [self.content[0]]
-229        for t in range(1, self.T):
-230            if (self.content[t] is None) or (self.content[self.T - t] is None):
-231                newcontent.append(None)
-232            else:
-233                newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
-234        if (all([x is None for x in newcontent])):
-235            raise Exception("Corr could not be symmetrized: No redundant values")
-236        return Corr(newcontent, prange=self.prange)
+            
    218    def anti_symmetric(self):
+219        """Anti-symmetrize the correlator around x0=0."""
+220        if self.N != 1:
+221            raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
+222        if self.T % 2 != 0:
+223            raise Exception("Can not symmetrize odd T")
+224
+225        test = 1 * self
+226        test.gamma_method()
+227        if not all([o.is_zero_within_error(3) for o in test.content[0]]):
+228            warnings.warn("Correlator does not seem to be anti-symmetric around x0=0.", RuntimeWarning)
+229
+230        newcontent = [self.content[0]]
+231        for t in range(1, self.T):
+232            if (self.content[t] is None) or (self.content[self.T - t] is None):
+233                newcontent.append(None)
+234            else:
+235                newcontent.append(0.5 * (self.content[t] - self.content[self.T - t]))
+236        if (all([x is None for x in newcontent])):
+237            raise Exception("Corr could not be symmetrized: No redundant values")
+238        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -3174,20 +3210,20 @@ timeslice and the error on each timeslice.
    - 
    238    def is_matrix_symmetric(self):
-239        """Checks whether a correlator matrices is symmetric on every timeslice."""
-240        if self.N == 1:
-241            raise Exception("Only works for correlator matrices.")
-242        for t in range(self.T):
-243            if self[t] is None:
-244                continue
-245            for i in range(self.N):
-246                for j in range(i + 1, self.N):
-247                    if self[t][i, j] is self[t][j, i]:
-248                        continue
-249                    if hash(self[t][i, j]) != hash(self[t][j, i]):
-250                        return False
-251        return True
+            
    240    def is_matrix_symmetric(self):
+241        """Checks whether a correlator matrices is symmetric on every timeslice."""
+242        if self.N == 1:
+243            raise Exception("Only works for correlator matrices.")
+244        for t in range(self.T):
+245            if self[t] is None:
+246                continue
+247            for i in range(self.N):
+248                for j in range(i + 1, self.N):
+249                    if self[t][i, j] is self[t][j, i]:
+250                        continue
+251                    if hash(self[t][i, j]) != hash(self[t][j, i]):
+252                        return False
+253        return True
 
    
 
 
@@ -3207,15 +3243,15 @@ timeslice and the error on each timeslice.
    - 
    253    def matrix_symmetric(self):
-254        """Symmetrizes the correlator matrices on every timeslice."""
-255        if self.N == 1:
-256            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
-257        if self.is_matrix_symmetric():
-258            return 1.0 * self
-259        else:
-260            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
-261            return 0.5 * (Corr(transposed) + self)
+            
    255    def matrix_symmetric(self):
+256        """Symmetrizes the correlator matrices on every timeslice."""
+257        if self.N == 1:
+258            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
+259        if self.is_matrix_symmetric():
+260            return 1.0 * self
+261        else:
+262            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
+263            return 0.5 * (Corr(transposed) + self)
 
    
 
 
@@ -3235,84 +3271,84 @@ timeslice and the error on each timeslice.
    - 
    263    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
-264        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
-265
-266        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
-267        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
-268        ```python
-269        C.GEVP(t0=2)[0]  # Ground state vector(s)
-270        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
-271        ```
-272
-273        Parameters
-274        ----------
-275        t0 : int
-276            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
-277        ts : int
-278            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
-279            If sort="Eigenvector" it gives a reference point for the sorting method.
-280        sort : string
-281            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.
-282            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-283            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
-284              The reference state is identified by its eigenvalue at $t=t_s$.
-285
-286        Other Parameters
-287        ----------------
-288        state : int
-289           Returns only the vector(s) for a specified state. The lowest state is zero.
-290        '''
-291
-292        if self.N == 1:
-293            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
-294        if ts is not None:
-295            if (ts <= t0):
-296                raise Exception("ts has to be larger than t0.")
-297
-298        if "sorted_list" in kwargs:
-299            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
-300            sort = kwargs.get("sorted_list")
-301
-302        if self.is_matrix_symmetric():
-303            symmetric_corr = self
-304        else:
-305            symmetric_corr = self.matrix_symmetric()
-306
-307        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
-308        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
-309
-310        if sort is None:
-311            if (ts is None):
-312                raise Exception("ts is required if sort=None.")
-313            if (self.content[t0] is None) or (self.content[ts] is None):
-314                raise Exception("Corr not defined at t0/ts.")
-315            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
-316            reordered_vecs = _GEVP_solver(Gt, G0)
-317
-318        elif sort in ["Eigenvalue", "Eigenvector"]:
-319            if sort == "Eigenvalue" and ts is not None:
-320                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
-321            all_vecs = [None] * (t0 + 1)
-322            for t in range(t0 + 1, self.T):
-323                try:
-324                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
-325                    all_vecs.append(_GEVP_solver(Gt, G0))
-326                except Exception:
-327                    all_vecs.append(None)
-328            if sort == "Eigenvector":
-329                if ts is None:
-330                    raise Exception("ts is required for the Eigenvector sorting method.")
-331                all_vecs = _sort_vectors(all_vecs, ts)
-332
-333            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
-334        else:
-335            raise Exception("Unkown value for 'sort'.")
-336
-337        if "state" in kwargs:
-338            return reordered_vecs[kwargs.get("state")]
-339        else:
-340            return reordered_vecs
+            
    265    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
+266        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
+267
+268        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
+269        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
+270        ```python
+271        C.GEVP(t0=2)[0]  # Ground state vector(s)
+272        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
+273        ```
+274
+275        Parameters
+276        ----------
+277        t0 : int
+278            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
+279        ts : int
+280            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
+281            If sort="Eigenvector" it gives a reference point for the sorting method.
+282        sort : string
+283            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.
+284            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
+285            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
+286              The reference state is identified by its eigenvalue at $t=t_s$.
+287
+288        Other Parameters
+289        ----------------
+290        state : int
+291           Returns only the vector(s) for a specified state. The lowest state is zero.
+292        '''
+293
+294        if self.N == 1:
+295            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
+296        if ts is not None:
+297            if (ts <= t0):
+298                raise Exception("ts has to be larger than t0.")
+299
+300        if "sorted_list" in kwargs:
+301            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
+302            sort = kwargs.get("sorted_list")
+303
+304        if self.is_matrix_symmetric():
+305            symmetric_corr = self
+306        else:
+307            symmetric_corr = self.matrix_symmetric()
+308
+309        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
+310        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
+311
+312        if sort is None:
+313            if (ts is None):
+314                raise Exception("ts is required if sort=None.")
+315            if (self.content[t0] is None) or (self.content[ts] is None):
+316                raise Exception("Corr not defined at t0/ts.")
+317            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
+318            reordered_vecs = _GEVP_solver(Gt, G0)
+319
+320        elif sort in ["Eigenvalue", "Eigenvector"]:
+321            if sort == "Eigenvalue" and ts is not None:
+322                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
+323            all_vecs = [None] * (t0 + 1)
+324            for t in range(t0 + 1, self.T):
+325                try:
+326                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
+327                    all_vecs.append(_GEVP_solver(Gt, G0))
+328                except Exception:
+329                    all_vecs.append(None)
+330            if sort == "Eigenvector":
+331                if ts is None:
+332                    raise Exception("ts is required for the Eigenvector sorting method.")
+333                all_vecs = _sort_vectors(all_vecs, ts)
+334
+335            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
+336        else:
+337            raise Exception("Unkown value for 'sort'.")
+338
+339        if "state" in kwargs:
+340            return reordered_vecs[kwargs.get("state")]
+341        else:
+342            return reordered_vecs
 
    
 
 
@@ -3365,18 +3401,18 @@ Returns only the vector(s) for a specified state. The lowest state is zero.
    - 
    342    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
-343        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
-344
-345        Parameters
-346        ----------
-347        state : int
-348            The state one is interested in ordered by energy. The lowest state is zero.
-349
-350        All other parameters are identical to the ones of Corr.GEVP.
-351        """
-352        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
-353        return self.projected(vec)
+            
    344    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
+345        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
+346
+347        Parameters
+348        ----------
+349        state : int
+350            The state one is interested in ordered by energy. The lowest state is zero.
+351
+352        All other parameters are identical to the ones of Corr.GEVP.
+353        """
+354        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
+355        return self.projected(vec)
 
    
 
 
@@ -3404,46 +3440,46 @@ The state one is interested in ordered by energy. The lowest state is zero.
    - 
    355    def Hankel(self, N, periodic=False):
-356        """Constructs an NxN Hankel matrix
-357
-358        C(t) c(t+1) ... c(t+n-1)
-359        C(t+1) c(t+2) ... c(t+n)
-360        .................
-361        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
-362
-363        Parameters
-364        ----------
-365        N : int
-366            Dimension of the Hankel matrix
-367        periodic : bool, optional
-368            determines whether the matrix is extended periodically
-369        """
-370
-371        if self.N != 1:
-372            raise Exception("Multi-operator Prony not implemented!")
-373
-374        array = np.empty([N, N], dtype="object")
-375        new_content = []
-376        for t in range(self.T):
-377            new_content.append(array.copy())
-378
-379        def wrap(i):
-380            while i >= self.T:
-381                i -= self.T
-382            return i
-383
-384        for t in range(self.T):
-385            for i in range(N):
-386                for j in range(N):
-387                    if periodic:
-388                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
-389                    elif (t + i + j) >= self.T:
-390                        new_content[t] = None
-391                    else:
-392                        new_content[t][i, j] = self.content[t + i + j][0]
-393
-394        return Corr(new_content)
+            
    357    def Hankel(self, N, periodic=False):
+358        """Constructs an NxN Hankel matrix
+359
+360        C(t) c(t+1) ... c(t+n-1)
+361        C(t+1) c(t+2) ... c(t+n)
+362        .................
+363        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
+364
+365        Parameters
+366        ----------
+367        N : int
+368            Dimension of the Hankel matrix
+369        periodic : bool, optional
+370            determines whether the matrix is extended periodically
+371        """
+372
+373        if self.N != 1:
+374            raise Exception("Multi-operator Prony not implemented!")
+375
+376        array = np.empty([N, N], dtype="object")
+377        new_content = []
+378        for t in range(self.T):
+379            new_content.append(array.copy())
+380
+381        def wrap(i):
+382            while i >= self.T:
+383                i -= self.T
+384            return i
+385
+386        for t in range(self.T):
+387            for i in range(N):
+388                for j in range(N):
+389                    if periodic:
+390                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
+391                    elif (t + i + j) >= self.T:
+392                        new_content[t] = None
+393                    else:
+394                        new_content[t][i, j] = self.content[t + i + j][0]
+395
+396        return Corr(new_content)
 
    
 
 
@@ -3477,15 +3513,15 @@ determines whether the matrix is extended periodically
    - 
    396    def roll(self, dt):
-397        """Periodically shift the correlator by dt timeslices
-398
-399        Parameters
-400        ----------
-401        dt : int
-402            number of timeslices
-403        """
-404        return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))
+            
    398    def roll(self, dt):
+399        """Periodically shift the correlator by dt timeslices
+400
+401        Parameters
+402        ----------
+403        dt : int
+404            number of timeslices
+405        """
+406        return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))
 
    
 
 
@@ -3512,9 +3548,9 @@ number of timeslices
    - 
    406    def reverse(self):
-407        """Reverse the time ordering of the Corr"""
-408        return Corr(self.content[:: -1])
+            
    408    def reverse(self):
+409        """Reverse the time ordering of the Corr"""
+410        return Corr(self.content[:: -1])
 
    
 
 
@@ -3534,23 +3570,23 @@ number of timeslices
    - 
    410    def thin(self, spacing=2, offset=0):
-411        """Thin out a correlator to suppress correlations
-412
-413        Parameters
-414        ----------
-415        spacing : int
-416            Keep only every 'spacing'th entry of the correlator
-417        offset : int
-418            Offset the equal spacing
-419        """
-420        new_content = []
-421        for t in range(self.T):
-422            if (offset + t) % spacing != 0:
-423                new_content.append(None)
-424            else:
-425                new_content.append(self.content[t])
-426        return Corr(new_content)
+            
    412    def thin(self, spacing=2, offset=0):
+413        """Thin out a correlator to suppress correlations
+414
+415        Parameters
+416        ----------
+417        spacing : int
+418            Keep only every 'spacing'th entry of the correlator
+419        offset : int
+420            Offset the equal spacing
+421        """
+422        new_content = []
+423        for t in range(self.T):
+424            if (offset + t) % spacing != 0:
+425                new_content.append(None)
+426            else:
+427                new_content.append(self.content[t])
+428        return Corr(new_content)
 
    
 
 
@@ -3579,34 +3615,34 @@ Offset the equal spacing
    - 
    428    def correlate(self, partner):
-429        """Correlate the correlator with another correlator or Obs
-430
-431        Parameters
-432        ----------
-433        partner : Obs or Corr
-434            partner to correlate the correlator with.
-435            Can either be an Obs which is correlated with all entries of the
-436            correlator or a Corr of same length.
-437        """
-438        if self.N != 1:
-439            raise Exception("Only one-dimensional correlators can be safely correlated.")
-440        new_content = []
-441        for x0, t_slice in enumerate(self.content):
-442            if _check_for_none(self, t_slice):
-443                new_content.append(None)
-444            else:
-445                if isinstance(partner, Corr):
-446                    if _check_for_none(partner, partner.content[x0]):
-447                        new_content.append(None)
-448                    else:
-449                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
-450                elif isinstance(partner, Obs):  # Should this include CObs?
-451                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
-452                else:
-453                    raise Exception("Can only correlate with an Obs or a Corr.")
-454
-455        return Corr(new_content)
+            
    430    def correlate(self, partner):
+431        """Correlate the correlator with another correlator or Obs
+432
+433        Parameters
+434        ----------
+435        partner : Obs or Corr
+436            partner to correlate the correlator with.
+437            Can either be an Obs which is correlated with all entries of the
+438            correlator or a Corr of same length.
+439        """
+440        if self.N != 1:
+441            raise Exception("Only one-dimensional correlators can be safely correlated.")
+442        new_content = []
+443        for x0, t_slice in enumerate(self.content):
+444            if _check_for_none(self, t_slice):
+445                new_content.append(None)
+446            else:
+447                if isinstance(partner, Corr):
+448                    if _check_for_none(partner, partner.content[x0]):
+449                        new_content.append(None)
+450                    else:
+451                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
+452                elif isinstance(partner, Obs):  # Should this include CObs?
+453                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
+454                else:
+455                    raise Exception("Can only correlate with an Obs or a Corr.")
+456
+457        return Corr(new_content)
 
    
 
 
@@ -3635,28 +3671,28 @@ correlator or a Corr of same length.
    - 
    457    def reweight(self, weight, **kwargs):
-458        """Reweight the correlator.
-459
-460        Parameters
-461        ----------
-462        weight : Obs
-463            Reweighting factor. An Observable that has to be defined on a superset of the
-464            configurations in obs[i].idl for all i.
-465        all_configs : bool
-466            if True, the reweighted observables are normalized by the average of
-467            the reweighting factor on all configurations in weight.idl and not
-468            on the configurations in obs[i].idl.
-469        """
-470        if self.N != 1:
-471            raise Exception("Reweighting only implemented for one-dimensional correlators.")
-472        new_content = []
-473        for t_slice in self.content:
-474            if _check_for_none(self, t_slice):
-475                new_content.append(None)
-476            else:
-477                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
-478        return Corr(new_content)
+            
    459    def reweight(self, weight, **kwargs):
+460        """Reweight the correlator.
+461
+462        Parameters
+463        ----------
+464        weight : Obs
+465            Reweighting factor. An Observable that has to be defined on a superset of the
+466            configurations in obs[i].idl for all i.
+467        all_configs : bool
+468            if True, the reweighted observables are normalized by the average of
+469            the reweighting factor on all configurations in weight.idl and not
+470            on the configurations in obs[i].idl.
+471        """
+472        if self.N != 1:
+473            raise Exception("Reweighting only implemented for one-dimensional correlators.")
+474        new_content = []
+475        for t_slice in self.content:
+476            if _check_for_none(self, t_slice):
+477                new_content.append(None)
+478            else:
+479                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
+480        return Corr(new_content)
 
    
 
 
@@ -3688,35 +3724,35 @@ on the configurations in obs[i].idl.
    - 
    480    def T_symmetry(self, partner, parity=+1):
-481        """Return the time symmetry average of the correlator and its partner
-482
-483        Parameters
-484        ----------
-485        partner : Corr
-486            Time symmetry partner of the Corr
-487        partity : int
-488            Parity quantum number of the correlator, can be +1 or -1
-489        """
-490        if self.N != 1:
-491            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
-492        if not isinstance(partner, Corr):
-493            raise Exception("T partner has to be a Corr object.")
-494        if parity not in [+1, -1]:
-495            raise Exception("Parity has to be +1 or -1.")
-496        T_partner = parity * partner.reverse()
-497
-498        t_slices = []
-499        test = (self - T_partner)
-500        test.gamma_method()
-501        for x0, t_slice in enumerate(test.content):
-502            if t_slice is not None:
-503                if not t_slice[0].is_zero_within_error(5):
-504                    t_slices.append(x0)
-505        if t_slices:
-506            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
-507
-508        return (self + T_partner) / 2
+            
    482    def T_symmetry(self, partner, parity=+1):
+483        """Return the time symmetry average of the correlator and its partner
+484
+485        Parameters
+486        ----------
+487        partner : Corr
+488            Time symmetry partner of the Corr
+489        partity : int
+490            Parity quantum number of the correlator, can be +1 or -1
+491        """
+492        if self.N != 1:
+493            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
+494        if not isinstance(partner, Corr):
+495            raise Exception("T partner has to be a Corr object.")
+496        if parity not in [+1, -1]:
+497            raise Exception("Parity has to be +1 or -1.")
+498        T_partner = parity * partner.reverse()
+499
+500        t_slices = []
+501        test = (self - T_partner)
+502        test.gamma_method()
+503        for x0, t_slice in enumerate(test.content):
+504            if t_slice is not None:
+505                if not t_slice[0].is_zero_within_error(5):
+506                    t_slices.append(x0)
+507        if t_slices:
+508            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
+509
+510        return (self + T_partner) / 2
 
    
 
 
@@ -3745,70 +3781,70 @@ Parity quantum number of the correlator, can be +1 or -1
    - 
    510    def deriv(self, variant="symmetric"):
-511        """Return the first derivative of the correlator with respect to x0.
-512
-513        Parameters
-514        ----------
-515        variant : str
-516            decides which definition of the finite differences derivative is used.
-517            Available choice: symmetric, forward, backward, improved, log, default: symmetric
-518        """
-519        if self.N != 1:
-520            raise Exception("deriv only implemented for one-dimensional correlators.")
-521        if variant == "symmetric":
-522            newcontent = []
-523            for t in range(1, self.T - 1):
-524                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-525                    newcontent.append(None)
-526                else:
-527                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
-528            if (all([x is None for x in newcontent])):
-529                raise Exception('Derivative is undefined at all timeslices')
-530            return Corr(newcontent, padding=[1, 1])
-531        elif variant == "forward":
-532            newcontent = []
-533            for t in range(self.T - 1):
-534                if (self.content[t] is None) or (self.content[t + 1] is None):
-535                    newcontent.append(None)
-536                else:
-537                    newcontent.append(self.content[t + 1] - self.content[t])
-538            if (all([x is None for x in newcontent])):
-539                raise Exception("Derivative is undefined at all timeslices")
-540            return Corr(newcontent, padding=[0, 1])
-541        elif variant == "backward":
-542            newcontent = []
-543            for t in range(1, self.T):
-544                if (self.content[t - 1] is None) or (self.content[t] is None):
-545                    newcontent.append(None)
-546                else:
-547                    newcontent.append(self.content[t] - self.content[t - 1])
-548            if (all([x is None for x in newcontent])):
-549                raise Exception("Derivative is undefined at all timeslices")
-550            return Corr(newcontent, padding=[1, 0])
-551        elif variant == "improved":
-552            newcontent = []
-553            for t in range(2, self.T - 2):
-554                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):
-555                    newcontent.append(None)
-556                else:
-557                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
-558            if (all([x is None for x in newcontent])):
-559                raise Exception('Derivative is undefined at all timeslices')
-560            return Corr(newcontent, padding=[2, 2])
-561        elif variant == 'log':
-562            newcontent = []
-563            for t in range(self.T):
-564                if (self.content[t] is None) or (self.content[t] <= 0):
-565                    newcontent.append(None)
-566                else:
-567                    newcontent.append(np.log(self.content[t]))
-568            if (all([x is None for x in newcontent])):
-569                raise Exception("Log is undefined at all timeslices")
-570            logcorr = Corr(newcontent)
-571            return self * logcorr.deriv('symmetric')
-572        else:
-573            raise Exception("Unknown variant.")
+            
    512    def deriv(self, variant="symmetric"):
+513        """Return the first derivative of the correlator with respect to x0.
+514
+515        Parameters
+516        ----------
+517        variant : str
+518            decides which definition of the finite differences derivative is used.
+519            Available choice: symmetric, forward, backward, improved, log, default: symmetric
+520        """
+521        if self.N != 1:
+522            raise Exception("deriv only implemented for one-dimensional correlators.")
+523        if variant == "symmetric":
+524            newcontent = []
+525            for t in range(1, self.T - 1):
+526                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+527                    newcontent.append(None)
+528                else:
+529                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
+530            if (all([x is None for x in newcontent])):
+531                raise Exception('Derivative is undefined at all timeslices')
+532            return Corr(newcontent, padding=[1, 1])
+533        elif variant == "forward":
+534            newcontent = []
+535            for t in range(self.T - 1):
+536                if (self.content[t] is None) or (self.content[t + 1] is None):
+537                    newcontent.append(None)
+538                else:
+539                    newcontent.append(self.content[t + 1] - self.content[t])
+540            if (all([x is None for x in newcontent])):
+541                raise Exception("Derivative is undefined at all timeslices")
+542            return Corr(newcontent, padding=[0, 1])
+543        elif variant == "backward":
+544            newcontent = []
+545            for t in range(1, self.T):
+546                if (self.content[t - 1] is None) or (self.content[t] is None):
+547                    newcontent.append(None)
+548                else:
+549                    newcontent.append(self.content[t] - self.content[t - 1])
+550            if (all([x is None for x in newcontent])):
+551                raise Exception("Derivative is undefined at all timeslices")
+552            return Corr(newcontent, padding=[1, 0])
+553        elif variant == "improved":
+554            newcontent = []
+555            for t in range(2, self.T - 2):
+556                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):
+557                    newcontent.append(None)
+558                else:
+559                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
+560            if (all([x is None for x in newcontent])):
+561                raise Exception('Derivative is undefined at all timeslices')
+562            return Corr(newcontent, padding=[2, 2])
+563        elif variant == 'log':
+564            newcontent = []
+565            for t in range(self.T):
+566                if (self.content[t] is None) or (self.content[t] <= 0):
+567                    newcontent.append(None)
+568                else:
+569                    newcontent.append(np.log(self.content[t]))
+570            if (all([x is None for x in newcontent])):
+571                raise Exception("Log is undefined at all timeslices")
+572            logcorr = Corr(newcontent)
+573            return self * logcorr.deriv('symmetric')
+574        else:
+575            raise Exception("Unknown variant.")
 
    
 
 
@@ -3836,50 +3872,50 @@ Available choice: symmetric, forward, backward, improved, log, default: symmetri
    - 
    575    def second_deriv(self, variant="symmetric"):
-576        """Return the second derivative of the correlator with respect to x0.
-577
-578        Parameters
-579        ----------
-580        variant : str
-581            decides which definition of the finite differences derivative is used.
-582            Available choice: symmetric, improved, log, default: symmetric
-583        """
-584        if self.N != 1:
-585            raise Exception("second_deriv only implemented for one-dimensional correlators.")
-586        if variant == "symmetric":
-587            newcontent = []
-588            for t in range(1, self.T - 1):
-589                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-590                    newcontent.append(None)
-591                else:
-592                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
-593            if (all([x is None for x in newcontent])):
-594                raise Exception("Derivative is undefined at all timeslices")
-595            return Corr(newcontent, padding=[1, 1])
-596        elif variant == "improved":
-597            newcontent = []
-598            for t in range(2, self.T - 2):
-599                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):
-600                    newcontent.append(None)
-601                else:
-602                    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]))
-603            if (all([x is None for x in newcontent])):
-604                raise Exception("Derivative is undefined at all timeslices")
-605            return Corr(newcontent, padding=[2, 2])
-606        elif variant == 'log':
-607            newcontent = []
-608            for t in range(self.T):
-609                if (self.content[t] is None) or (self.content[t] <= 0):
-610                    newcontent.append(None)
-611                else:
-612                    newcontent.append(np.log(self.content[t]))
-613            if (all([x is None for x in newcontent])):
-614                raise Exception("Log is undefined at all timeslices")
-615            logcorr = Corr(newcontent)
-616            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
-617        else:
-618            raise Exception("Unknown variant.")
+            
    577    def second_deriv(self, variant="symmetric"):
+578        """Return the second derivative of the correlator with respect to x0.
+579
+580        Parameters
+581        ----------
+582        variant : str
+583            decides which definition of the finite differences derivative is used.
+584            Available choice: symmetric, improved, log, default: symmetric
+585        """
+586        if self.N != 1:
+587            raise Exception("second_deriv only implemented for one-dimensional correlators.")
+588        if variant == "symmetric":
+589            newcontent = []
+590            for t in range(1, self.T - 1):
+591                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+592                    newcontent.append(None)
+593                else:
+594                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
+595            if (all([x is None for x in newcontent])):
+596                raise Exception("Derivative is undefined at all timeslices")
+597            return Corr(newcontent, padding=[1, 1])
+598        elif variant == "improved":
+599            newcontent = []
+600            for t in range(2, self.T - 2):
+601                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):
+602                    newcontent.append(None)
+603                else:
+604                    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]))
+605            if (all([x is None for x in newcontent])):
+606                raise Exception("Derivative is undefined at all timeslices")
+607            return Corr(newcontent, padding=[2, 2])
+608        elif variant == 'log':
+609            newcontent = []
+610            for t in range(self.T):
+611                if (self.content[t] is None) or (self.content[t] <= 0):
+612                    newcontent.append(None)
+613                else:
+614                    newcontent.append(np.log(self.content[t]))
+615            if (all([x is None for x in newcontent])):
+616                raise Exception("Log is undefined at all timeslices")
+617            logcorr = Corr(newcontent)
+618            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
+619        else:
+620            raise Exception("Unknown variant.")
 
    
 
 
@@ -3907,89 +3943,89 @@ Available choice: symmetric, improved, log, default: symmetric
    - 
    620    def m_eff(self, variant='log', guess=1.0):
-621        """Returns the effective mass of the correlator as correlator object
-622
-623        Parameters
-624        ----------
-625        variant : str
-626            log : uses the standard effective mass log(C(t) / C(t+1))
-627            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.
-628            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.
-629            See, e.g., arXiv:1205.5380
-630            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
-631            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
-632        guess : float
-633            guess for the root finder, only relevant for the root variant
-634        """
-635        if self.N != 1:
-636            raise Exception('Correlator must be projected before getting m_eff')
-637        if variant == 'log':
-638            newcontent = []
-639            for t in range(self.T - 1):
-640                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-641                    newcontent.append(None)
-642                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+            
    622    def m_eff(self, variant='log', guess=1.0):
+623        """Returns the effective mass of the correlator as correlator object
+624
+625        Parameters
+626        ----------
+627        variant : str
+628            log : uses the standard effective mass log(C(t) / C(t+1))
+629            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.
+630            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.
+631            See, e.g., arXiv:1205.5380
+632            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+633            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
+634        guess : float
+635            guess for the root finder, only relevant for the root variant
+636        """
+637        if self.N != 1:
+638            raise Exception('Correlator must be projected before getting m_eff')
+639        if variant == 'log':
+640            newcontent = []
+641            for t in range(self.T - 1):
+642                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
 643                    newcontent.append(None)
-644                else:
-645                    newcontent.append(self.content[t] / self.content[t + 1])
-646            if (all([x is None for x in newcontent])):
-647                raise Exception('m_eff is undefined at all timeslices')
-648
-649            return np.log(Corr(newcontent, padding=[0, 1]))
+644                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+645                    newcontent.append(None)
+646                else:
+647                    newcontent.append(self.content[t] / self.content[t + 1])
+648            if (all([x is None for x in newcontent])):
+649                raise Exception('m_eff is undefined at all timeslices')
 650
-651        elif variant == 'logsym':
-652            newcontent = []
-653            for t in range(1, self.T - 1):
-654                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-655                    newcontent.append(None)
-656                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
+651            return np.log(Corr(newcontent, padding=[0, 1]))
+652
+653        elif variant == 'logsym':
+654            newcontent = []
+655            for t in range(1, self.T - 1):
+656                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
 657                    newcontent.append(None)
-658                else:
-659                    newcontent.append(self.content[t - 1] / self.content[t + 1])
-660            if (all([x is None for x in newcontent])):
-661                raise Exception('m_eff is undefined at all timeslices')
-662
-663            return np.log(Corr(newcontent, padding=[1, 1])) / 2
+658                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
+659                    newcontent.append(None)
+660                else:
+661                    newcontent.append(self.content[t - 1] / self.content[t + 1])
+662            if (all([x is None for x in newcontent])):
+663                raise Exception('m_eff is undefined at all timeslices')
 664
-665        elif variant in ['periodic', 'cosh', 'sinh']:
-666            if variant in ['periodic', 'cosh']:
-667                func = anp.cosh
-668            else:
-669                func = anp.sinh
-670
-671            def root_function(x, d):
-672                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
-673
-674            newcontent = []
-675            for t in range(self.T - 1):
-676                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
-677                    newcontent.append(None)
-678                # Fill the two timeslices in the middle of the lattice with their predecessors
-679                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
-680                    newcontent.append(newcontent[-1])
-681                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-682                    newcontent.append(None)
-683                else:
-684                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
-685            if (all([x is None for x in newcontent])):
-686                raise Exception('m_eff is undefined at all timeslices')
-687
-688            return Corr(newcontent, padding=[0, 1])
+665            return np.log(Corr(newcontent, padding=[1, 1])) / 2
+666
+667        elif variant in ['periodic', 'cosh', 'sinh']:
+668            if variant in ['periodic', 'cosh']:
+669                func = anp.cosh
+670            else:
+671                func = anp.sinh
+672
+673            def root_function(x, d):
+674                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
+675
+676            newcontent = []
+677            for t in range(self.T - 1):
+678                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+679                    newcontent.append(None)
+680                # Fill the two timeslices in the middle of the lattice with their predecessors
+681                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
+682                    newcontent.append(newcontent[-1])
+683                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+684                    newcontent.append(None)
+685                else:
+686                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
+687            if (all([x is None for x in newcontent])):
+688                raise Exception('m_eff is undefined at all timeslices')
 689
-690        elif variant == 'arccosh':
-691            newcontent = []
-692            for t in range(1, self.T - 1):
-693                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):
-694                    newcontent.append(None)
-695                else:
-696                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
-697            if (all([x is None for x in newcontent])):
-698                raise Exception("m_eff is undefined at all timeslices")
-699            return np.arccosh(Corr(newcontent, padding=[1, 1]))
-700
-701        else:
-702            raise Exception('Unknown variant.')
+690            return Corr(newcontent, padding=[0, 1])
+691
+692        elif variant == 'arccosh':
+693            newcontent = []
+694            for t in range(1, self.T - 1):
+695                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):
+696                    newcontent.append(None)
+697                else:
+698                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+699            if (all([x is None for x in newcontent])):
+700                raise Exception("m_eff is undefined at all timeslices")
+701            return np.arccosh(Corr(newcontent, padding=[1, 1]))
+702
+703        else:
+704            raise Exception('Unknown variant.')
 
    
 
 
@@ -4023,39 +4059,39 @@ guess for the root finder, only relevant for the root variant
    - 
    704    def fit(self, function, fitrange=None, silent=False, **kwargs):
-705        r'''Fits function to the data
-706
-707        Parameters
-708        ----------
-709        function : obj
-710            function to fit to the data. See fits.least_squares for details.
-711        fitrange : list
-712            Two element list containing the timeslices on which the fit is supposed to start and stop.
-713            Caution: This range is inclusive as opposed to standard python indexing.
-714            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
-715            If not specified, self.prange or all timeslices are used.
-716        silent : bool
-717            Decides whether output is printed to the standard output.
-718        '''
-719        if self.N != 1:
-720            raise Exception("Correlator must be projected before fitting")
-721
-722        if fitrange is None:
-723            if self.prange:
-724                fitrange = self.prange
-725            else:
-726                fitrange = [0, self.T - 1]
-727        else:
-728            if not isinstance(fitrange, list):
-729                raise Exception("fitrange has to be a list with two elements")
-730            if len(fitrange) != 2:
-731                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
-732
-733        xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
-734        ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
-735        result = least_squares(xs, ys, function, silent=silent, **kwargs)
-736        return result
+            
    706    def fit(self, function, fitrange=None, silent=False, **kwargs):
+707        r'''Fits function to the data
+708
+709        Parameters
+710        ----------
+711        function : obj
+712            function to fit to the data. See fits.least_squares for details.
+713        fitrange : list
+714            Two element list containing the timeslices on which the fit is supposed to start and stop.
+715            Caution: This range is inclusive as opposed to standard python indexing.
+716            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
+717            If not specified, self.prange or all timeslices are used.
+718        silent : bool
+719            Decides whether output is printed to the standard output.
+720        '''
+721        if self.N != 1:
+722            raise Exception("Correlator must be projected before fitting")
+723
+724        if fitrange is None:
+725            if self.prange:
+726                fitrange = self.prange
+727            else:
+728                fitrange = [0, self.T - 1]
+729        else:
+730            if not isinstance(fitrange, list):
+731                raise Exception("fitrange has to be a list with two elements")
+732            if len(fitrange) != 2:
+733                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
+734
+735        xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
+736        ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
+737        result = least_squares(xs, ys, function, silent=silent, **kwargs)
+738        return result
 
    
 
 
@@ -4089,42 +4125,42 @@ Decides whether output is printed to the standard output.
    - 
    738    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
-739        """ Extract a plateau value from a Corr object
-740
-741        Parameters
-742        ----------
-743        plateau_range : list
-744            list with two entries, indicating the first and the last timeslice
-745            of the plateau region.
-746        method : str
-747            method to extract the plateau.
-748                'fit' fits a constant to the plateau region
-749                'avg', 'average' or 'mean' just average over the given timeslices.
-750        auto_gamma : bool
-751            apply gamma_method with default parameters to the Corr. Defaults to None
-752        """
-753        if not plateau_range:
-754            if self.prange:
-755                plateau_range = self.prange
-756            else:
-757                raise Exception("no plateau range provided")
-758        if self.N != 1:
-759            raise Exception("Correlator must be projected before getting a plateau.")
-760        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
-761            raise Exception("plateau is undefined at all timeslices in plateaurange.")
-762        if auto_gamma:
-763            self.gamma_method()
-764        if method == "fit":
-765            def const_func(a, t):
-766                return a[0]
-767            return self.fit(const_func, plateau_range)[0]
-768        elif method in ["avg", "average", "mean"]:
-769            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
-770            return returnvalue
-771
-772        else:
-773            raise Exception("Unsupported plateau method: " + method)
+            
    740    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+741        """ Extract a plateau value from a Corr object
+742
+743        Parameters
+744        ----------
+745        plateau_range : list
+746            list with two entries, indicating the first and the last timeslice
+747            of the plateau region.
+748        method : str
+749            method to extract the plateau.
+750                'fit' fits a constant to the plateau region
+751                'avg', 'average' or 'mean' just average over the given timeslices.
+752        auto_gamma : bool
+753            apply gamma_method with default parameters to the Corr. Defaults to None
+754        """
+755        if not plateau_range:
+756            if self.prange:
+757                plateau_range = self.prange
+758            else:
+759                raise Exception("no plateau range provided")
+760        if self.N != 1:
+761            raise Exception("Correlator must be projected before getting a plateau.")
+762        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
+763            raise Exception("plateau is undefined at all timeslices in plateaurange.")
+764        if auto_gamma:
+765            self.gamma_method()
+766        if method == "fit":
+767            def const_func(a, t):
+768                return a[0]
+769            return self.fit(const_func, plateau_range)[0]
+770        elif method in ["avg", "average", "mean"]:
+771            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
+772            return returnvalue
+773
+774        else:
+775            raise Exception("Unsupported plateau method: " + method)
 
    
 
 
@@ -4158,17 +4194,17 @@ apply gamma_method with default parameters to the Corr. Defaults to None
    - 
    775    def set_prange(self, prange):
-776        """Sets the attribute prange of the Corr object."""
-777        if not len(prange) == 2:
-778            raise Exception("prange must be a list or array with two values")
-779        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
-780            raise Exception("Start and end point must be integers")
-781        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
-782            raise Exception("Start and end point must define a range in the interval 0,T")
-783
-784        self.prange = prange
-785        return
+            
    777    def set_prange(self, prange):
+778        """Sets the attribute prange of the Corr object."""
+779        if not len(prange) == 2:
+780            raise Exception("prange must be a list or array with two values")
+781        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
+782            raise Exception("Start and end point must be integers")
+783        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
+784            raise Exception("Start and end point must define a range in the interval 0,T")
+785
+786        self.prange = prange
+787        return
 
    
 
 
@@ -4188,124 +4224,124 @@ apply gamma_method with default parameters to the Corr. Defaults to None
    - 
    787    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
-788        """Plots the correlator using the tag of the correlator as label if available.
-789
-790        Parameters
-791        ----------
-792        x_range : list
-793            list of two values, determining the range of the x-axis e.g. [4, 8].
-794        comp : Corr or list of Corr
-795            Correlator or list of correlators which are plotted for comparison.
-796            The tags of these correlators are used as labels if available.
-797        logscale : bool
-798            Sets y-axis to logscale.
-799        plateau : Obs
-800            Plateau value to be visualized in the figure.
-801        fit_res : Fit_result
-802            Fit_result object to be visualized.
-803        ylabel : str
-804            Label for the y-axis.
-805        save : str
-806            path to file in which the figure should be saved.
-807        auto_gamma : bool
-808            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
-809        hide_sigma : float
-810            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
-811        references : list
-812            List of floating point values that are displayed as horizontal lines for reference.
-813        title : string
-814            Optional title of the figure.
-815        """
-816        if self.N != 1:
-817            raise Exception("Correlator must be projected before plotting")
-818
-819        if auto_gamma:
-820            self.gamma_method()
-821
-822        if x_range is None:
-823            x_range = [0, self.T - 1]
-824
-825        fig = plt.figure()
-826        ax1 = fig.add_subplot(111)
-827
-828        x, y, y_err = self.plottable()
-829        if hide_sigma:
-830            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-831        else:
-832            hide_from = None
-833        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
-834        if logscale:
-835            ax1.set_yscale('log')
-836        else:
-837            if y_range is None:
-838                try:
-839                    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)])
-840                    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)])
-841                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
-842                except Exception:
-843                    pass
-844            else:
-845                ax1.set_ylim(y_range)
-846        if comp:
-847            if isinstance(comp, (Corr, list)):
-848                for corr in comp if isinstance(comp, list) else [comp]:
-849                    if auto_gamma:
-850                        corr.gamma_method()
-851                    x, y, y_err = corr.plottable()
-852                    if hide_sigma:
-853                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-854                    else:
-855                        hide_from = None
-856                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
-857            else:
-858                raise Exception("'comp' must be a correlator or a list of correlators.")
-859
-860        if plateau:
-861            if isinstance(plateau, Obs):
-862                if auto_gamma:
-863                    plateau.gamma_method()
-864                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
-865                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
-866            else:
-867                raise Exception("'plateau' must be an Obs")
-868
-869        if references:
-870            if isinstance(references, list):
-871                for ref in references:
-872                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
-873            else:
-874                raise Exception("'references' must be a list of floating pint values.")
-875
-876        if self.prange:
-877            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
-878            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
-879
-880        if fit_res:
-881            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
-882            ax1.plot(x_samples,
-883                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
-884                     ls='-', marker=',', lw=2)
-885
-886        ax1.set_xlabel(r'$x_0 / a$')
-887        if ylabel:
-888            ax1.set_ylabel(ylabel)
-889        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
-890
-891        handles, labels = ax1.get_legend_handles_labels()
-892        if labels:
-893            ax1.legend()
-894
-895        if title:
-896            plt.title(title)
-897
-898        plt.draw()
+            
    789    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
+790        """Plots the correlator using the tag of the correlator as label if available.
+791
+792        Parameters
+793        ----------
+794        x_range : list
+795            list of two values, determining the range of the x-axis e.g. [4, 8].
+796        comp : Corr or list of Corr
+797            Correlator or list of correlators which are plotted for comparison.
+798            The tags of these correlators are used as labels if available.
+799        logscale : bool
+800            Sets y-axis to logscale.
+801        plateau : Obs
+802            Plateau value to be visualized in the figure.
+803        fit_res : Fit_result
+804            Fit_result object to be visualized.
+805        ylabel : str
+806            Label for the y-axis.
+807        save : str
+808            path to file in which the figure should be saved.
+809        auto_gamma : bool
+810            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
+811        hide_sigma : float
+812            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
+813        references : list
+814            List of floating point values that are displayed as horizontal lines for reference.
+815        title : string
+816            Optional title of the figure.
+817        """
+818        if self.N != 1:
+819            raise Exception("Correlator must be projected before plotting")
+820
+821        if auto_gamma:
+822            self.gamma_method()
+823
+824        if x_range is None:
+825            x_range = [0, self.T - 1]
+826
+827        fig = plt.figure()
+828        ax1 = fig.add_subplot(111)
+829
+830        x, y, y_err = self.plottable()
+831        if hide_sigma:
+832            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+833        else:
+834            hide_from = None
+835        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
+836        if logscale:
+837            ax1.set_yscale('log')
+838        else:
+839            if y_range is None:
+840                try:
+841                    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)])
+842                    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)])
+843                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
+844                except Exception:
+845                    pass
+846            else:
+847                ax1.set_ylim(y_range)
+848        if comp:
+849            if isinstance(comp, (Corr, list)):
+850                for corr in comp if isinstance(comp, list) else [comp]:
+851                    if auto_gamma:
+852                        corr.gamma_method()
+853                    x, y, y_err = corr.plottable()
+854                    if hide_sigma:
+855                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+856                    else:
+857                        hide_from = None
+858                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
+859            else:
+860                raise Exception("'comp' must be a correlator or a list of correlators.")
+861
+862        if plateau:
+863            if isinstance(plateau, Obs):
+864                if auto_gamma:
+865                    plateau.gamma_method()
+866                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
+867                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+868            else:
+869                raise Exception("'plateau' must be an Obs")
+870
+871        if references:
+872            if isinstance(references, list):
+873                for ref in references:
+874                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
+875            else:
+876                raise Exception("'references' must be a list of floating pint values.")
+877
+878        if self.prange:
+879            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
+880            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
+881
+882        if fit_res:
+883            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
+884            ax1.plot(x_samples,
+885                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
+886                     ls='-', marker=',', lw=2)
+887
+888        ax1.set_xlabel(r'$x_0 / a$')
+889        if ylabel:
+890            ax1.set_ylabel(ylabel)
+891        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
+892
+893        handles, labels = ax1.get_legend_handles_labels()
+894        if labels:
+895            ax1.legend()
+896
+897        if title:
+898            plt.title(title)
 899
-900        if save:
-901            if isinstance(save, str):
-902                fig.savefig(save, bbox_inches='tight')
-903            else:
-904                raise Exception("'save' has to be a string.")
+900        plt.draw()
+901
+902        if save:
+903            if isinstance(save, str):
+904                fig.savefig(save, bbox_inches='tight')
+905            else:
+906                raise Exception("'save' has to be a string.")
 
    
 
 
@@ -4353,34 +4389,34 @@ Optional title of the figure.
    - 
    906    def spaghetti_plot(self, logscale=True):
-907        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-908
-909        Parameters
-910        ----------
-911        logscale : bool
-912            Determines whether the scale of the y-axis is logarithmic or standard.
-913        """
-914        if self.N != 1:
-915            raise Exception("Correlator needs to be projected first.")
-916
-917        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]))
-918        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
-919
-920        for name in mc_names:
-921            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
-922
-923            fig = plt.figure()
-924            ax = fig.add_subplot(111)
-925            for dat in data:
-926                ax.plot(x0_vals, dat, ls='-', marker='')
-927
-928            if logscale is True:
-929                ax.set_yscale('log')
-930
-931            ax.set_xlabel(r'$x_0 / a$')
-932            plt.title(name)
-933            plt.draw()
+            
    908    def spaghetti_plot(self, logscale=True):
+909        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+910
+911        Parameters
+912        ----------
+913        logscale : bool
+914            Determines whether the scale of the y-axis is logarithmic or standard.
+915        """
+916        if self.N != 1:
+917            raise Exception("Correlator needs to be projected first.")
+918
+919        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]))
+920        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+921
+922        for name in mc_names:
+923            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+924
+925            fig = plt.figure()
+926            ax = fig.add_subplot(111)
+927            for dat in data:
+928                ax.plot(x0_vals, dat, ls='-', marker='')
+929
+930            if logscale is True:
+931                ax.set_yscale('log')
+932
+933            ax.set_xlabel(r'$x_0 / a$')
+934            plt.title(name)
+935            plt.draw()
 
    
 
 
@@ -4407,29 +4443,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.
    - 
    935    def dump(self, filename, datatype="json.gz", **kwargs):
-936        """Dumps the Corr into a file of chosen type
-937        Parameters
-938        ----------
-939        filename : str
-940            Name of the file to be saved.
-941        datatype : str
-942            Format of the exported file. Supported formats include
-943            "json.gz" and "pickle"
-944        path : str
-945            specifies a custom path for the file (default '.')
-946        """
-947        if datatype == "json.gz":
-948            from .input.json import dump_to_json
-949            if 'path' in kwargs:
-950                file_name = kwargs.get('path') + '/' + filename
-951            else:
-952                file_name = filename
-953            dump_to_json(self, file_name)
-954        elif datatype == "pickle":
-955            dump_object(self, filename, **kwargs)
-956        else:
-957            raise Exception("Unknown datatype " + str(datatype))
+            
    937    def dump(self, filename, datatype="json.gz", **kwargs):
+938        """Dumps the Corr into a file of chosen type
+939        Parameters
+940        ----------
+941        filename : str
+942            Name of the file to be saved.
+943        datatype : str
+944            Format of the exported file. Supported formats include
+945            "json.gz" and "pickle"
+946        path : str
+947            specifies a custom path for the file (default '.')
+948        """
+949        if datatype == "json.gz":
+950            from .input.json import dump_to_json
+951            if 'path' in kwargs:
+952                file_name = kwargs.get('path') + '/' + filename
+953            else:
+954                file_name = filename
+955            dump_to_json(self, file_name)
+956        elif datatype == "pickle":
+957            dump_object(self, filename, **kwargs)
+958        else:
+959            raise Exception("Unknown datatype " + str(datatype))
 
    
 
 
@@ -4461,8 +4497,8 @@ specifies a custom path for the file (default '.')
    - 
    959    def print(self, print_range=None):
-960        print(self.__repr__(print_range))
+            
    961    def print(self, print_range=None):
+962        print(self.__repr__(print_range))
 
    
 
 
@@ -4480,8 +4516,8 @@ specifies a custom path for the file (default '.')
    - 
    1126    def sqrt(self):
-1127        return self ** 0.5
+            
    1128    def sqrt(self):
+1129        return self ** 0.5
 
    
 
 
@@ -4499,9 +4535,9 @@ specifies a custom path for the file (default '.')
    - 
    1129    def log(self):
-1130        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1131        return Corr(newcontent, prange=self.prange)
+            
    1131    def log(self):
+1132        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1133        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4519,9 +4555,9 @@ specifies a custom path for the file (default '.')
    - 
    1133    def exp(self):
-1134        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1135        return Corr(newcontent, prange=self.prange)
+            
    1135    def exp(self):
+1136        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1137        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4539,8 +4575,8 @@ specifies a custom path for the file (default '.')
    - 
    1150    def sin(self):
-1151        return self._apply_func_to_corr(np.sin)
+            
    1152    def sin(self):
+1153        return self._apply_func_to_corr(np.sin)
 
    
 
 
@@ -4558,8 +4594,8 @@ specifies a custom path for the file (default '.')
    - 
    1153    def cos(self):
-1154        return self._apply_func_to_corr(np.cos)
+            
    1155    def cos(self):
+1156        return self._apply_func_to_corr(np.cos)
 
    
 
 
@@ -4577,8 +4613,8 @@ specifies a custom path for the file (default '.')
    - 
    1156    def tan(self):
-1157        return self._apply_func_to_corr(np.tan)
+            
    1158    def tan(self):
+1159        return self._apply_func_to_corr(np.tan)
 
    
 
 
@@ -4596,8 +4632,8 @@ specifies a custom path for the file (default '.')
    - 
    1159    def sinh(self):
-1160        return self._apply_func_to_corr(np.sinh)
+            
    1161    def sinh(self):
+1162        return self._apply_func_to_corr(np.sinh)
 
    
 
 
@@ -4615,8 +4651,8 @@ specifies a custom path for the file (default '.')
    - 
    1162    def cosh(self):
-1163        return self._apply_func_to_corr(np.cosh)
+            
    1164    def cosh(self):
+1165        return self._apply_func_to_corr(np.cosh)
 
    
 
 
@@ -4634,8 +4670,8 @@ specifies a custom path for the file (default '.')
    - 
    1165    def tanh(self):
-1166        return self._apply_func_to_corr(np.tanh)
+            
    1167    def tanh(self):
+1168        return self._apply_func_to_corr(np.tanh)
 
    
 
 
@@ -4653,8 +4689,8 @@ specifies a custom path for the file (default '.')
    - 
    1168    def arcsin(self):
-1169        return self._apply_func_to_corr(np.arcsin)
+            
    1170    def arcsin(self):
+1171        return self._apply_func_to_corr(np.arcsin)
 
    
 
 
@@ -4672,8 +4708,8 @@ specifies a custom path for the file (default '.')
    - 
    1171    def arccos(self):
-1172        return self._apply_func_to_corr(np.arccos)
+            
    1173    def arccos(self):
+1174        return self._apply_func_to_corr(np.arccos)
 
    
 
 
@@ -4691,8 +4727,8 @@ specifies a custom path for the file (default '.')
    - 
    1174    def arctan(self):
-1175        return self._apply_func_to_corr(np.arctan)
+            
    1176    def arctan(self):
+1177        return self._apply_func_to_corr(np.arctan)
 
    
 
 
@@ -4710,8 +4746,8 @@ specifies a custom path for the file (default '.')
    - 
    1177    def arcsinh(self):
-1178        return self._apply_func_to_corr(np.arcsinh)
+            
    1179    def arcsinh(self):
+1180        return self._apply_func_to_corr(np.arcsinh)
 
    
 
 
@@ -4729,8 +4765,8 @@ specifies a custom path for the file (default '.')
    - 
    1180    def arccosh(self):
-1181        return self._apply_func_to_corr(np.arccosh)
+            
    1182    def arccosh(self):
+1183        return self._apply_func_to_corr(np.arccosh)
 
    
 
 
@@ -4748,8 +4784,8 @@ specifies a custom path for the file (default '.')
    - 
    1183    def arctanh(self):
-1184        return self._apply_func_to_corr(np.arctanh)
+            
    1185    def arctanh(self):
+1186        return self._apply_func_to_corr(np.arctanh)
 
    
 
 
@@ -4767,62 +4803,62 @@ specifies a custom path for the file (default '.')
    - 
    1219    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1220        r''' Project large correlation matrix to lowest states
-1221
-1222        This method can be used to reduce the size of an (N x N) correlation matrix
-1223        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1224        is still small.
-1225
-1226        Parameters
-1227        ----------
-1228        Ntrunc: int
-1229            Rank of the target matrix.
-1230        tproj: int
-1231            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1232            The default value is 3.
-1233        t0proj: int
-1234            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1235            discouraged for O(a) improved theories, since the correctness of the procedure
-1236            cannot be granted in this case. The default value is 2.
-1237        basematrix : Corr
-1238            Correlation matrix that is used to determine the eigenvectors of the
-1239            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1240            is is not specified.
-1241
-1242        Notes
-1243        -----
-1244        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1245        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1246        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1247        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1248        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1249        correlation matrix and to remove some noise that is added by irrelevant operators.
-1250        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1251        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1252        '''
-1253
-1254        if self.N == 1:
-1255            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1256        if basematrix is None:
-1257            basematrix = self
-1258        if Ntrunc >= basematrix.N:
-1259            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1260        if basematrix.N != self.N:
-1261            raise Exception('basematrix and targetmatrix have to be of the same size.')
-1262
-1263        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+            
    1221    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1222        r''' Project large correlation matrix to lowest states
+1223
+1224        This method can be used to reduce the size of an (N x N) correlation matrix
+1225        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1226        is still small.
+1227
+1228        Parameters
+1229        ----------
+1230        Ntrunc: int
+1231            Rank of the target matrix.
+1232        tproj: int
+1233            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1234            The default value is 3.
+1235        t0proj: int
+1236            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1237            discouraged for O(a) improved theories, since the correctness of the procedure
+1238            cannot be granted in this case. The default value is 2.
+1239        basematrix : Corr
+1240            Correlation matrix that is used to determine the eigenvectors of the
+1241            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1242            is is not specified.
+1243
+1244        Notes
+1245        -----
+1246        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1247        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1248        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1249        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1250        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1251        correlation matrix and to remove some noise that is added by irrelevant operators.
+1252        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1253        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1254        '''
+1255
+1256        if self.N == 1:
+1257            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1258        if basematrix is None:
+1259            basematrix = self
+1260        if Ntrunc >= basematrix.N:
+1261            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1262        if basematrix.N != self.N:
+1263            raise Exception('basematrix and targetmatrix have to be of the same size.')
 1264
-1265        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1266        rmat = []
-1267        for t in range(basematrix.T):
-1268            for i in range(Ntrunc):
-1269                for j in range(Ntrunc):
-1270                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1271            rmat.append(np.copy(tmpmat))
-1272
-1273        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1274        return Corr(newcontent)
+1265        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1266
+1267        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1268        rmat = []
+1269        for t in range(basematrix.T):
+1270            for i in range(Ntrunc):
+1271                for j in range(Ntrunc):
+1272                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1273            rmat.append(np.copy(tmpmat))
+1274
+1275        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1276        return Corr(newcontent)
 
    
 
 
diff --git a/docs/pyerrors/fits.html b/docs/pyerrors/fits.html
index 15ed89b9..0be3cb04 100644
--- a/docs/pyerrors/fits.html
+++ b/docs/pyerrors/fits.html
@@ -61,6 +61,9 @@
                         
  • 
                                 gamma_method
                         
    • 
+                        
  • 
+                                gm
+                        
    • 
                 
 
             
@@ -154,754 +157,756 @@
      46        """Apply the gamma method to all fit parameters"""
  47        [o.gamma_method(**kwargs) for o in self.fit_parameters]
  48
- 49    def __str__(self):
- 50        my_str = 'Goodness of fit:\n'
- 51        if hasattr(self, 'chisquare_by_dof'):
- 52            my_str += '\u03C7\u00b2/d.o.f. = ' + f'{self.chisquare_by_dof:2.6f}' + '\n'
- 53        elif hasattr(self, 'residual_variance'):
- 54            my_str += 'residual variance = ' + f'{self.residual_variance:2.6f}' + '\n'
- 55        if hasattr(self, 'chisquare_by_expected_chisquare'):
- 56            my_str += '\u03C7\u00b2/\u03C7\u00b2exp  = ' + f'{self.chisquare_by_expected_chisquare:2.6f}' + '\n'
- 57        if hasattr(self, 'p_value'):
- 58            my_str += 'p-value   = ' + f'{self.p_value:2.4f}' + '\n'
- 59        if hasattr(self, 't2_p_value'):
- 60            my_str += 't\u00B2p-value = ' + f'{self.t2_p_value:2.4f}' + '\n'
- 61        my_str += 'Fit parameters:\n'
- 62        for i_par, par in enumerate(self.fit_parameters):
- 63            my_str += str(i_par) + '\t' + ' ' * int(par >= 0) + str(par).rjust(int(par < 0.0)) + '\n'
- 64        return my_str
- 65
- 66    def __repr__(self):
- 67        m = max(map(len, list(self.__dict__.keys()))) + 1
- 68        return '\n'.join([key.rjust(m) + ': ' + repr(value) for key, value in sorted(self.__dict__.items())])
- 69
- 70
- 71def least_squares(x, y, func, priors=None, silent=False, **kwargs):
- 72    r'''Performs a non-linear fit to y = func(x).
- 73
- 74    Parameters
- 75    ----------
- 76    x : list
- 77        list of floats.
- 78    y : list
- 79        list of Obs.
- 80    func : object
- 81        fit function, has to be of the form
- 82
- 83        ```python
- 84        import autograd.numpy as anp
- 85
- 86        def func(a, x):
- 87            return a[0] + a[1] * x + a[2] * anp.sinh(x)
- 88        ```
- 89
- 90        For multiple x values func can be of the form
+ 49    gm = gamma_method
+ 50
+ 51    def __str__(self):
+ 52        my_str = 'Goodness of fit:\n'
+ 53        if hasattr(self, 'chisquare_by_dof'):
+ 54            my_str += '\u03C7\u00b2/d.o.f. = ' + f'{self.chisquare_by_dof:2.6f}' + '\n'
+ 55        elif hasattr(self, 'residual_variance'):
+ 56            my_str += 'residual variance = ' + f'{self.residual_variance:2.6f}' + '\n'
+ 57        if hasattr(self, 'chisquare_by_expected_chisquare'):
+ 58            my_str += '\u03C7\u00b2/\u03C7\u00b2exp  = ' + f'{self.chisquare_by_expected_chisquare:2.6f}' + '\n'
+ 59        if hasattr(self, 'p_value'):
+ 60            my_str += 'p-value   = ' + f'{self.p_value:2.4f}' + '\n'
+ 61        if hasattr(self, 't2_p_value'):
+ 62            my_str += 't\u00B2p-value = ' + f'{self.t2_p_value:2.4f}' + '\n'
+ 63        my_str += 'Fit parameters:\n'
+ 64        for i_par, par in enumerate(self.fit_parameters):
+ 65            my_str += str(i_par) + '\t' + ' ' * int(par >= 0) + str(par).rjust(int(par < 0.0)) + '\n'
+ 66        return my_str
+ 67
+ 68    def __repr__(self):
+ 69        m = max(map(len, list(self.__dict__.keys()))) + 1
+ 70        return '\n'.join([key.rjust(m) + ': ' + repr(value) for key, value in sorted(self.__dict__.items())])
+ 71
+ 72
+ 73def least_squares(x, y, func, priors=None, silent=False, **kwargs):
+ 74    r'''Performs a non-linear fit to y = func(x).
+ 75
+ 76    Parameters
+ 77    ----------
+ 78    x : list
+ 79        list of floats.
+ 80    y : list
+ 81        list of Obs.
+ 82    func : object
+ 83        fit function, has to be of the form
+ 84
+ 85        ```python
+ 86        import autograd.numpy as anp
+ 87
+ 88        def func(a, x):
+ 89            return a[0] + a[1] * x + a[2] * anp.sinh(x)
+ 90        ```
  91
- 92        ```python
- 93        def func(a, x):
- 94            (x1, x2) = x
- 95            return a[0] * x1 ** 2 + a[1] * x2
- 96        ```
- 97
- 98        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
- 99        will not work.
-100    priors : list, optional
-101        priors has to be a list with an entry for every parameter in the fit. The entries can either be
-102        Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like
-103        0.548(23), 500(40) or 0.5(0.4)
-104    silent : bool, optional
-105        If true all output to the console is omitted (default False).
-106    initial_guess : list
-107        can provide an initial guess for the input parameters. Relevant for
-108        non-linear fits with many parameters. In case of correlated fits the guess is used to perform
-109        an uncorrelated fit which then serves as guess for the correlated fit.
-110    method : str, optional
-111        can be used to choose an alternative method for the minimization of chisquare.
-112        The possible methods are the ones which can be used for scipy.optimize.minimize and
-113        migrad of iminuit. If no method is specified, Levenberg-Marquard is used.
-114        Reliable alternatives are migrad, Powell and Nelder-Mead.
-115    correlated_fit : bool
-116        If True, use the full inverse covariance matrix in the definition of the chisquare cost function.
-117        For details about how the covariance matrix is estimated see `pyerrors.obs.covariance`.
-118        In practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).
-119        This procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
-120        At the moment this option only works for `prior==None` and when no `method` is given.
-121    expected_chisquare : bool
-122        If True estimates the expected chisquare which is
-123        corrected by effects caused by correlated input data (default False).
-124    resplot : bool
-125        If True, a plot which displays fit, data and residuals is generated (default False).
-126    qqplot : bool
-127        If True, a quantile-quantile plot of the fit result is generated (default False).
-128    num_grad : bool
-129        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
-130    '''
-131    if priors is not None:
-132        return _prior_fit(x, y, func, priors, silent=silent, **kwargs)
-133    else:
-134        return _standard_fit(x, y, func, silent=silent, **kwargs)
-135
-136
-137def total_least_squares(x, y, func, silent=False, **kwargs):
-138    r'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
-139
-140    Parameters
-141    ----------
-142    x : list
-143        list of Obs, or a tuple of lists of Obs
-144    y : list
-145        list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
-146    func : object
-147        func has to be of the form
-148
-149        ```python
-150        import autograd.numpy as anp
-151
-152        def func(a, x):
-153            return a[0] + a[1] * x + a[2] * anp.sinh(x)
-154        ```
-155
-156        For multiple x values func can be of the form
+ 92        For multiple x values func can be of the form
+ 93
+ 94        ```python
+ 95        def func(a, x):
+ 96            (x1, x2) = x
+ 97            return a[0] * x1 ** 2 + a[1] * x2
+ 98        ```
+ 99
+100        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
+101        will not work.
+102    priors : list, optional
+103        priors has to be a list with an entry for every parameter in the fit. The entries can either be
+104        Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like
+105        0.548(23), 500(40) or 0.5(0.4)
+106    silent : bool, optional
+107        If true all output to the console is omitted (default False).
+108    initial_guess : list
+109        can provide an initial guess for the input parameters. Relevant for
+110        non-linear fits with many parameters. In case of correlated fits the guess is used to perform
+111        an uncorrelated fit which then serves as guess for the correlated fit.
+112    method : str, optional
+113        can be used to choose an alternative method for the minimization of chisquare.
+114        The possible methods are the ones which can be used for scipy.optimize.minimize and
+115        migrad of iminuit. If no method is specified, Levenberg-Marquard is used.
+116        Reliable alternatives are migrad, Powell and Nelder-Mead.
+117    correlated_fit : bool
+118        If True, use the full inverse covariance matrix in the definition of the chisquare cost function.
+119        For details about how the covariance matrix is estimated see `pyerrors.obs.covariance`.
+120        In practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).
+121        This procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
+122        At the moment this option only works for `prior==None` and when no `method` is given.
+123    expected_chisquare : bool
+124        If True estimates the expected chisquare which is
+125        corrected by effects caused by correlated input data (default False).
+126    resplot : bool
+127        If True, a plot which displays fit, data and residuals is generated (default False).
+128    qqplot : bool
+129        If True, a quantile-quantile plot of the fit result is generated (default False).
+130    num_grad : bool
+131        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
+132    '''
+133    if priors is not None:
+134        return _prior_fit(x, y, func, priors, silent=silent, **kwargs)
+135    else:
+136        return _standard_fit(x, y, func, silent=silent, **kwargs)
+137
+138
+139def total_least_squares(x, y, func, silent=False, **kwargs):
+140    r'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
+141
+142    Parameters
+143    ----------
+144    x : list
+145        list of Obs, or a tuple of lists of Obs
+146    y : list
+147        list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
+148    func : object
+149        func has to be of the form
+150
+151        ```python
+152        import autograd.numpy as anp
+153
+154        def func(a, x):
+155            return a[0] + a[1] * x + a[2] * anp.sinh(x)
+156        ```
 157
-158        ```python
-159        def func(a, x):
-160            (x1, x2) = x
-161            return a[0] * x1 ** 2 + a[1] * x2
-162        ```
-163
-164        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
-165        will not work.
-166    silent : bool, optional
-167        If true all output to the console is omitted (default False).
-168    initial_guess : list
-169        can provide an initial guess for the input parameters. Relevant for non-linear
-170        fits with many parameters.
-171    expected_chisquare : bool
-172        If true prints the expected chisquare which is
-173        corrected by effects caused by correlated input data.
-174        This can take a while as the full correlation matrix
-175        has to be calculated (default False).
-176    num_grad : bool
-177        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
-178
-179    Notes
-180    -----
-181    Based on the orthogonal distance regression module of scipy
-182    '''
-183
-184    output = Fit_result()
+158        For multiple x values func can be of the form
+159
+160        ```python
+161        def func(a, x):
+162            (x1, x2) = x
+163            return a[0] * x1 ** 2 + a[1] * x2
+164        ```
+165
+166        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
+167        will not work.
+168    silent : bool, optional
+169        If true all output to the console is omitted (default False).
+170    initial_guess : list
+171        can provide an initial guess for the input parameters. Relevant for non-linear
+172        fits with many parameters.
+173    expected_chisquare : bool
+174        If true prints the expected chisquare which is
+175        corrected by effects caused by correlated input data.
+176        This can take a while as the full correlation matrix
+177        has to be calculated (default False).
+178    num_grad : bool
+179        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
+180
+181    Notes
+182    -----
+183    Based on the orthogonal distance regression module of scipy
+184    '''
 185
-186    output.fit_function = func
+186    output = Fit_result()
 187
-188    x = np.array(x)
+188    output.fit_function = func
 189
-190    x_shape = x.shape
+190    x = np.array(x)
 191
-192    if kwargs.get('num_grad') is True:
-193        jacobian = num_jacobian
-194        hessian = num_hessian
-195    else:
-196        jacobian = auto_jacobian
-197        hessian = auto_hessian
-198
-199    if not callable(func):
-200        raise TypeError('func has to be a function.')
-201
-202    for i in range(42):
-203        try:
-204            func(np.arange(i), x.T[0])
-205        except TypeError:
-206            continue
-207        except IndexError:
+192    x_shape = x.shape
+193
+194    if kwargs.get('num_grad') is True:
+195        jacobian = num_jacobian
+196        hessian = num_hessian
+197    else:
+198        jacobian = auto_jacobian
+199        hessian = auto_hessian
+200
+201    if not callable(func):
+202        raise TypeError('func has to be a function.')
+203
+204    for i in range(42):
+205        try:
+206            func(np.arange(i), x.T[0])
+207        except TypeError:
 208            continue
-209        else:
-210            break
-211    else:
-212        raise RuntimeError("Fit function is not valid.")
-213
-214    n_parms = i
-215    if not silent:
-216        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
-217
-218    x_f = np.vectorize(lambda o: o.value)(x)
-219    dx_f = np.vectorize(lambda o: o.dvalue)(x)
-220    y_f = np.array([o.value for o in y])
-221    dy_f = np.array([o.dvalue for o in y])
-222
-223    if np.any(np.asarray(dx_f) <= 0.0):
-224        raise Exception('No x errors available, run the gamma method first.')
-225
-226    if np.any(np.asarray(dy_f) <= 0.0):
-227        raise Exception('No y errors available, run the gamma method first.')
-228
-229    if 'initial_guess' in kwargs:
-230        x0 = kwargs.get('initial_guess')
-231        if len(x0) != n_parms:
-232            raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
-233    else:
-234        x0 = [1] * n_parms
-235
-236    data = RealData(x_f, y_f, sx=dx_f, sy=dy_f)
-237    model = Model(func)
-238    odr = ODR(data, model, x0, partol=np.finfo(np.float64).eps)
-239    odr.set_job(fit_type=0, deriv=1)
-240    out = odr.run()
-241
-242    output.residual_variance = out.res_var
+209        except IndexError:
+210            continue
+211        else:
+212            break
+213    else:
+214        raise RuntimeError("Fit function is not valid.")
+215
+216    n_parms = i
+217    if not silent:
+218        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
+219
+220    x_f = np.vectorize(lambda o: o.value)(x)
+221    dx_f = np.vectorize(lambda o: o.dvalue)(x)
+222    y_f = np.array([o.value for o in y])
+223    dy_f = np.array([o.dvalue for o in y])
+224
+225    if np.any(np.asarray(dx_f) <= 0.0):
+226        raise Exception('No x errors available, run the gamma method first.')
+227
+228    if np.any(np.asarray(dy_f) <= 0.0):
+229        raise Exception('No y errors available, run the gamma method first.')
+230
+231    if 'initial_guess' in kwargs:
+232        x0 = kwargs.get('initial_guess')
+233        if len(x0) != n_parms:
+234            raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
+235    else:
+236        x0 = [1] * n_parms
+237
+238    data = RealData(x_f, y_f, sx=dx_f, sy=dy_f)
+239    model = Model(func)
+240    odr = ODR(data, model, x0, partol=np.finfo(np.float64).eps)
+241    odr.set_job(fit_type=0, deriv=1)
+242    out = odr.run()
 243
-244    output.method = 'ODR'
+244    output.residual_variance = out.res_var
 245
-246    output.message = out.stopreason
+246    output.method = 'ODR'
 247
-248    output.xplus = out.xplus
+248    output.message = out.stopreason
 249
-250    if not silent:
-251        print('Method: ODR')
-252        print(*out.stopreason)
-253        print('Residual variance:', output.residual_variance)
-254
-255    if out.info > 3:
-256        raise Exception('The minimization procedure did not converge.')
-257
-258    m = x_f.size
+250    output.xplus = out.xplus
+251
+252    if not silent:
+253        print('Method: ODR')
+254        print(*out.stopreason)
+255        print('Residual variance:', output.residual_variance)
+256
+257    if out.info > 3:
+258        raise Exception('The minimization procedure did not converge.')
 259
-260    def odr_chisquare(p):
-261        model = func(p[:n_parms], p[n_parms:].reshape(x_shape))
-262        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((x_f - p[n_parms:].reshape(x_shape)) / dx_f) ** 2)
-263        return chisq
-264
-265    if kwargs.get('expected_chisquare') is True:
-266        W = np.diag(1 / np.asarray(np.concatenate((dy_f.ravel(), dx_f.ravel()))))
-267
-268        if kwargs.get('covariance') is not None:
-269            cov = kwargs.get('covariance')
-270        else:
-271            cov = covariance(np.concatenate((y, x.ravel())))
-272
-273        number_of_x_parameters = int(m / x_f.shape[-1])
+260    m = x_f.size
+261
+262    def odr_chisquare(p):
+263        model = func(p[:n_parms], p[n_parms:].reshape(x_shape))
+264        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((x_f - p[n_parms:].reshape(x_shape)) / dx_f) ** 2)
+265        return chisq
+266
+267    if kwargs.get('expected_chisquare') is True:
+268        W = np.diag(1 / np.asarray(np.concatenate((dy_f.ravel(), dx_f.ravel()))))
+269
+270        if kwargs.get('covariance') is not None:
+271            cov = kwargs.get('covariance')
+272        else:
+273            cov = covariance(np.concatenate((y, x.ravel())))
 274
-275        old_jac = jacobian(func)(out.beta, out.xplus)
-276        fused_row1 = np.concatenate((old_jac, np.concatenate((number_of_x_parameters * [np.zeros(old_jac.shape)]), axis=0)))
-277        fused_row2 = np.concatenate((jacobian(lambda x, y: func(y, x))(out.xplus, out.beta).reshape(x_f.shape[-1], x_f.shape[-1] * number_of_x_parameters), np.identity(number_of_x_parameters * old_jac.shape[0])))
-278        new_jac = np.concatenate((fused_row1, fused_row2), axis=1)
-279
-280        A = W @ new_jac
-281        P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
-282        expected_chisquare = np.trace((np.identity(P_phi.shape[0]) - P_phi) @ W @ cov @ W)
-283        if expected_chisquare <= 0.0:
-284            warnings.warn("Negative expected_chisquare.", RuntimeWarning)
-285            expected_chisquare = np.abs(expected_chisquare)
-286        output.chisquare_by_expected_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel()))) / expected_chisquare
-287        if not silent:
-288            print('chisquare/expected_chisquare:',
-289                  output.chisquare_by_expected_chisquare)
-290
-291    fitp = out.beta
-292    try:
-293        hess = hessian(odr_chisquare)(np.concatenate((fitp, out.xplus.ravel())))
-294    except TypeError:
-295        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
-296
-297    def odr_chisquare_compact_x(d):
-298        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
-299        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((d[n_parms + m:].reshape(x_shape) - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
-300        return chisq
-301
-302    jac_jac_x = hessian(odr_chisquare_compact_x)(np.concatenate((fitp, out.xplus.ravel(), x_f.ravel())))
+275        number_of_x_parameters = int(m / x_f.shape[-1])
+276
+277        old_jac = jacobian(func)(out.beta, out.xplus)
+278        fused_row1 = np.concatenate((old_jac, np.concatenate((number_of_x_parameters * [np.zeros(old_jac.shape)]), axis=0)))
+279        fused_row2 = np.concatenate((jacobian(lambda x, y: func(y, x))(out.xplus, out.beta).reshape(x_f.shape[-1], x_f.shape[-1] * number_of_x_parameters), np.identity(number_of_x_parameters * old_jac.shape[0])))
+280        new_jac = np.concatenate((fused_row1, fused_row2), axis=1)
+281
+282        A = W @ new_jac
+283        P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
+284        expected_chisquare = np.trace((np.identity(P_phi.shape[0]) - P_phi) @ W @ cov @ W)
+285        if expected_chisquare <= 0.0:
+286            warnings.warn("Negative expected_chisquare.", RuntimeWarning)
+287            expected_chisquare = np.abs(expected_chisquare)
+288        output.chisquare_by_expected_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel()))) / expected_chisquare
+289        if not silent:
+290            print('chisquare/expected_chisquare:',
+291                  output.chisquare_by_expected_chisquare)
+292
+293    fitp = out.beta
+294    try:
+295        hess = hessian(odr_chisquare)(np.concatenate((fitp, out.xplus.ravel())))
+296    except TypeError:
+297        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+298
+299    def odr_chisquare_compact_x(d):
+300        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
+301        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((d[n_parms + m:].reshape(x_shape) - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
+302        return chisq
 303
-304    # Compute hess^{-1} @ jac_jac_x[:n_parms + m, n_parms + m:] using LAPACK dgesv
-305    try:
-306        deriv_x = -scipy.linalg.solve(hess, jac_jac_x[:n_parms + m, n_parms + m:])
-307    except np.linalg.LinAlgError:
-308        raise Exception("Cannot invert hessian matrix.")
-309
-310    def odr_chisquare_compact_y(d):
-311        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
-312        chisq = anp.sum(((d[n_parms + m:] - model) / dy_f) ** 2) + anp.sum(((x_f - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
-313        return chisq
-314
-315    jac_jac_y = hessian(odr_chisquare_compact_y)(np.concatenate((fitp, out.xplus.ravel(), y_f)))
+304    jac_jac_x = hessian(odr_chisquare_compact_x)(np.concatenate((fitp, out.xplus.ravel(), x_f.ravel())))
+305
+306    # Compute hess^{-1} @ jac_jac_x[:n_parms + m, n_parms + m:] using LAPACK dgesv
+307    try:
+308        deriv_x = -scipy.linalg.solve(hess, jac_jac_x[:n_parms + m, n_parms + m:])
+309    except np.linalg.LinAlgError:
+310        raise Exception("Cannot invert hessian matrix.")
+311
+312    def odr_chisquare_compact_y(d):
+313        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
+314        chisq = anp.sum(((d[n_parms + m:] - model) / dy_f) ** 2) + anp.sum(((x_f - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
+315        return chisq
 316
-317    # Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv
-318    try:
-319        deriv_y = -scipy.linalg.solve(hess, jac_jac_y[:n_parms + m, n_parms + m:])
-320    except np.linalg.LinAlgError:
-321        raise Exception("Cannot invert hessian matrix.")
-322
-323    result = []
-324    for i in range(n_parms):
-325        result.append(derived_observable(lambda my_var, **kwargs: (my_var[0] + np.finfo(np.float64).eps) / (x.ravel()[0].value + np.finfo(np.float64).eps) * out.beta[i], list(x.ravel()) + list(y), man_grad=list(deriv_x[i]) + list(deriv_y[i])))
-326
-327    output.fit_parameters = result
+317    jac_jac_y = hessian(odr_chisquare_compact_y)(np.concatenate((fitp, out.xplus.ravel(), y_f)))
+318
+319    # Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv
+320    try:
+321        deriv_y = -scipy.linalg.solve(hess, jac_jac_y[:n_parms + m, n_parms + m:])
+322    except np.linalg.LinAlgError:
+323        raise Exception("Cannot invert hessian matrix.")
+324
+325    result = []
+326    for i in range(n_parms):
+327        result.append(derived_observable(lambda my_var, **kwargs: (my_var[0] + np.finfo(np.float64).eps) / (x.ravel()[0].value + np.finfo(np.float64).eps) * out.beta[i], list(x.ravel()) + list(y), man_grad=list(deriv_x[i]) + list(deriv_y[i])))
 328
-329    output.odr_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel())))
-330    output.dof = x.shape[-1] - n_parms
-331    output.p_value = 1 - scipy.stats.chi2.cdf(output.odr_chisquare, output.dof)
-332
-333    return output
+329    output.fit_parameters = result
+330
+331    output.odr_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel())))
+332    output.dof = x.shape[-1] - n_parms
+333    output.p_value = 1 - scipy.stats.chi2.cdf(output.odr_chisquare, output.dof)
 334
-335
-336def _prior_fit(x, y, func, priors, silent=False, **kwargs):
-337    output = Fit_result()
-338
-339    output.fit_function = func
+335    return output
+336
+337
+338def _prior_fit(x, y, func, priors, silent=False, **kwargs):
+339    output = Fit_result()
 340
-341    x = np.asarray(x)
+341    output.fit_function = func
 342
-343    if kwargs.get('num_grad') is True:
-344        hessian = num_hessian
-345    else:
-346        hessian = auto_hessian
-347
-348    if not callable(func):
-349        raise TypeError('func has to be a function.')
-350
-351    for i in range(100):
-352        try:
-353            func(np.arange(i), 0)
-354        except TypeError:
-355            continue
-356        except IndexError:
+343    x = np.asarray(x)
+344
+345    if kwargs.get('num_grad') is True:
+346        hessian = num_hessian
+347    else:
+348        hessian = auto_hessian
+349
+350    if not callable(func):
+351        raise TypeError('func has to be a function.')
+352
+353    for i in range(100):
+354        try:
+355            func(np.arange(i), 0)
+356        except TypeError:
 357            continue
-358        else:
-359            break
-360    else:
-361        raise RuntimeError("Fit function is not valid.")
-362
-363    n_parms = i
+358        except IndexError:
+359            continue
+360        else:
+361            break
+362    else:
+363        raise RuntimeError("Fit function is not valid.")
 364
-365    if n_parms != len(priors):
-366        raise Exception('Priors does not have the correct length.')
-367
-368    def extract_val_and_dval(string):
-369        split_string = string.split('(')
-370        if '.' in split_string[0] and '.' not in split_string[1][:-1]:
-371            factor = 10 ** -len(split_string[0].partition('.')[2])
-372        else:
-373            factor = 1
-374        return float(split_string[0]), float(split_string[1][:-1]) * factor
-375
-376    loc_priors = []
-377    for i_n, i_prior in enumerate(priors):
-378        if isinstance(i_prior, Obs):
-379            loc_priors.append(i_prior)
-380        else:
-381            loc_val, loc_dval = extract_val_and_dval(i_prior)
-382            loc_priors.append(cov_Obs(loc_val, loc_dval ** 2, '#prior' + str(i_n) + f"_{np.random.randint(2147483647):010d}"))
-383
-384    output.priors = loc_priors
+365    n_parms = i
+366
+367    if n_parms != len(priors):
+368        raise Exception('Priors does not have the correct length.')
+369
+370    def extract_val_and_dval(string):
+371        split_string = string.split('(')
+372        if '.' in split_string[0] and '.' not in split_string[1][:-1]:
+373            factor = 10 ** -len(split_string[0].partition('.')[2])
+374        else:
+375            factor = 1
+376        return float(split_string[0]), float(split_string[1][:-1]) * factor
+377
+378    loc_priors = []
+379    for i_n, i_prior in enumerate(priors):
+380        if isinstance(i_prior, Obs):
+381            loc_priors.append(i_prior)
+382        else:
+383            loc_val, loc_dval = extract_val_and_dval(i_prior)
+384            loc_priors.append(cov_Obs(loc_val, loc_dval ** 2, '#prior' + str(i_n) + f"_{np.random.randint(2147483647):010d}"))
 385
-386    if not silent:
-387        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
-388
-389    y_f = [o.value for o in y]
-390    dy_f = [o.dvalue for o in y]
-391
-392    if np.any(np.asarray(dy_f) <= 0.0):
-393        raise Exception('No y errors available, run the gamma method first.')
-394
-395    p_f = [o.value for o in loc_priors]
-396    dp_f = [o.dvalue for o in loc_priors]
-397
-398    if np.any(np.asarray(dp_f) <= 0.0):
-399        raise Exception('No prior errors available, run the gamma method first.')
-400
-401    if 'initial_guess' in kwargs:
-402        x0 = kwargs.get('initial_guess')
-403        if len(x0) != n_parms:
-404            raise Exception('Initial guess does not have the correct length.')
-405    else:
-406        x0 = p_f
-407
-408    def chisqfunc(p):
-409        model = func(p, x)
-410        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((p_f - p) / dp_f) ** 2)
-411        return chisq
-412
-413    if not silent:
-414        print('Method: migrad')
-415
-416    m = iminuit.Minuit(chisqfunc, x0)
-417    m.errordef = 1
-418    m.print_level = 0
-419    if 'tol' in kwargs:
-420        m.tol = kwargs.get('tol')
-421    else:
-422        m.tol = 1e-4
-423    m.migrad()
-424    params = np.asarray(m.values)
-425
-426    output.chisquare_by_dof = m.fval / len(x)
+386    output.priors = loc_priors
+387
+388    if not silent:
+389        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
+390
+391    y_f = [o.value for o in y]
+392    dy_f = [o.dvalue for o in y]
+393
+394    if np.any(np.asarray(dy_f) <= 0.0):
+395        raise Exception('No y errors available, run the gamma method first.')
+396
+397    p_f = [o.value for o in loc_priors]
+398    dp_f = [o.dvalue for o in loc_priors]
+399
+400    if np.any(np.asarray(dp_f) <= 0.0):
+401        raise Exception('No prior errors available, run the gamma method first.')
+402
+403    if 'initial_guess' in kwargs:
+404        x0 = kwargs.get('initial_guess')
+405        if len(x0) != n_parms:
+406            raise Exception('Initial guess does not have the correct length.')
+407    else:
+408        x0 = p_f
+409
+410    def chisqfunc(p):
+411        model = func(p, x)
+412        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((p_f - p) / dp_f) ** 2)
+413        return chisq
+414
+415    if not silent:
+416        print('Method: migrad')
+417
+418    m = iminuit.Minuit(chisqfunc, x0)
+419    m.errordef = 1
+420    m.print_level = 0
+421    if 'tol' in kwargs:
+422        m.tol = kwargs.get('tol')
+423    else:
+424        m.tol = 1e-4
+425    m.migrad()
+426    params = np.asarray(m.values)
 427
-428    output.method = 'migrad'
+428    output.chisquare_by_dof = m.fval / len(x)
 429
-430    if not silent:
-431        print('chisquare/d.o.f.:', output.chisquare_by_dof)
-432
-433    if not m.fmin.is_valid:
-434        raise Exception('The minimization procedure did not converge.')
-435
-436    hess = hessian(chisqfunc)(params)
-437    hess_inv = np.linalg.pinv(hess)
-438
-439    def chisqfunc_compact(d):
-440        model = func(d[:n_parms], x)
-441        chisq = anp.sum(((d[n_parms: n_parms + len(x)] - model) / dy_f) ** 2) + anp.sum(((d[n_parms + len(x):] - d[:n_parms]) / dp_f) ** 2)
-442        return chisq
-443
-444    jac_jac = hessian(chisqfunc_compact)(np.concatenate((params, y_f, p_f)))
+430    output.method = 'migrad'
+431
+432    if not silent:
+433        print('chisquare/d.o.f.:', output.chisquare_by_dof)
+434
+435    if not m.fmin.is_valid:
+436        raise Exception('The minimization procedure did not converge.')
+437
+438    hess = hessian(chisqfunc)(params)
+439    hess_inv = np.linalg.pinv(hess)
+440
+441    def chisqfunc_compact(d):
+442        model = func(d[:n_parms], x)
+443        chisq = anp.sum(((d[n_parms: n_parms + len(x)] - model) / dy_f) ** 2) + anp.sum(((d[n_parms + len(x):] - d[:n_parms]) / dp_f) ** 2)
+444        return chisq
 445
-446    deriv = -hess_inv @ jac_jac[:n_parms, n_parms:]
+446    jac_jac = hessian(chisqfunc_compact)(np.concatenate((params, y_f, p_f)))
 447
-448    result = []
-449    for i in range(n_parms):
-450        result.append(derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (y[0].value + np.finfo(np.float64).eps) * params[i], list(y) + list(loc_priors), man_grad=list(deriv[i])))
-451
-452    output.fit_parameters = result
-453    output.chisquare = chisqfunc(np.asarray(params))
-454
-455    if kwargs.get('resplot') is True:
-456        residual_plot(x, y, func, result)
-457
-458    if kwargs.get('qqplot') is True:
-459        qqplot(x, y, func, result)
-460
-461    return output
+448    deriv = -hess_inv @ jac_jac[:n_parms, n_parms:]
+449
+450    result = []
+451    for i in range(n_parms):
+452        result.append(derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (y[0].value + np.finfo(np.float64).eps) * params[i], list(y) + list(loc_priors), man_grad=list(deriv[i])))
+453
+454    output.fit_parameters = result
+455    output.chisquare = chisqfunc(np.asarray(params))
+456
+457    if kwargs.get('resplot') is True:
+458        residual_plot(x, y, func, result)
+459
+460    if kwargs.get('qqplot') is True:
+461        qqplot(x, y, func, result)
 462
-463
-464def _standard_fit(x, y, func, silent=False, **kwargs):
+463    return output
+464
 465
-466    output = Fit_result()
+466def _standard_fit(x, y, func, silent=False, **kwargs):
 467
-468    output.fit_function = func
+468    output = Fit_result()
 469
-470    x = np.asarray(x)
+470    output.fit_function = func
 471
-472    if kwargs.get('num_grad') is True:
-473        jacobian = num_jacobian
-474        hessian = num_hessian
-475    else:
-476        jacobian = auto_jacobian
-477        hessian = auto_hessian
-478
-479    if x.shape[-1] != len(y):
-480        raise Exception('x and y input have to have the same length')
-481
-482    if len(x.shape) > 2:
-483        raise Exception('Unknown format for x values')
-484
-485    if not callable(func):
-486        raise TypeError('func has to be a function.')
-487
-488    for i in range(42):
-489        try:
-490            func(np.arange(i), x.T[0])
-491        except TypeError:
-492            continue
-493        except IndexError:
+472    x = np.asarray(x)
+473
+474    if kwargs.get('num_grad') is True:
+475        jacobian = num_jacobian
+476        hessian = num_hessian
+477    else:
+478        jacobian = auto_jacobian
+479        hessian = auto_hessian
+480
+481    if x.shape[-1] != len(y):
+482        raise Exception('x and y input have to have the same length')
+483
+484    if len(x.shape) > 2:
+485        raise Exception('Unknown format for x values')
+486
+487    if not callable(func):
+488        raise TypeError('func has to be a function.')
+489
+490    for i in range(42):
+491        try:
+492            func(np.arange(i), x.T[0])
+493        except TypeError:
 494            continue
-495        else:
-496            break
-497    else:
-498        raise RuntimeError("Fit function is not valid.")
-499
-500    n_parms = i
+495        except IndexError:
+496            continue
+497        else:
+498            break
+499    else:
+500        raise RuntimeError("Fit function is not valid.")
 501
-502    if not silent:
-503        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
-504
-505    y_f = [o.value for o in y]
-506    dy_f = [o.dvalue for o in y]
-507
-508    if np.any(np.asarray(dy_f) <= 0.0):
-509        raise Exception('No y errors available, run the gamma method first.')
-510
-511    if 'initial_guess' in kwargs:
-512        x0 = kwargs.get('initial_guess')
-513        if len(x0) != n_parms:
-514            raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
-515    else:
-516        x0 = [0.1] * n_parms
-517
-518    if kwargs.get('correlated_fit') is True:
-519        corr = covariance(y, correlation=True, **kwargs)
-520        covdiag = np.diag(1 / np.asarray(dy_f))
-521        condn = np.linalg.cond(corr)
-522        if condn > 0.1 / np.finfo(float).eps:
-523            raise Exception(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
-524        if condn > 1e13:
-525            warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
-526        chol = np.linalg.cholesky(corr)
-527        chol_inv = scipy.linalg.solve_triangular(chol, covdiag, lower=True)
-528
-529        def chisqfunc_corr(p):
-530            model = func(p, x)
-531            chisq = anp.sum(anp.dot(chol_inv, (y_f - model)) ** 2)
-532            return chisq
-533
-534    def chisqfunc(p):
-535        model = func(p, x)
-536        chisq = anp.sum(((y_f - model) / dy_f) ** 2)
-537        return chisq
-538
-539    output.method = kwargs.get('method', 'Levenberg-Marquardt')
-540    if not silent:
-541        print('Method:', output.method)
-542
-543    if output.method != 'Levenberg-Marquardt':
-544        if output.method == 'migrad':
-545            fit_result = iminuit.minimize(chisqfunc, x0, tol=1e-4)  # Stopping criterion 0.002 * tol * errordef
-546            if kwargs.get('correlated_fit') is True:
-547                fit_result = iminuit.minimize(chisqfunc_corr, fit_result.x, tol=1e-4)  # Stopping criterion 0.002 * tol * errordef
-548            output.iterations = fit_result.nfev
-549        else:
-550            fit_result = scipy.optimize.minimize(chisqfunc, x0, method=kwargs.get('method'), tol=1e-12)
-551            if kwargs.get('correlated_fit') is True:
-552                fit_result = scipy.optimize.minimize(chisqfunc_corr, fit_result.x, method=kwargs.get('method'), tol=1e-12)
-553            output.iterations = fit_result.nit
-554
-555        chisquare = fit_result.fun
+502    n_parms = i
+503
+504    if not silent:
+505        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
+506
+507    y_f = [o.value for o in y]
+508    dy_f = [o.dvalue for o in y]
+509
+510    if np.any(np.asarray(dy_f) <= 0.0):
+511        raise Exception('No y errors available, run the gamma method first.')
+512
+513    if 'initial_guess' in kwargs:
+514        x0 = kwargs.get('initial_guess')
+515        if len(x0) != n_parms:
+516            raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
+517    else:
+518        x0 = [0.1] * n_parms
+519
+520    if kwargs.get('correlated_fit') is True:
+521        corr = covariance(y, correlation=True, **kwargs)
+522        covdiag = np.diag(1 / np.asarray(dy_f))
+523        condn = np.linalg.cond(corr)
+524        if condn > 0.1 / np.finfo(float).eps:
+525            raise Exception(f"Cannot invert correlation matrix as its condition number exceeds machine precision ({condn:1.2e})")
+526        if condn > 1e13:
+527            warnings.warn("Correlation matrix may be ill-conditioned, condition number: {%1.2e}" % (condn), RuntimeWarning)
+528        chol = np.linalg.cholesky(corr)
+529        chol_inv = scipy.linalg.solve_triangular(chol, covdiag, lower=True)
+530
+531        def chisqfunc_corr(p):
+532            model = func(p, x)
+533            chisq = anp.sum(anp.dot(chol_inv, (y_f - model)) ** 2)
+534            return chisq
+535
+536    def chisqfunc(p):
+537        model = func(p, x)
+538        chisq = anp.sum(((y_f - model) / dy_f) ** 2)
+539        return chisq
+540
+541    output.method = kwargs.get('method', 'Levenberg-Marquardt')
+542    if not silent:
+543        print('Method:', output.method)
+544
+545    if output.method != 'Levenberg-Marquardt':
+546        if output.method == 'migrad':
+547            fit_result = iminuit.minimize(chisqfunc, x0, tol=1e-4)  # Stopping criterion 0.002 * tol * errordef
+548            if kwargs.get('correlated_fit') is True:
+549                fit_result = iminuit.minimize(chisqfunc_corr, fit_result.x, tol=1e-4)  # Stopping criterion 0.002 * tol * errordef
+550            output.iterations = fit_result.nfev
+551        else:
+552            fit_result = scipy.optimize.minimize(chisqfunc, x0, method=kwargs.get('method'), tol=1e-12)
+553            if kwargs.get('correlated_fit') is True:
+554                fit_result = scipy.optimize.minimize(chisqfunc_corr, fit_result.x, method=kwargs.get('method'), tol=1e-12)
+555            output.iterations = fit_result.nit
 556
-557    else:
-558        if kwargs.get('correlated_fit') is True:
-559            def chisqfunc_residuals_corr(p):
-560                model = func(p, x)
-561                chisq = anp.dot(chol_inv, (y_f - model))
-562                return chisq
-563
-564        def chisqfunc_residuals(p):
-565            model = func(p, x)
-566            chisq = ((y_f - model) / dy_f)
-567            return chisq
-568
-569        fit_result = scipy.optimize.least_squares(chisqfunc_residuals, x0, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
-570        if kwargs.get('correlated_fit') is True:
-571            fit_result = scipy.optimize.least_squares(chisqfunc_residuals_corr, fit_result.x, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
-572
-573        chisquare = np.sum(fit_result.fun ** 2)
-574        if kwargs.get('correlated_fit') is True:
-575            assert np.isclose(chisquare, chisqfunc_corr(fit_result.x), atol=1e-14)
-576        else:
-577            assert np.isclose(chisquare, chisqfunc(fit_result.x), atol=1e-14)
-578
-579        output.iterations = fit_result.nfev
+557        chisquare = fit_result.fun
+558
+559    else:
+560        if kwargs.get('correlated_fit') is True:
+561            def chisqfunc_residuals_corr(p):
+562                model = func(p, x)
+563                chisq = anp.dot(chol_inv, (y_f - model))
+564                return chisq
+565
+566        def chisqfunc_residuals(p):
+567            model = func(p, x)
+568            chisq = ((y_f - model) / dy_f)
+569            return chisq
+570
+571        fit_result = scipy.optimize.least_squares(chisqfunc_residuals, x0, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
+572        if kwargs.get('correlated_fit') is True:
+573            fit_result = scipy.optimize.least_squares(chisqfunc_residuals_corr, fit_result.x, method='lm', ftol=1e-15, gtol=1e-15, xtol=1e-15)
+574
+575        chisquare = np.sum(fit_result.fun ** 2)
+576        if kwargs.get('correlated_fit') is True:
+577            assert np.isclose(chisquare, chisqfunc_corr(fit_result.x), atol=1e-14)
+578        else:
+579            assert np.isclose(chisquare, chisqfunc(fit_result.x), atol=1e-14)
 580
-581    if not fit_result.success:
-582        raise Exception('The minimization procedure did not converge.')
-583
-584    if x.shape[-1] - n_parms > 0:
-585        output.chisquare_by_dof = chisquare / (x.shape[-1] - n_parms)
-586    else:
-587        output.chisquare_by_dof = float('nan')
-588
-589    output.message = fit_result.message
-590    if not silent:
-591        print(fit_result.message)
-592        print('chisquare/d.o.f.:', output.chisquare_by_dof)
-593
-594    if kwargs.get('expected_chisquare') is True:
-595        if kwargs.get('correlated_fit') is not True:
-596            W = np.diag(1 / np.asarray(dy_f))
-597            cov = covariance(y)
-598            A = W @ jacobian(func)(fit_result.x, x)
-599            P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
-600            expected_chisquare = np.trace((np.identity(x.shape[-1]) - P_phi) @ W @ cov @ W)
-601            output.chisquare_by_expected_chisquare = chisquare / expected_chisquare
-602            if not silent:
-603                print('chisquare/expected_chisquare:',
-604                      output.chisquare_by_expected_chisquare)
-605
-606    fitp = fit_result.x
-607    try:
-608        if kwargs.get('correlated_fit') is True:
-609            hess = hessian(chisqfunc_corr)(fitp)
-610        else:
-611            hess = hessian(chisqfunc)(fitp)
-612    except TypeError:
-613        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
-614
-615    if kwargs.get('correlated_fit') is True:
-616        def chisqfunc_compact(d):
-617            model = func(d[:n_parms], x)
-618            chisq = anp.sum(anp.dot(chol_inv, (d[n_parms:] - model)) ** 2)
-619            return chisq
-620
-621    else:
-622        def chisqfunc_compact(d):
-623            model = func(d[:n_parms], x)
-624            chisq = anp.sum(((d[n_parms:] - model) / dy_f) ** 2)
-625            return chisq
-626
-627    jac_jac = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f)))
+581        output.iterations = fit_result.nfev
+582
+583    if not fit_result.success:
+584        raise Exception('The minimization procedure did not converge.')
+585
+586    if x.shape[-1] - n_parms > 0:
+587        output.chisquare_by_dof = chisquare / (x.shape[-1] - n_parms)
+588    else:
+589        output.chisquare_by_dof = float('nan')
+590
+591    output.message = fit_result.message
+592    if not silent:
+593        print(fit_result.message)
+594        print('chisquare/d.o.f.:', output.chisquare_by_dof)
+595
+596    if kwargs.get('expected_chisquare') is True:
+597        if kwargs.get('correlated_fit') is not True:
+598            W = np.diag(1 / np.asarray(dy_f))
+599            cov = covariance(y)
+600            A = W @ jacobian(func)(fit_result.x, x)
+601            P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
+602            expected_chisquare = np.trace((np.identity(x.shape[-1]) - P_phi) @ W @ cov @ W)
+603            output.chisquare_by_expected_chisquare = chisquare / expected_chisquare
+604            if not silent:
+605                print('chisquare/expected_chisquare:',
+606                      output.chisquare_by_expected_chisquare)
+607
+608    fitp = fit_result.x
+609    try:
+610        if kwargs.get('correlated_fit') is True:
+611            hess = hessian(chisqfunc_corr)(fitp)
+612        else:
+613            hess = hessian(chisqfunc)(fitp)
+614    except TypeError:
+615        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+616
+617    if kwargs.get('correlated_fit') is True:
+618        def chisqfunc_compact(d):
+619            model = func(d[:n_parms], x)
+620            chisq = anp.sum(anp.dot(chol_inv, (d[n_parms:] - model)) ** 2)
+621            return chisq
+622
+623    else:
+624        def chisqfunc_compact(d):
+625            model = func(d[:n_parms], x)
+626            chisq = anp.sum(((d[n_parms:] - model) / dy_f) ** 2)
+627            return chisq
 628
-629    # Compute hess^{-1} @ jac_jac[:n_parms, n_parms:] using LAPACK dgesv
-630    try:
-631        deriv = -scipy.linalg.solve(hess, jac_jac[:n_parms, n_parms:])
-632    except np.linalg.LinAlgError:
-633        raise Exception("Cannot invert hessian matrix.")
-634
-635    result = []
-636    for i in range(n_parms):
-637        result.append(derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (y[0].value + np.finfo(np.float64).eps) * fit_result.x[i], list(y), man_grad=list(deriv[i])))
-638
-639    output.fit_parameters = result
+629    jac_jac = hessian(chisqfunc_compact)(np.concatenate((fitp, y_f)))
+630
+631    # Compute hess^{-1} @ jac_jac[:n_parms, n_parms:] using LAPACK dgesv
+632    try:
+633        deriv = -scipy.linalg.solve(hess, jac_jac[:n_parms, n_parms:])
+634    except np.linalg.LinAlgError:
+635        raise Exception("Cannot invert hessian matrix.")
+636
+637    result = []
+638    for i in range(n_parms):
+639        result.append(derived_observable(lambda x, **kwargs: (x[0] + np.finfo(np.float64).eps) / (y[0].value + np.finfo(np.float64).eps) * fit_result.x[i], list(y), man_grad=list(deriv[i])))
 640
-641    output.chisquare = chisquare
-642    output.dof = x.shape[-1] - n_parms
-643    output.p_value = 1 - scipy.stats.chi2.cdf(output.chisquare, output.dof)
-644    # Hotelling t-squared p-value for correlated fits.
-645    if kwargs.get('correlated_fit') is True:
-646        n_cov = np.min(np.vectorize(lambda x: x.N)(y))
-647        output.t2_p_value = 1 - scipy.stats.f.cdf((n_cov - output.dof) / (output.dof * (n_cov - 1)) * output.chisquare,
-648                                                  output.dof, n_cov - output.dof)
-649
-650    if kwargs.get('resplot') is True:
-651        residual_plot(x, y, func, result)
-652
-653    if kwargs.get('qqplot') is True:
-654        qqplot(x, y, func, result)
-655
-656    return output
+641    output.fit_parameters = result
+642
+643    output.chisquare = chisquare
+644    output.dof = x.shape[-1] - n_parms
+645    output.p_value = 1 - scipy.stats.chi2.cdf(output.chisquare, output.dof)
+646    # Hotelling t-squared p-value for correlated fits.
+647    if kwargs.get('correlated_fit') is True:
+648        n_cov = np.min(np.vectorize(lambda x: x.N)(y))
+649        output.t2_p_value = 1 - scipy.stats.f.cdf((n_cov - output.dof) / (output.dof * (n_cov - 1)) * output.chisquare,
+650                                                  output.dof, n_cov - output.dof)
+651
+652    if kwargs.get('resplot') is True:
+653        residual_plot(x, y, func, result)
+654
+655    if kwargs.get('qqplot') is True:
+656        qqplot(x, y, func, result)
 657
-658
-659def fit_lin(x, y, **kwargs):
-660    """Performs a linear fit to y = n + m * x and returns two Obs n, m.
-661
-662    Parameters
-663    ----------
-664    x : list
-665        Can either be a list of floats in which case no xerror is assumed, or
-666        a list of Obs, where the dvalues of the Obs are used as xerror for the fit.
-667    y : list
-668        List of Obs, the dvalues of the Obs are used as yerror for the fit.
-669    """
-670
-671    def f(a, x):
-672        y = a[0] + a[1] * x
-673        return y
-674
-675    if all(isinstance(n, Obs) for n in x):
-676        out = total_least_squares(x, y, f, **kwargs)
-677        return out.fit_parameters
-678    elif all(isinstance(n, float) or isinstance(n, int) for n in x) or isinstance(x, np.ndarray):
-679        out = least_squares(x, y, f, **kwargs)
-680        return out.fit_parameters
-681    else:
-682        raise Exception('Unsupported types for x')
-683
-684
-685def qqplot(x, o_y, func, p):
-686    """Generates a quantile-quantile plot of the fit result which can be used to
-687       check if the residuals of the fit are gaussian distributed.
-688    """
-689
-690    residuals = []
-691    for i_x, i_y in zip(x, o_y):
-692        residuals.append((i_y - func(p, i_x)) / i_y.dvalue)
-693    residuals = sorted(residuals)
-694    my_y = [o.value for o in residuals]
-695    probplot = scipy.stats.probplot(my_y)
-696    my_x = probplot[0][0]
-697    plt.figure(figsize=(8, 8 / 1.618))
-698    plt.errorbar(my_x, my_y, fmt='o')
-699    fit_start = my_x[0]
-700    fit_stop = my_x[-1]
-701    samples = np.arange(fit_start, fit_stop, 0.01)
-702    plt.plot(samples, samples, 'k--', zorder=11, label='Standard normal distribution')
-703    plt.plot(samples, probplot[1][0] * samples + probplot[1][1], zorder=10, label='Least squares fit, r=' + str(np.around(probplot[1][2], 3)), marker='', ls='-')
-704
-705    plt.xlabel('Theoretical quantiles')
-706    plt.ylabel('Ordered Values')
-707    plt.legend()
-708    plt.draw()
-709
-710
-711def residual_plot(x, y, func, fit_res):
-712    """ Generates a plot which compares the fit to the data and displays the corresponding residuals"""
-713    sorted_x = sorted(x)
-714    xstart = sorted_x[0] - 0.5 * (sorted_x[1] - sorted_x[0])
-715    xstop = sorted_x[-1] + 0.5 * (sorted_x[-1] - sorted_x[-2])
-716    x_samples = np.arange(xstart, xstop + 0.01, 0.01)
-717
-718    plt.figure(figsize=(8, 8 / 1.618))
-719    gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0)
-720    ax0 = plt.subplot(gs[0])
-721    ax0.errorbar(x, [o.value for o in y], yerr=[o.dvalue for o in y], ls='none', fmt='o', capsize=3, markersize=5, label='Data')
-722    ax0.plot(x_samples, func([o.value for o in fit_res], x_samples), label='Fit', zorder=10, ls='-', ms=0)
-723    ax0.set_xticklabels([])
-724    ax0.set_xlim([xstart, xstop])
+658    return output
+659
+660
+661def fit_lin(x, y, **kwargs):
+662    """Performs a linear fit to y = n + m * x and returns two Obs n, m.
+663
+664    Parameters
+665    ----------
+666    x : list
+667        Can either be a list of floats in which case no xerror is assumed, or
+668        a list of Obs, where the dvalues of the Obs are used as xerror for the fit.
+669    y : list
+670        List of Obs, the dvalues of the Obs are used as yerror for the fit.
+671    """
+672
+673    def f(a, x):
+674        y = a[0] + a[1] * x
+675        return y
+676
+677    if all(isinstance(n, Obs) for n in x):
+678        out = total_least_squares(x, y, f, **kwargs)
+679        return out.fit_parameters
+680    elif all(isinstance(n, float) or isinstance(n, int) for n in x) or isinstance(x, np.ndarray):
+681        out = least_squares(x, y, f, **kwargs)
+682        return out.fit_parameters
+683    else:
+684        raise Exception('Unsupported types for x')
+685
+686
+687def qqplot(x, o_y, func, p):
+688    """Generates a quantile-quantile plot of the fit result which can be used to
+689       check if the residuals of the fit are gaussian distributed.
+690    """
+691
+692    residuals = []
+693    for i_x, i_y in zip(x, o_y):
+694        residuals.append((i_y - func(p, i_x)) / i_y.dvalue)
+695    residuals = sorted(residuals)
+696    my_y = [o.value for o in residuals]
+697    probplot = scipy.stats.probplot(my_y)
+698    my_x = probplot[0][0]
+699    plt.figure(figsize=(8, 8 / 1.618))
+700    plt.errorbar(my_x, my_y, fmt='o')
+701    fit_start = my_x[0]
+702    fit_stop = my_x[-1]
+703    samples = np.arange(fit_start, fit_stop, 0.01)
+704    plt.plot(samples, samples, 'k--', zorder=11, label='Standard normal distribution')
+705    plt.plot(samples, probplot[1][0] * samples + probplot[1][1], zorder=10, label='Least squares fit, r=' + str(np.around(probplot[1][2], 3)), marker='', ls='-')
+706
+707    plt.xlabel('Theoretical quantiles')
+708    plt.ylabel('Ordered Values')
+709    plt.legend()
+710    plt.draw()
+711
+712
+713def residual_plot(x, y, func, fit_res):
+714    """ Generates a plot which compares the fit to the data and displays the corresponding residuals"""
+715    sorted_x = sorted(x)
+716    xstart = sorted_x[0] - 0.5 * (sorted_x[1] - sorted_x[0])
+717    xstop = sorted_x[-1] + 0.5 * (sorted_x[-1] - sorted_x[-2])
+718    x_samples = np.arange(xstart, xstop + 0.01, 0.01)
+719
+720    plt.figure(figsize=(8, 8 / 1.618))
+721    gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0)
+722    ax0 = plt.subplot(gs[0])
+723    ax0.errorbar(x, [o.value for o in y], yerr=[o.dvalue for o in y], ls='none', fmt='o', capsize=3, markersize=5, label='Data')
+724    ax0.plot(x_samples, func([o.value for o in fit_res], x_samples), label='Fit', zorder=10, ls='-', ms=0)
 725    ax0.set_xticklabels([])
-726    ax0.legend()
-727
-728    residuals = (np.asarray([o.value for o in y]) - func([o.value for o in fit_res], x)) / np.asarray([o.dvalue for o in y])
-729    ax1 = plt.subplot(gs[1])
-730    ax1.plot(x, residuals, 'ko', ls='none', markersize=5)
-731    ax1.tick_params(direction='out')
-732    ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True)
-733    ax1.axhline(y=0.0, ls='--', color='k', marker=" ")
-734    ax1.fill_between(x_samples, -1.0, 1.0, alpha=0.1, facecolor='k')
-735    ax1.set_xlim([xstart, xstop])
-736    ax1.set_ylabel('Residuals')
-737    plt.subplots_adjust(wspace=None, hspace=None)
-738    plt.draw()
-739
-740
-741def error_band(x, func, beta):
-742    """Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""
-743    cov = covariance(beta)
-744    if np.any(np.abs(cov - cov.T) > 1000 * np.finfo(np.float64).eps):
-745        warnings.warn("Covariance matrix is not symmetric within floating point precision", RuntimeWarning)
-746
-747    deriv = []
-748    for i, item in enumerate(x):
-749        deriv.append(np.array(egrad(func)([o.value for o in beta], item)))
-750
-751    err = []
-752    for i, item in enumerate(x):
-753        err.append(np.sqrt(deriv[i] @ cov @ deriv[i]))
-754    err = np.array(err)
-755
-756    return err
+726    ax0.set_xlim([xstart, xstop])
+727    ax0.set_xticklabels([])
+728    ax0.legend()
+729
+730    residuals = (np.asarray([o.value for o in y]) - func([o.value for o in fit_res], x)) / np.asarray([o.dvalue for o in y])
+731    ax1 = plt.subplot(gs[1])
+732    ax1.plot(x, residuals, 'ko', ls='none', markersize=5)
+733    ax1.tick_params(direction='out')
+734    ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True)
+735    ax1.axhline(y=0.0, ls='--', color='k', marker=" ")
+736    ax1.fill_between(x_samples, -1.0, 1.0, alpha=0.1, facecolor='k')
+737    ax1.set_xlim([xstart, xstop])
+738    ax1.set_ylabel('Residuals')
+739    plt.subplots_adjust(wspace=None, hspace=None)
+740    plt.draw()
+741
+742
+743def error_band(x, func, beta):
+744    """Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""
+745    cov = covariance(beta)
+746    if np.any(np.abs(cov - cov.T) > 1000 * np.finfo(np.float64).eps):
+747        warnings.warn("Covariance matrix is not symmetric within floating point precision", RuntimeWarning)
+748
+749    deriv = []
+750    for i, item in enumerate(x):
+751        deriv.append(np.array(egrad(func)([o.value for o in beta], item)))
+752
+753    err = []
+754    for i, item in enumerate(x):
+755        err.append(np.sqrt(deriv[i] @ cov @ deriv[i]))
+756    err = np.array(err)
 757
-758
-759def ks_test(objects=None):
-760    """Performs a Kolmogorov–Smirnov test for the p-values of all fit object.
-761
-762    Parameters
-763    ----------
-764    objects : list
-765        List of fit results to include in the analysis (optional).
-766    """
-767
-768    if objects is None:
-769        obs_list = []
-770        for obj in gc.get_objects():
-771            if isinstance(obj, Fit_result):
-772                obs_list.append(obj)
-773    else:
-774        obs_list = objects
-775
-776    p_values = [o.p_value for o in obs_list]
+758    return err
+759
+760
+761def ks_test(objects=None):
+762    """Performs a Kolmogorov–Smirnov test for the p-values of all fit object.
+763
+764    Parameters
+765    ----------
+766    objects : list
+767        List of fit results to include in the analysis (optional).
+768    """
+769
+770    if objects is None:
+771        obs_list = []
+772        for obj in gc.get_objects():
+773            if isinstance(obj, Fit_result):
+774                obs_list.append(obj)
+775    else:
+776        obs_list = objects
 777
-778    bins = len(p_values)
-779    x = np.arange(0, 1.001, 0.001)
-780    plt.plot(x, x, 'k', zorder=1)
-781    plt.xlim(0, 1)
-782    plt.ylim(0, 1)
-783    plt.xlabel('p-value')
-784    plt.ylabel('Cumulative probability')
-785    plt.title(str(bins) + ' p-values')
-786
-787    n = np.arange(1, bins + 1) / np.float64(bins)
-788    Xs = np.sort(p_values)
-789    plt.step(Xs, n)
-790    diffs = n - Xs
-791    loc_max_diff = np.argmax(np.abs(diffs))
-792    loc = Xs[loc_max_diff]
-793    plt.annotate('', xy=(loc, loc), xytext=(loc, loc + diffs[loc_max_diff]), arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
-794    plt.draw()
-795
-796    print(scipy.stats.kstest(p_values, 'uniform'))
+778    p_values = [o.p_value for o in obs_list]
+779
+780    bins = len(p_values)
+781    x = np.arange(0, 1.001, 0.001)
+782    plt.plot(x, x, 'k', zorder=1)
+783    plt.xlim(0, 1)
+784    plt.ylim(0, 1)
+785    plt.xlabel('p-value')
+786    plt.ylabel('Cumulative probability')
+787    plt.title(str(bins) + ' p-values')
+788
+789    n = np.arange(1, bins + 1) / np.float64(bins)
+790    Xs = np.sort(p_values)
+791    plt.step(Xs, n)
+792    diffs = n - Xs
+793    loc_max_diff = np.argmax(np.abs(diffs))
+794    loc = Xs[loc_max_diff]
+795    plt.annotate('', xy=(loc, loc), xytext=(loc, loc + diffs[loc_max_diff]), arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
+796    plt.draw()
+797
+798    print(scipy.stats.kstest(p_values, 'uniform'))
    @@ -946,26 +951,28 @@ 47 """Apply the gamma method to all fit parameters""" 48 [o.gamma_method(**kwargs) for o in self.fit_parameters] 49 -50 def __str__(self): -51 my_str = 'Goodness of fit:\n' -52 if hasattr(self, 'chisquare_by_dof'): -53 my_str += '\u03C7\u00b2/d.o.f. = ' + f'{self.chisquare_by_dof:2.6f}' + '\n' -54 elif hasattr(self, 'residual_variance'): -55 my_str += 'residual variance = ' + f'{self.residual_variance:2.6f}' + '\n' -56 if hasattr(self, 'chisquare_by_expected_chisquare'): -57 my_str += '\u03C7\u00b2/\u03C7\u00b2exp = ' + f'{self.chisquare_by_expected_chisquare:2.6f}' + '\n' -58 if hasattr(self, 'p_value'): -59 my_str += 'p-value = ' + f'{self.p_value:2.4f}' + '\n' -60 if hasattr(self, 't2_p_value'): -61 my_str += 't\u00B2p-value = ' + f'{self.t2_p_value:2.4f}' + '\n' -62 my_str += 'Fit parameters:\n' -63 for i_par, par in enumerate(self.fit_parameters): -64 my_str += str(i_par) + '\t' + ' ' * int(par >= 0) + str(par).rjust(int(par < 0.0)) + '\n' -65 return my_str -66 -67 def __repr__(self): -68 m = max(map(len, list(self.__dict__.keys()))) + 1 -69 return '\n'.join([key.rjust(m) + ': ' + repr(value) for key, value in sorted(self.__dict__.items())]) +50 gm = gamma_method +51 +52 def __str__(self): +53 my_str = 'Goodness of fit:\n' +54 if hasattr(self, 'chisquare_by_dof'): +55 my_str += '\u03C7\u00b2/d.o.f. = ' + f'{self.chisquare_by_dof:2.6f}' + '\n' +56 elif hasattr(self, 'residual_variance'): +57 my_str += 'residual variance = ' + f'{self.residual_variance:2.6f}' + '\n' +58 if hasattr(self, 'chisquare_by_expected_chisquare'): +59 my_str += '\u03C7\u00b2/\u03C7\u00b2exp = ' + f'{self.chisquare_by_expected_chisquare:2.6f}' + '\n' +60 if hasattr(self, 'p_value'): +61 my_str += 'p-value = ' + f'{self.p_value:2.4f}' + '\n' +62 if hasattr(self, 't2_p_value'): +63 my_str += 't\u00B2p-value = ' + f'{self.t2_p_value:2.4f}' + '\n' +64 my_str += 'Fit parameters:\n' +65 for i_par, par in enumerate(self.fit_parameters): +66 my_str += str(i_par) + '\t' + ' ' * int(par >= 0) + str(par).rjust(int(par < 0.0)) + '\n' +67 return my_str +68 +69 def __repr__(self): +70 m = max(map(len, list(self.__dict__.keys()))) + 1 +71 return '\n'.join([key.rjust(m) + ': ' + repr(value) for key, value in sorted(self.__dict__.items())]) @@ -1022,6 +1029,28 @@ Hotelling t-squared p-value for correlated fits. +

    Apply the gamma method to all fit parameters

    +
    + + + +
    + +
    + + def + gm(self, **kwargs): + + + +
    + + 
    46    def gamma_method(self, **kwargs):
+47        """Apply the gamma method to all fit parameters"""
+48        [o.gamma_method(**kwargs) for o in self.fit_parameters]
+
    + +

    Apply the gamma method to all fit parameters

    @@ -1049,70 +1078,70 @@ Hotelling t-squared p-value for correlated fits.
    - 
     72def least_squares(x, y, func, priors=None, silent=False, **kwargs):
- 73    r'''Performs a non-linear fit to y = func(x).
- 74
- 75    Parameters
- 76    ----------
- 77    x : list
- 78        list of floats.
- 79    y : list
- 80        list of Obs.
- 81    func : object
- 82        fit function, has to be of the form
- 83
- 84        ```python
- 85        import autograd.numpy as anp
- 86
- 87        def func(a, x):
- 88            return a[0] + a[1] * x + a[2] * anp.sinh(x)
- 89        ```
- 90
- 91        For multiple x values func can be of the form
+            
     74def least_squares(x, y, func, priors=None, silent=False, **kwargs):
+ 75    r'''Performs a non-linear fit to y = func(x).
+ 76
+ 77    Parameters
+ 78    ----------
+ 79    x : list
+ 80        list of floats.
+ 81    y : list
+ 82        list of Obs.
+ 83    func : object
+ 84        fit function, has to be of the form
+ 85
+ 86        ```python
+ 87        import autograd.numpy as anp
+ 88
+ 89        def func(a, x):
+ 90            return a[0] + a[1] * x + a[2] * anp.sinh(x)
+ 91        ```
  92
- 93        ```python
- 94        def func(a, x):
- 95            (x1, x2) = x
- 96            return a[0] * x1 ** 2 + a[1] * x2
- 97        ```
- 98
- 99        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
-100        will not work.
-101    priors : list, optional
-102        priors has to be a list with an entry for every parameter in the fit. The entries can either be
-103        Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like
-104        0.548(23), 500(40) or 0.5(0.4)
-105    silent : bool, optional
-106        If true all output to the console is omitted (default False).
-107    initial_guess : list
-108        can provide an initial guess for the input parameters. Relevant for
-109        non-linear fits with many parameters. In case of correlated fits the guess is used to perform
-110        an uncorrelated fit which then serves as guess for the correlated fit.
-111    method : str, optional
-112        can be used to choose an alternative method for the minimization of chisquare.
-113        The possible methods are the ones which can be used for scipy.optimize.minimize and
-114        migrad of iminuit. If no method is specified, Levenberg-Marquard is used.
-115        Reliable alternatives are migrad, Powell and Nelder-Mead.
-116    correlated_fit : bool
-117        If True, use the full inverse covariance matrix in the definition of the chisquare cost function.
-118        For details about how the covariance matrix is estimated see `pyerrors.obs.covariance`.
-119        In practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).
-120        This procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
-121        At the moment this option only works for `prior==None` and when no `method` is given.
-122    expected_chisquare : bool
-123        If True estimates the expected chisquare which is
-124        corrected by effects caused by correlated input data (default False).
-125    resplot : bool
-126        If True, a plot which displays fit, data and residuals is generated (default False).
-127    qqplot : bool
-128        If True, a quantile-quantile plot of the fit result is generated (default False).
-129    num_grad : bool
-130        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
-131    '''
-132    if priors is not None:
-133        return _prior_fit(x, y, func, priors, silent=silent, **kwargs)
-134    else:
-135        return _standard_fit(x, y, func, silent=silent, **kwargs)
+ 93        For multiple x values func can be of the form
+ 94
+ 95        ```python
+ 96        def func(a, x):
+ 97            (x1, x2) = x
+ 98            return a[0] * x1 ** 2 + a[1] * x2
+ 99        ```
+100
+101        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
+102        will not work.
+103    priors : list, optional
+104        priors has to be a list with an entry for every parameter in the fit. The entries can either be
+105        Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like
+106        0.548(23), 500(40) or 0.5(0.4)
+107    silent : bool, optional
+108        If true all output to the console is omitted (default False).
+109    initial_guess : list
+110        can provide an initial guess for the input parameters. Relevant for
+111        non-linear fits with many parameters. In case of correlated fits the guess is used to perform
+112        an uncorrelated fit which then serves as guess for the correlated fit.
+113    method : str, optional
+114        can be used to choose an alternative method for the minimization of chisquare.
+115        The possible methods are the ones which can be used for scipy.optimize.minimize and
+116        migrad of iminuit. If no method is specified, Levenberg-Marquard is used.
+117        Reliable alternatives are migrad, Powell and Nelder-Mead.
+118    correlated_fit : bool
+119        If True, use the full inverse covariance matrix in the definition of the chisquare cost function.
+120        For details about how the covariance matrix is estimated see `pyerrors.obs.covariance`.
+121        In practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).
+122        This procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
+123        At the moment this option only works for `prior==None` and when no `method` is given.
+124    expected_chisquare : bool
+125        If True estimates the expected chisquare which is
+126        corrected by effects caused by correlated input data (default False).
+127    resplot : bool
+128        If True, a plot which displays fit, data and residuals is generated (default False).
+129    qqplot : bool
+130        If True, a quantile-quantile plot of the fit result is generated (default False).
+131    num_grad : bool
+132        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
+133    '''
+134    if priors is not None:
+135        return _prior_fit(x, y, func, priors, silent=silent, **kwargs)
+136    else:
+137        return _standard_fit(x, y, func, silent=silent, **kwargs)
 
    
 
 
@@ -1193,203 +1222,203 @@ Use numerical differentation instead of automatic differentiation to perform the
    - 
    138def total_least_squares(x, y, func, silent=False, **kwargs):
-139    r'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
-140
-141    Parameters
-142    ----------
-143    x : list
-144        list of Obs, or a tuple of lists of Obs
-145    y : list
-146        list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
-147    func : object
-148        func has to be of the form
-149
-150        ```python
-151        import autograd.numpy as anp
-152
-153        def func(a, x):
-154            return a[0] + a[1] * x + a[2] * anp.sinh(x)
-155        ```
-156
-157        For multiple x values func can be of the form
+            
    140def total_least_squares(x, y, func, silent=False, **kwargs):
+141    r'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
+142
+143    Parameters
+144    ----------
+145    x : list
+146        list of Obs, or a tuple of lists of Obs
+147    y : list
+148        list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
+149    func : object
+150        func has to be of the form
+151
+152        ```python
+153        import autograd.numpy as anp
+154
+155        def func(a, x):
+156            return a[0] + a[1] * x + a[2] * anp.sinh(x)
+157        ```
 158
-159        ```python
-160        def func(a, x):
-161            (x1, x2) = x
-162            return a[0] * x1 ** 2 + a[1] * x2
-163        ```
-164
-165        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
-166        will not work.
-167    silent : bool, optional
-168        If true all output to the console is omitted (default False).
-169    initial_guess : list
-170        can provide an initial guess for the input parameters. Relevant for non-linear
-171        fits with many parameters.
-172    expected_chisquare : bool
-173        If true prints the expected chisquare which is
-174        corrected by effects caused by correlated input data.
-175        This can take a while as the full correlation matrix
-176        has to be calculated (default False).
-177    num_grad : bool
-178        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
-179
-180    Notes
-181    -----
-182    Based on the orthogonal distance regression module of scipy
-183    '''
-184
-185    output = Fit_result()
+159        For multiple x values func can be of the form
+160
+161        ```python
+162        def func(a, x):
+163            (x1, x2) = x
+164            return a[0] * x1 ** 2 + a[1] * x2
+165        ```
+166
+167        It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
+168        will not work.
+169    silent : bool, optional
+170        If true all output to the console is omitted (default False).
+171    initial_guess : list
+172        can provide an initial guess for the input parameters. Relevant for non-linear
+173        fits with many parameters.
+174    expected_chisquare : bool
+175        If true prints the expected chisquare which is
+176        corrected by effects caused by correlated input data.
+177        This can take a while as the full correlation matrix
+178        has to be calculated (default False).
+179    num_grad : bool
+180        Use numerical differentation instead of automatic differentiation to perform the error propagation (default False).
+181
+182    Notes
+183    -----
+184    Based on the orthogonal distance regression module of scipy
+185    '''
 186
-187    output.fit_function = func
+187    output = Fit_result()
 188
-189    x = np.array(x)
+189    output.fit_function = func
 190
-191    x_shape = x.shape
+191    x = np.array(x)
 192
-193    if kwargs.get('num_grad') is True:
-194        jacobian = num_jacobian
-195        hessian = num_hessian
-196    else:
-197        jacobian = auto_jacobian
-198        hessian = auto_hessian
-199
-200    if not callable(func):
-201        raise TypeError('func has to be a function.')
-202
-203    for i in range(42):
-204        try:
-205            func(np.arange(i), x.T[0])
-206        except TypeError:
-207            continue
-208        except IndexError:
+193    x_shape = x.shape
+194
+195    if kwargs.get('num_grad') is True:
+196        jacobian = num_jacobian
+197        hessian = num_hessian
+198    else:
+199        jacobian = auto_jacobian
+200        hessian = auto_hessian
+201
+202    if not callable(func):
+203        raise TypeError('func has to be a function.')
+204
+205    for i in range(42):
+206        try:
+207            func(np.arange(i), x.T[0])
+208        except TypeError:
 209            continue
-210        else:
-211            break
-212    else:
-213        raise RuntimeError("Fit function is not valid.")
-214
-215    n_parms = i
-216    if not silent:
-217        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
-218
-219    x_f = np.vectorize(lambda o: o.value)(x)
-220    dx_f = np.vectorize(lambda o: o.dvalue)(x)
-221    y_f = np.array([o.value for o in y])
-222    dy_f = np.array([o.dvalue for o in y])
-223
-224    if np.any(np.asarray(dx_f) <= 0.0):
-225        raise Exception('No x errors available, run the gamma method first.')
-226
-227    if np.any(np.asarray(dy_f) <= 0.0):
-228        raise Exception('No y errors available, run the gamma method first.')
-229
-230    if 'initial_guess' in kwargs:
-231        x0 = kwargs.get('initial_guess')
-232        if len(x0) != n_parms:
-233            raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
-234    else:
-235        x0 = [1] * n_parms
-236
-237    data = RealData(x_f, y_f, sx=dx_f, sy=dy_f)
-238    model = Model(func)
-239    odr = ODR(data, model, x0, partol=np.finfo(np.float64).eps)
-240    odr.set_job(fit_type=0, deriv=1)
-241    out = odr.run()
-242
-243    output.residual_variance = out.res_var
+210        except IndexError:
+211            continue
+212        else:
+213            break
+214    else:
+215        raise RuntimeError("Fit function is not valid.")
+216
+217    n_parms = i
+218    if not silent:
+219        print('Fit with', n_parms, 'parameter' + 's' * (n_parms > 1))
+220
+221    x_f = np.vectorize(lambda o: o.value)(x)
+222    dx_f = np.vectorize(lambda o: o.dvalue)(x)
+223    y_f = np.array([o.value for o in y])
+224    dy_f = np.array([o.dvalue for o in y])
+225
+226    if np.any(np.asarray(dx_f) <= 0.0):
+227        raise Exception('No x errors available, run the gamma method first.')
+228
+229    if np.any(np.asarray(dy_f) <= 0.0):
+230        raise Exception('No y errors available, run the gamma method first.')
+231
+232    if 'initial_guess' in kwargs:
+233        x0 = kwargs.get('initial_guess')
+234        if len(x0) != n_parms:
+235            raise Exception('Initial guess does not have the correct length: %d vs. %d' % (len(x0), n_parms))
+236    else:
+237        x0 = [1] * n_parms
+238
+239    data = RealData(x_f, y_f, sx=dx_f, sy=dy_f)
+240    model = Model(func)
+241    odr = ODR(data, model, x0, partol=np.finfo(np.float64).eps)
+242    odr.set_job(fit_type=0, deriv=1)
+243    out = odr.run()
 244
-245    output.method = 'ODR'
+245    output.residual_variance = out.res_var
 246
-247    output.message = out.stopreason
+247    output.method = 'ODR'
 248
-249    output.xplus = out.xplus
+249    output.message = out.stopreason
 250
-251    if not silent:
-252        print('Method: ODR')
-253        print(*out.stopreason)
-254        print('Residual variance:', output.residual_variance)
-255
-256    if out.info > 3:
-257        raise Exception('The minimization procedure did not converge.')
-258
-259    m = x_f.size
+251    output.xplus = out.xplus
+252
+253    if not silent:
+254        print('Method: ODR')
+255        print(*out.stopreason)
+256        print('Residual variance:', output.residual_variance)
+257
+258    if out.info > 3:
+259        raise Exception('The minimization procedure did not converge.')
 260
-261    def odr_chisquare(p):
-262        model = func(p[:n_parms], p[n_parms:].reshape(x_shape))
-263        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((x_f - p[n_parms:].reshape(x_shape)) / dx_f) ** 2)
-264        return chisq
-265
-266    if kwargs.get('expected_chisquare') is True:
-267        W = np.diag(1 / np.asarray(np.concatenate((dy_f.ravel(), dx_f.ravel()))))
-268
-269        if kwargs.get('covariance') is not None:
-270            cov = kwargs.get('covariance')
-271        else:
-272            cov = covariance(np.concatenate((y, x.ravel())))
-273
-274        number_of_x_parameters = int(m / x_f.shape[-1])
+261    m = x_f.size
+262
+263    def odr_chisquare(p):
+264        model = func(p[:n_parms], p[n_parms:].reshape(x_shape))
+265        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((x_f - p[n_parms:].reshape(x_shape)) / dx_f) ** 2)
+266        return chisq
+267
+268    if kwargs.get('expected_chisquare') is True:
+269        W = np.diag(1 / np.asarray(np.concatenate((dy_f.ravel(), dx_f.ravel()))))
+270
+271        if kwargs.get('covariance') is not None:
+272            cov = kwargs.get('covariance')
+273        else:
+274            cov = covariance(np.concatenate((y, x.ravel())))
 275
-276        old_jac = jacobian(func)(out.beta, out.xplus)
-277        fused_row1 = np.concatenate((old_jac, np.concatenate((number_of_x_parameters * [np.zeros(old_jac.shape)]), axis=0)))
-278        fused_row2 = np.concatenate((jacobian(lambda x, y: func(y, x))(out.xplus, out.beta).reshape(x_f.shape[-1], x_f.shape[-1] * number_of_x_parameters), np.identity(number_of_x_parameters * old_jac.shape[0])))
-279        new_jac = np.concatenate((fused_row1, fused_row2), axis=1)
-280
-281        A = W @ new_jac
-282        P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
-283        expected_chisquare = np.trace((np.identity(P_phi.shape[0]) - P_phi) @ W @ cov @ W)
-284        if expected_chisquare <= 0.0:
-285            warnings.warn("Negative expected_chisquare.", RuntimeWarning)
-286            expected_chisquare = np.abs(expected_chisquare)
-287        output.chisquare_by_expected_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel()))) / expected_chisquare
-288        if not silent:
-289            print('chisquare/expected_chisquare:',
-290                  output.chisquare_by_expected_chisquare)
-291
-292    fitp = out.beta
-293    try:
-294        hess = hessian(odr_chisquare)(np.concatenate((fitp, out.xplus.ravel())))
-295    except TypeError:
-296        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
-297
-298    def odr_chisquare_compact_x(d):
-299        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
-300        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((d[n_parms + m:].reshape(x_shape) - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
-301        return chisq
-302
-303    jac_jac_x = hessian(odr_chisquare_compact_x)(np.concatenate((fitp, out.xplus.ravel(), x_f.ravel())))
+276        number_of_x_parameters = int(m / x_f.shape[-1])
+277
+278        old_jac = jacobian(func)(out.beta, out.xplus)
+279        fused_row1 = np.concatenate((old_jac, np.concatenate((number_of_x_parameters * [np.zeros(old_jac.shape)]), axis=0)))
+280        fused_row2 = np.concatenate((jacobian(lambda x, y: func(y, x))(out.xplus, out.beta).reshape(x_f.shape[-1], x_f.shape[-1] * number_of_x_parameters), np.identity(number_of_x_parameters * old_jac.shape[0])))
+281        new_jac = np.concatenate((fused_row1, fused_row2), axis=1)
+282
+283        A = W @ new_jac
+284        P_phi = A @ np.linalg.pinv(A.T @ A) @ A.T
+285        expected_chisquare = np.trace((np.identity(P_phi.shape[0]) - P_phi) @ W @ cov @ W)
+286        if expected_chisquare <= 0.0:
+287            warnings.warn("Negative expected_chisquare.", RuntimeWarning)
+288            expected_chisquare = np.abs(expected_chisquare)
+289        output.chisquare_by_expected_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel()))) / expected_chisquare
+290        if not silent:
+291            print('chisquare/expected_chisquare:',
+292                  output.chisquare_by_expected_chisquare)
+293
+294    fitp = out.beta
+295    try:
+296        hess = hessian(odr_chisquare)(np.concatenate((fitp, out.xplus.ravel())))
+297    except TypeError:
+298        raise Exception("It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details.") from None
+299
+300    def odr_chisquare_compact_x(d):
+301        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
+302        chisq = anp.sum(((y_f - model) / dy_f) ** 2) + anp.sum(((d[n_parms + m:].reshape(x_shape) - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
+303        return chisq
 304
-305    # Compute hess^{-1} @ jac_jac_x[:n_parms + m, n_parms + m:] using LAPACK dgesv
-306    try:
-307        deriv_x = -scipy.linalg.solve(hess, jac_jac_x[:n_parms + m, n_parms + m:])
-308    except np.linalg.LinAlgError:
-309        raise Exception("Cannot invert hessian matrix.")
-310
-311    def odr_chisquare_compact_y(d):
-312        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
-313        chisq = anp.sum(((d[n_parms + m:] - model) / dy_f) ** 2) + anp.sum(((x_f - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
-314        return chisq
-315
-316    jac_jac_y = hessian(odr_chisquare_compact_y)(np.concatenate((fitp, out.xplus.ravel(), y_f)))
+305    jac_jac_x = hessian(odr_chisquare_compact_x)(np.concatenate((fitp, out.xplus.ravel(), x_f.ravel())))
+306
+307    # Compute hess^{-1} @ jac_jac_x[:n_parms + m, n_parms + m:] using LAPACK dgesv
+308    try:
+309        deriv_x = -scipy.linalg.solve(hess, jac_jac_x[:n_parms + m, n_parms + m:])
+310    except np.linalg.LinAlgError:
+311        raise Exception("Cannot invert hessian matrix.")
+312
+313    def odr_chisquare_compact_y(d):
+314        model = func(d[:n_parms], d[n_parms:n_parms + m].reshape(x_shape))
+315        chisq = anp.sum(((d[n_parms + m:] - model) / dy_f) ** 2) + anp.sum(((x_f - d[n_parms:n_parms + m].reshape(x_shape)) / dx_f) ** 2)
+316        return chisq
 317
-318    # Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv
-319    try:
-320        deriv_y = -scipy.linalg.solve(hess, jac_jac_y[:n_parms + m, n_parms + m:])
-321    except np.linalg.LinAlgError:
-322        raise Exception("Cannot invert hessian matrix.")
-323
-324    result = []
-325    for i in range(n_parms):
-326        result.append(derived_observable(lambda my_var, **kwargs: (my_var[0] + np.finfo(np.float64).eps) / (x.ravel()[0].value + np.finfo(np.float64).eps) * out.beta[i], list(x.ravel()) + list(y), man_grad=list(deriv_x[i]) + list(deriv_y[i])))
-327
-328    output.fit_parameters = result
+318    jac_jac_y = hessian(odr_chisquare_compact_y)(np.concatenate((fitp, out.xplus.ravel(), y_f)))
+319
+320    # Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv
+321    try:
+322        deriv_y = -scipy.linalg.solve(hess, jac_jac_y[:n_parms + m, n_parms + m:])
+323    except np.linalg.LinAlgError:
+324        raise Exception("Cannot invert hessian matrix.")
+325
+326    result = []
+327    for i in range(n_parms):
+328        result.append(derived_observable(lambda my_var, **kwargs: (my_var[0] + np.finfo(np.float64).eps) / (x.ravel()[0].value + np.finfo(np.float64).eps) * out.beta[i], list(x.ravel()) + list(y), man_grad=list(deriv_x[i]) + list(deriv_y[i])))
 329
-330    output.odr_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel())))
-331    output.dof = x.shape[-1] - n_parms
-332    output.p_value = 1 - scipy.stats.chi2.cdf(output.odr_chisquare, output.dof)
-333
-334    return output
+330    output.fit_parameters = result
+331
+332    output.odr_chisquare = odr_chisquare(np.concatenate((out.beta, out.xplus.ravel())))
+333    output.dof = x.shape[-1] - n_parms
+334    output.p_value = 1 - scipy.stats.chi2.cdf(output.odr_chisquare, output.dof)
+335
+336    return output
 
    
 
 
@@ -1456,30 +1485,30 @@ Use numerical differentation instead of automatic differentiation to perform the
    - 
    660def fit_lin(x, y, **kwargs):
-661    """Performs a linear fit to y = n + m * x and returns two Obs n, m.
-662
-663    Parameters
-664    ----------
-665    x : list
-666        Can either be a list of floats in which case no xerror is assumed, or
-667        a list of Obs, where the dvalues of the Obs are used as xerror for the fit.
-668    y : list
-669        List of Obs, the dvalues of the Obs are used as yerror for the fit.
-670    """
-671
-672    def f(a, x):
-673        y = a[0] + a[1] * x
-674        return y
-675
-676    if all(isinstance(n, Obs) for n in x):
-677        out = total_least_squares(x, y, f, **kwargs)
-678        return out.fit_parameters
-679    elif all(isinstance(n, float) or isinstance(n, int) for n in x) or isinstance(x, np.ndarray):
-680        out = least_squares(x, y, f, **kwargs)
-681        return out.fit_parameters
-682    else:
-683        raise Exception('Unsupported types for x')
+            
    662def fit_lin(x, y, **kwargs):
+663    """Performs a linear fit to y = n + m * x and returns two Obs n, m.
+664
+665    Parameters
+666    ----------
+667    x : list
+668        Can either be a list of floats in which case no xerror is assumed, or
+669        a list of Obs, where the dvalues of the Obs are used as xerror for the fit.
+670    y : list
+671        List of Obs, the dvalues of the Obs are used as yerror for the fit.
+672    """
+673
+674    def f(a, x):
+675        y = a[0] + a[1] * x
+676        return y
+677
+678    if all(isinstance(n, Obs) for n in x):
+679        out = total_least_squares(x, y, f, **kwargs)
+680        return out.fit_parameters
+681    elif all(isinstance(n, float) or isinstance(n, int) for n in x) or isinstance(x, np.ndarray):
+682        out = least_squares(x, y, f, **kwargs)
+683        return out.fit_parameters
+684    else:
+685        raise Exception('Unsupported types for x')
 
    
 
 
@@ -1509,30 +1538,30 @@ List of Obs, the dvalues of the Obs are used as yerror for the fit.
    - 
    686def qqplot(x, o_y, func, p):
-687    """Generates a quantile-quantile plot of the fit result which can be used to
-688       check if the residuals of the fit are gaussian distributed.
-689    """
-690
-691    residuals = []
-692    for i_x, i_y in zip(x, o_y):
-693        residuals.append((i_y - func(p, i_x)) / i_y.dvalue)
-694    residuals = sorted(residuals)
-695    my_y = [o.value for o in residuals]
-696    probplot = scipy.stats.probplot(my_y)
-697    my_x = probplot[0][0]
-698    plt.figure(figsize=(8, 8 / 1.618))
-699    plt.errorbar(my_x, my_y, fmt='o')
-700    fit_start = my_x[0]
-701    fit_stop = my_x[-1]
-702    samples = np.arange(fit_start, fit_stop, 0.01)
-703    plt.plot(samples, samples, 'k--', zorder=11, label='Standard normal distribution')
-704    plt.plot(samples, probplot[1][0] * samples + probplot[1][1], zorder=10, label='Least squares fit, r=' + str(np.around(probplot[1][2], 3)), marker='', ls='-')
-705
-706    plt.xlabel('Theoretical quantiles')
-707    plt.ylabel('Ordered Values')
-708    plt.legend()
-709    plt.draw()
+            
    688def qqplot(x, o_y, func, p):
+689    """Generates a quantile-quantile plot of the fit result which can be used to
+690       check if the residuals of the fit are gaussian distributed.
+691    """
+692
+693    residuals = []
+694    for i_x, i_y in zip(x, o_y):
+695        residuals.append((i_y - func(p, i_x)) / i_y.dvalue)
+696    residuals = sorted(residuals)
+697    my_y = [o.value for o in residuals]
+698    probplot = scipy.stats.probplot(my_y)
+699    my_x = probplot[0][0]
+700    plt.figure(figsize=(8, 8 / 1.618))
+701    plt.errorbar(my_x, my_y, fmt='o')
+702    fit_start = my_x[0]
+703    fit_stop = my_x[-1]
+704    samples = np.arange(fit_start, fit_stop, 0.01)
+705    plt.plot(samples, samples, 'k--', zorder=11, label='Standard normal distribution')
+706    plt.plot(samples, probplot[1][0] * samples + probplot[1][1], zorder=10, label='Least squares fit, r=' + str(np.around(probplot[1][2], 3)), marker='', ls='-')
+707
+708    plt.xlabel('Theoretical quantiles')
+709    plt.ylabel('Ordered Values')
+710    plt.legend()
+711    plt.draw()
 
    
 
 
@@ -1553,34 +1582,34 @@ check if the residuals of the fit are gaussian distributed.
    - 
    712def residual_plot(x, y, func, fit_res):
-713    """ Generates a plot which compares the fit to the data and displays the corresponding residuals"""
-714    sorted_x = sorted(x)
-715    xstart = sorted_x[0] - 0.5 * (sorted_x[1] - sorted_x[0])
-716    xstop = sorted_x[-1] + 0.5 * (sorted_x[-1] - sorted_x[-2])
-717    x_samples = np.arange(xstart, xstop + 0.01, 0.01)
-718
-719    plt.figure(figsize=(8, 8 / 1.618))
-720    gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0)
-721    ax0 = plt.subplot(gs[0])
-722    ax0.errorbar(x, [o.value for o in y], yerr=[o.dvalue for o in y], ls='none', fmt='o', capsize=3, markersize=5, label='Data')
-723    ax0.plot(x_samples, func([o.value for o in fit_res], x_samples), label='Fit', zorder=10, ls='-', ms=0)
-724    ax0.set_xticklabels([])
-725    ax0.set_xlim([xstart, xstop])
+            
    714def residual_plot(x, y, func, fit_res):
+715    """ Generates a plot which compares the fit to the data and displays the corresponding residuals"""
+716    sorted_x = sorted(x)
+717    xstart = sorted_x[0] - 0.5 * (sorted_x[1] - sorted_x[0])
+718    xstop = sorted_x[-1] + 0.5 * (sorted_x[-1] - sorted_x[-2])
+719    x_samples = np.arange(xstart, xstop + 0.01, 0.01)
+720
+721    plt.figure(figsize=(8, 8 / 1.618))
+722    gs = gridspec.GridSpec(2, 1, height_ratios=[3, 1], wspace=0.0, hspace=0.0)
+723    ax0 = plt.subplot(gs[0])
+724    ax0.errorbar(x, [o.value for o in y], yerr=[o.dvalue for o in y], ls='none', fmt='o', capsize=3, markersize=5, label='Data')
+725    ax0.plot(x_samples, func([o.value for o in fit_res], x_samples), label='Fit', zorder=10, ls='-', ms=0)
 726    ax0.set_xticklabels([])
-727    ax0.legend()
-728
-729    residuals = (np.asarray([o.value for o in y]) - func([o.value for o in fit_res], x)) / np.asarray([o.dvalue for o in y])
-730    ax1 = plt.subplot(gs[1])
-731    ax1.plot(x, residuals, 'ko', ls='none', markersize=5)
-732    ax1.tick_params(direction='out')
-733    ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True)
-734    ax1.axhline(y=0.0, ls='--', color='k', marker=" ")
-735    ax1.fill_between(x_samples, -1.0, 1.0, alpha=0.1, facecolor='k')
-736    ax1.set_xlim([xstart, xstop])
-737    ax1.set_ylabel('Residuals')
-738    plt.subplots_adjust(wspace=None, hspace=None)
-739    plt.draw()
+727    ax0.set_xlim([xstart, xstop])
+728    ax0.set_xticklabels([])
+729    ax0.legend()
+730
+731    residuals = (np.asarray([o.value for o in y]) - func([o.value for o in fit_res], x)) / np.asarray([o.dvalue for o in y])
+732    ax1 = plt.subplot(gs[1])
+733    ax1.plot(x, residuals, 'ko', ls='none', markersize=5)
+734    ax1.tick_params(direction='out')
+735    ax1.tick_params(axis="x", bottom=True, top=True, labelbottom=True)
+736    ax1.axhline(y=0.0, ls='--', color='k', marker=" ")
+737    ax1.fill_between(x_samples, -1.0, 1.0, alpha=0.1, facecolor='k')
+738    ax1.set_xlim([xstart, xstop])
+739    ax1.set_ylabel('Residuals')
+740    plt.subplots_adjust(wspace=None, hspace=None)
+741    plt.draw()
 
    
 
 
@@ -1600,22 +1629,22 @@ check if the residuals of the fit are gaussian distributed.
    - 
    742def error_band(x, func, beta):
-743    """Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""
-744    cov = covariance(beta)
-745    if np.any(np.abs(cov - cov.T) > 1000 * np.finfo(np.float64).eps):
-746        warnings.warn("Covariance matrix is not symmetric within floating point precision", RuntimeWarning)
-747
-748    deriv = []
-749    for i, item in enumerate(x):
-750        deriv.append(np.array(egrad(func)([o.value for o in beta], item)))
-751
-752    err = []
-753    for i, item in enumerate(x):
-754        err.append(np.sqrt(deriv[i] @ cov @ deriv[i]))
-755    err = np.array(err)
-756
-757    return err
+            
    744def error_band(x, func, beta):
+745    """Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""
+746    cov = covariance(beta)
+747    if np.any(np.abs(cov - cov.T) > 1000 * np.finfo(np.float64).eps):
+748        warnings.warn("Covariance matrix is not symmetric within floating point precision", RuntimeWarning)
+749
+750    deriv = []
+751    for i, item in enumerate(x):
+752        deriv.append(np.array(egrad(func)([o.value for o in beta], item)))
+753
+754    err = []
+755    for i, item in enumerate(x):
+756        err.append(np.sqrt(deriv[i] @ cov @ deriv[i]))
+757    err = np.array(err)
+758
+759    return err
 
    
 
 
@@ -1635,44 +1664,44 @@ check if the residuals of the fit are gaussian distributed.
    - 
    760def ks_test(objects=None):
-761    """Performs a Kolmogorov–Smirnov test for the p-values of all fit object.
-762
-763    Parameters
-764    ----------
-765    objects : list
-766        List of fit results to include in the analysis (optional).
-767    """
-768
-769    if objects is None:
-770        obs_list = []
-771        for obj in gc.get_objects():
-772            if isinstance(obj, Fit_result):
-773                obs_list.append(obj)
-774    else:
-775        obs_list = objects
-776
-777    p_values = [o.p_value for o in obs_list]
+            
    762def ks_test(objects=None):
+763    """Performs a Kolmogorov–Smirnov test for the p-values of all fit object.
+764
+765    Parameters
+766    ----------
+767    objects : list
+768        List of fit results to include in the analysis (optional).
+769    """
+770
+771    if objects is None:
+772        obs_list = []
+773        for obj in gc.get_objects():
+774            if isinstance(obj, Fit_result):
+775                obs_list.append(obj)
+776    else:
+777        obs_list = objects
 778
-779    bins = len(p_values)
-780    x = np.arange(0, 1.001, 0.001)
-781    plt.plot(x, x, 'k', zorder=1)
-782    plt.xlim(0, 1)
-783    plt.ylim(0, 1)
-784    plt.xlabel('p-value')
-785    plt.ylabel('Cumulative probability')
-786    plt.title(str(bins) + ' p-values')
-787
-788    n = np.arange(1, bins + 1) / np.float64(bins)
-789    Xs = np.sort(p_values)
-790    plt.step(Xs, n)
-791    diffs = n - Xs
-792    loc_max_diff = np.argmax(np.abs(diffs))
-793    loc = Xs[loc_max_diff]
-794    plt.annotate('', xy=(loc, loc), xytext=(loc, loc + diffs[loc_max_diff]), arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
-795    plt.draw()
-796
-797    print(scipy.stats.kstest(p_values, 'uniform'))
+779    p_values = [o.p_value for o in obs_list]
+780
+781    bins = len(p_values)
+782    x = np.arange(0, 1.001, 0.001)
+783    plt.plot(x, x, 'k', zorder=1)
+784    plt.xlim(0, 1)
+785    plt.ylim(0, 1)
+786    plt.xlabel('p-value')
+787    plt.ylabel('Cumulative probability')
+788    plt.title(str(bins) + ' p-values')
+789
+790    n = np.arange(1, bins + 1) / np.float64(bins)
+791    Xs = np.sort(p_values)
+792    plt.step(Xs, n)
+793    diffs = n - Xs
+794    loc_max_diff = np.argmax(np.abs(diffs))
+795    loc = Xs[loc_max_diff]
+796    plt.annotate('', xy=(loc, loc), xytext=(loc, loc + diffs[loc_max_diff]), arrowprops=dict(arrowstyle='<->', shrinkA=0, shrinkB=0))
+797    plt.draw()
+798
+799    print(scipy.stats.kstest(p_values, 'uniform'))
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index 24bf5557..38f25af0 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. [arXiv:2209.14371 [hep-lat]].
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.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
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. 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
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\tfname,\tnoempty=False,\tfull_output=False,\tgz=True,\tseparator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "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.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.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.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "kind": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. [arXiv:2209.14371 [hep-lat]].
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. 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
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\tfname,\tnoempty=False,\tfull_output=False,\tgz=True,\tseparator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "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.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.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.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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