diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index 3a73ce43..52f4ee38 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -74,6 +74,9 @@
  • anti_symmetric
    • +
  • + is_matrix_symmetric +
  • matrix_symmetric
    • @@ -451,1029 +454,1050 @@ 237 raise Exception("Corr could not be symmetrized: No redundant values") 238 return Corr(newcontent, prange=self.prange) 239 - 240 def matrix_symmetric(self): - 241 """Symmetrizes the correlator matrices on every timeslice.""" - 242 if self.N > 1: - 243 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 244 return 0.5 * (Corr(transposed) + self) - 245 if self.N == 1: - 246 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 247 - 248 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 249 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 250 - 251 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 252 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 253 ```python - 254 C.GEVP(t0=2)[0] # Ground state vector(s) - 255 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 256 ``` - 257 - 258 Parameters - 259 ---------- - 260 t0 : int - 261 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 262 ts : int - 263 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 264 If sort="Eigenvector" it gives a reference point for the sorting method. - 265 sort : string - 266 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. - 267 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 268 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 269 The reference state is identified by its eigenvalue at $t=t_s$. - 270 - 271 Other Parameters - 272 ---------------- - 273 state : int - 274 Returns only the vector(s) for a specified state. The lowest state is zero. - 275 ''' - 276 - 277 if self.N == 1: - 278 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 279 if ts is not None: - 280 if (ts <= t0): - 281 raise Exception("ts has to be larger than t0.") - 282 - 283 if "sorted_list" in kwargs: - 284 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 285 sort = kwargs.get("sorted_list") - 286 - 287 symmetric_corr = self.matrix_symmetric() - 288 if sort is None: - 289 if (ts is None): - 290 raise Exception("ts is required if sort=None.") - 291 if (self.content[t0] is None) or (self.content[ts] is None): - 292 raise Exception("Corr not defined at t0/ts.") - 293 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") - 294 for i in range(self.N): - 295 for j in range(self.N): - 296 G0[i, j] = symmetric_corr[t0][i, j].value - 297 Gt[i, j] = symmetric_corr[ts][i, j].value - 298 - 299 reordered_vecs = _GEVP_solver(Gt, G0) - 300 - 301 elif sort in ["Eigenvalue", "Eigenvector"]: - 302 if sort == "Eigenvalue" and ts is not None: - 303 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) - 304 all_vecs = [None] * (t0 + 1) - 305 for t in range(t0 + 1, self.T): - 306 try: - 307 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") - 308 for i in range(self.N): - 309 for j in range(self.N): - 310 G0[i, j] = symmetric_corr[t0][i, j].value - 311 Gt[i, j] = symmetric_corr[t][i, j].value - 312 - 313 all_vecs.append(_GEVP_solver(Gt, G0)) - 314 except Exception: - 315 all_vecs.append(None) - 316 if sort == "Eigenvector": - 317 if (ts is None): - 318 raise Exception("ts is required for the Eigenvector sorting method.") - 319 all_vecs = _sort_vectors(all_vecs, ts) - 320 - 321 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 322 else: - 323 raise Exception("Unkown value for 'sort'.") - 324 - 325 if "state" in kwargs: - 326 return reordered_vecs[kwargs.get("state")] - 327 else: - 328 return reordered_vecs - 329 - 330 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 331 """Determines the eigenvalue of the GEVP by solving and projecting the correlator - 332 - 333 Parameters - 334 ---------- - 335 state : int - 336 The state one is interested in ordered by energy. The lowest state is zero. - 337 - 338 All other parameters are identical to the ones of Corr.GEVP. - 339 """ - 340 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 341 return self.projected(vec) - 342 - 343 def Hankel(self, N, periodic=False): - 344 """Constructs an NxN Hankel matrix + 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 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 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") + 315 for i in range(self.N): + 316 for j in range(self.N): + 317 G0[i, j] = symmetric_corr[t0][i, j].value + 318 Gt[i, j] = symmetric_corr[ts][i, j].value + 319 + 320 reordered_vecs = _GEVP_solver(Gt, G0) + 321 + 322 elif sort in ["Eigenvalue", "Eigenvector"]: + 323 if sort == "Eigenvalue" and ts is not None: + 324 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) + 325 all_vecs = [None] * (t0 + 1) + 326 for t in range(t0 + 1, self.T): + 327 try: + 328 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") + 329 for i in range(self.N): + 330 for j in range(self.N): + 331 G0[i, j] = symmetric_corr[t0][i, j].value + 332 Gt[i, j] = symmetric_corr[t][i, j].value + 333 + 334 all_vecs.append(_GEVP_solver(Gt, G0)) + 335 except Exception: + 336 all_vecs.append(None) + 337 if sort == "Eigenvector": + 338 if (ts is None): + 339 raise Exception("ts is required for the Eigenvector sorting method.") + 340 all_vecs = _sort_vectors(all_vecs, ts) + 341 + 342 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] + 343 else: + 344 raise Exception("Unkown value for 'sort'.") 345 - 346 C(t) c(t+1) ... c(t+n-1) - 347 C(t+1) c(t+2) ... c(t+n) - 348 ................. - 349 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) + 346 if "state" in kwargs: + 347 return reordered_vecs[kwargs.get("state")] + 348 else: + 349 return reordered_vecs 350 - 351 Parameters - 352 ---------- - 353 N : int - 354 Dimension of the Hankel matrix - 355 periodic : bool, optional - 356 determines whether the matrix is extended periodically - 357 """ + 351 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): + 352 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 353 + 354 Parameters + 355 ---------- + 356 state : int + 357 The state one is interested in ordered by energy. The lowest state is zero. 358 - 359 if self.N != 1: - 360 raise Exception("Multi-operator Prony not implemented!") - 361 - 362 array = np.empty([N, N], dtype="object") - 363 new_content = [] - 364 for t in range(self.T): - 365 new_content.append(array.copy()) + 359 All other parameters are identical to the ones of Corr.GEVP. + 360 """ + 361 vec = self.GEVP(t0, ts=ts, sort=sort)[state] + 362 return self.projected(vec) + 363 + 364 def Hankel(self, N, periodic=False): + 365 """Constructs an NxN Hankel matrix 366 - 367 def wrap(i): - 368 while i >= self.T: - 369 i -= self.T - 370 return i + 367 C(t) c(t+1) ... c(t+n-1) + 368 C(t+1) c(t+2) ... c(t+n) + 369 ................. + 370 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) 371 - 372 for t in range(self.T): - 373 for i in range(N): - 374 for j in range(N): - 375 if periodic: - 376 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 377 elif (t + i + j) >= self.T: - 378 new_content[t] = None - 379 else: - 380 new_content[t][i, j] = self.content[t + i + j][0] - 381 - 382 return Corr(new_content) - 383 - 384 def roll(self, dt): - 385 """Periodically shift the correlator by dt timeslices - 386 - 387 Parameters - 388 ---------- - 389 dt : int - 390 number of timeslices - 391 """ - 392 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) - 393 - 394 def reverse(self): - 395 """Reverse the time ordering of the Corr""" - 396 return Corr(self.content[:: -1]) - 397 - 398 def thin(self, spacing=2, offset=0): - 399 """Thin out a correlator to suppress correlations - 400 - 401 Parameters - 402 ---------- - 403 spacing : int - 404 Keep only every 'spacing'th entry of the correlator - 405 offset : int - 406 Offset the equal spacing - 407 """ - 408 new_content = [] - 409 for t in range(self.T): - 410 if (offset + t) % spacing != 0: - 411 new_content.append(None) - 412 else: - 413 new_content.append(self.content[t]) - 414 return Corr(new_content) - 415 - 416 def correlate(self, partner): - 417 """Correlate the correlator with another correlator or Obs + 372 Parameters + 373 ---------- + 374 N : int + 375 Dimension of the Hankel matrix + 376 periodic : bool, optional + 377 determines whether the matrix is extended periodically + 378 """ + 379 + 380 if self.N != 1: + 381 raise Exception("Multi-operator Prony not implemented!") + 382 + 383 array = np.empty([N, N], dtype="object") + 384 new_content = [] + 385 for t in range(self.T): + 386 new_content.append(array.copy()) + 387 + 388 def wrap(i): + 389 while i >= self.T: + 390 i -= self.T + 391 return i + 392 + 393 for t in range(self.T): + 394 for i in range(N): + 395 for j in range(N): + 396 if periodic: + 397 new_content[t][i, j] = self.content[wrap(t + i + j)][0] + 398 elif (t + i + j) >= self.T: + 399 new_content[t] = None + 400 else: + 401 new_content[t][i, j] = self.content[t + i + j][0] + 402 + 403 return Corr(new_content) + 404 + 405 def roll(self, dt): + 406 """Periodically shift the correlator by dt timeslices + 407 + 408 Parameters + 409 ---------- + 410 dt : int + 411 number of timeslices + 412 """ + 413 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) + 414 + 415 def reverse(self): + 416 """Reverse the time ordering of the Corr""" + 417 return Corr(self.content[:: -1]) 418 - 419 Parameters - 420 ---------- - 421 partner : Obs or Corr - 422 partner to correlate the correlator with. - 423 Can either be an Obs which is correlated with all entries of the - 424 correlator or a Corr of same length. - 425 """ - 426 if self.N != 1: - 427 raise Exception("Only one-dimensional correlators can be safely correlated.") - 428 new_content = [] - 429 for x0, t_slice in enumerate(self.content): - 430 if _check_for_none(self, t_slice): - 431 new_content.append(None) - 432 else: - 433 if isinstance(partner, Corr): - 434 if _check_for_none(partner, partner.content[x0]): - 435 new_content.append(None) - 436 else: - 437 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 438 elif isinstance(partner, Obs): # Should this include CObs? - 439 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 440 else: - 441 raise Exception("Can only correlate with an Obs or a Corr.") - 442 - 443 return Corr(new_content) - 444 - 445 def reweight(self, weight, **kwargs): - 446 """Reweight the correlator. - 447 - 448 Parameters - 449 ---------- - 450 weight : Obs - 451 Reweighting factor. An Observable that has to be defined on a superset of the - 452 configurations in obs[i].idl for all i. - 453 all_configs : bool - 454 if True, the reweighted observables are normalized by the average of - 455 the reweighting factor on all configurations in weight.idl and not - 456 on the configurations in obs[i].idl. - 457 """ - 458 if self.N != 1: - 459 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 460 new_content = [] - 461 for t_slice in self.content: - 462 if _check_for_none(self, t_slice): - 463 new_content.append(None) - 464 else: - 465 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 466 return Corr(new_content) - 467 - 468 def T_symmetry(self, partner, parity=+1): - 469 """Return the time symmetry average of the correlator and its partner - 470 - 471 Parameters - 472 ---------- - 473 partner : Corr - 474 Time symmetry partner of the Corr - 475 partity : int - 476 Parity quantum number of the correlator, can be +1 or -1 - 477 """ - 478 if self.N != 1: - 479 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 480 if not isinstance(partner, Corr): - 481 raise Exception("T partner has to be a Corr object.") - 482 if parity not in [+1, -1]: - 483 raise Exception("Parity has to be +1 or -1.") - 484 T_partner = parity * partner.reverse() - 485 - 486 t_slices = [] - 487 test = (self - T_partner) - 488 test.gamma_method() - 489 for x0, t_slice in enumerate(test.content): - 490 if t_slice is not None: - 491 if not t_slice[0].is_zero_within_error(5): - 492 t_slices.append(x0) - 493 if t_slices: - 494 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) - 495 - 496 return (self + T_partner) / 2 - 497 - 498 def deriv(self, variant="symmetric"): - 499 """Return the first derivative of the correlator with respect to x0. - 500 - 501 Parameters - 502 ---------- - 503 variant : str - 504 decides which definition of the finite differences derivative is used. - 505 Available choice: symmetric, forward, backward, improved, default: symmetric - 506 """ - 507 if self.N != 1: - 508 raise Exception("deriv only implemented for one-dimensional correlators.") - 509 if variant == "symmetric": - 510 newcontent = [] - 511 for t in range(1, self.T - 1): - 512 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 513 newcontent.append(None) - 514 else: - 515 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 516 if(all([x is None for x in newcontent])): - 517 raise Exception('Derivative is undefined at all timeslices') - 518 return Corr(newcontent, padding=[1, 1]) - 519 elif variant == "forward": - 520 newcontent = [] - 521 for t in range(self.T - 1): - 522 if (self.content[t] is None) or (self.content[t + 1] is None): - 523 newcontent.append(None) - 524 else: - 525 newcontent.append(self.content[t + 1] - self.content[t]) - 526 if(all([x is None for x in newcontent])): - 527 raise Exception("Derivative is undefined at all timeslices") - 528 return Corr(newcontent, padding=[0, 1]) - 529 elif variant == "backward": - 530 newcontent = [] - 531 for t in range(1, self.T): - 532 if (self.content[t - 1] is None) or (self.content[t] is None): - 533 newcontent.append(None) - 534 else: - 535 newcontent.append(self.content[t] - self.content[t - 1]) - 536 if(all([x is None for x in newcontent])): - 537 raise Exception("Derivative is undefined at all timeslices") - 538 return Corr(newcontent, padding=[1, 0]) - 539 elif variant == "improved": - 540 newcontent = [] - 541 for t in range(2, self.T - 2): - 542 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): - 543 newcontent.append(None) - 544 else: - 545 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 546 if(all([x is None for x in newcontent])): - 547 raise Exception('Derivative is undefined at all timeslices') - 548 return Corr(newcontent, padding=[2, 2]) - 549 else: - 550 raise Exception("Unknown variant.") - 551 - 552 def second_deriv(self, variant="symmetric"): - 553 """Return the second derivative of the correlator with respect to x0. - 554 - 555 Parameters - 556 ---------- - 557 variant : str - 558 decides which definition of the finite differences derivative is used. - 559 Available choice: symmetric, improved, default: symmetric - 560 """ - 561 if self.N != 1: - 562 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 563 if variant == "symmetric": - 564 newcontent = [] - 565 for t in range(1, self.T - 1): - 566 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 567 newcontent.append(None) - 568 else: - 569 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 570 if(all([x is None for x in newcontent])): - 571 raise Exception("Derivative is undefined at all timeslices") - 572 return Corr(newcontent, padding=[1, 1]) - 573 elif variant == "improved": - 574 newcontent = [] - 575 for t in range(2, self.T - 2): - 576 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): - 577 newcontent.append(None) - 578 else: - 579 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])) - 580 if(all([x is None for x in newcontent])): - 581 raise Exception("Derivative is undefined at all timeslices") - 582 return Corr(newcontent, padding=[2, 2]) - 583 else: - 584 raise Exception("Unknown variant.") - 585 - 586 def m_eff(self, variant='log', guess=1.0): - 587 """Returns the effective mass of the correlator as correlator object - 588 - 589 Parameters - 590 ---------- - 591 variant : str - 592 log : uses the standard effective mass log(C(t) / C(t+1)) - 593 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. - 594 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. - 595 See, e.g., arXiv:1205.5380 - 596 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 597 guess : float - 598 guess for the root finder, only relevant for the root variant - 599 """ - 600 if self.N != 1: - 601 raise Exception('Correlator must be projected before getting m_eff') - 602 if variant == 'log': - 603 newcontent = [] - 604 for t in range(self.T - 1): - 605 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 606 newcontent.append(None) - 607 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 608 newcontent.append(None) - 609 else: - 610 newcontent.append(self.content[t] / self.content[t + 1]) - 611 if(all([x is None for x in newcontent])): - 612 raise Exception('m_eff is undefined at all timeslices') - 613 - 614 return np.log(Corr(newcontent, padding=[0, 1])) - 615 - 616 elif variant in ['periodic', 'cosh', 'sinh']: - 617 if variant in ['periodic', 'cosh']: - 618 func = anp.cosh - 619 else: - 620 func = anp.sinh - 621 - 622 def root_function(x, d): - 623 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 624 - 625 newcontent = [] - 626 for t in range(self.T - 1): - 627 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 628 newcontent.append(None) - 629 # Fill the two timeslices in the middle of the lattice with their predecessors - 630 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 631 newcontent.append(newcontent[-1]) - 632 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 633 newcontent.append(None) - 634 else: - 635 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 636 if(all([x is None for x in newcontent])): - 637 raise Exception('m_eff is undefined at all timeslices') - 638 - 639 return Corr(newcontent, padding=[0, 1]) - 640 - 641 elif variant == 'arccosh': - 642 newcontent = [] - 643 for t in range(1, self.T - 1): - 644 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): - 645 newcontent.append(None) - 646 else: - 647 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) - 648 if(all([x is None for x in newcontent])): - 649 raise Exception("m_eff is undefined at all timeslices") - 650 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 651 - 652 else: - 653 raise Exception('Unknown variant.') - 654 - 655 def fit(self, function, fitrange=None, silent=False, **kwargs): - 656 r'''Fits function to the data - 657 - 658 Parameters - 659 ---------- - 660 function : obj - 661 function to fit to the data. See fits.least_squares for details. - 662 fitrange : list - 663 Two element list containing the timeslices on which the fit is supposed to start and stop. - 664 Caution: This range is inclusive as opposed to standard python indexing. - 665 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 666 If not specified, self.prange or all timeslices are used. - 667 silent : bool - 668 Decides whether output is printed to the standard output. - 669 ''' - 670 if self.N != 1: - 671 raise Exception("Correlator must be projected before fitting") + 419 def thin(self, spacing=2, offset=0): + 420 """Thin out a correlator to suppress correlations + 421 + 422 Parameters + 423 ---------- + 424 spacing : int + 425 Keep only every 'spacing'th entry of the correlator + 426 offset : int + 427 Offset the equal spacing + 428 """ + 429 new_content = [] + 430 for t in range(self.T): + 431 if (offset + t) % spacing != 0: + 432 new_content.append(None) + 433 else: + 434 new_content.append(self.content[t]) + 435 return Corr(new_content) + 436 + 437 def correlate(self, partner): + 438 """Correlate the correlator with another correlator or Obs + 439 + 440 Parameters + 441 ---------- + 442 partner : Obs or Corr + 443 partner to correlate the correlator with. + 444 Can either be an Obs which is correlated with all entries of the + 445 correlator or a Corr of same length. + 446 """ + 447 if self.N != 1: + 448 raise Exception("Only one-dimensional correlators can be safely correlated.") + 449 new_content = [] + 450 for x0, t_slice in enumerate(self.content): + 451 if _check_for_none(self, t_slice): + 452 new_content.append(None) + 453 else: + 454 if isinstance(partner, Corr): + 455 if _check_for_none(partner, partner.content[x0]): + 456 new_content.append(None) + 457 else: + 458 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) + 459 elif isinstance(partner, Obs): # Should this include CObs? + 460 new_content.append(np.array([correlate(o, partner) for o in t_slice])) + 461 else: + 462 raise Exception("Can only correlate with an Obs or a Corr.") + 463 + 464 return Corr(new_content) + 465 + 466 def reweight(self, weight, **kwargs): + 467 """Reweight the correlator. + 468 + 469 Parameters + 470 ---------- + 471 weight : Obs + 472 Reweighting factor. An Observable that has to be defined on a superset of the + 473 configurations in obs[i].idl for all i. + 474 all_configs : bool + 475 if True, the reweighted observables are normalized by the average of + 476 the reweighting factor on all configurations in weight.idl and not + 477 on the configurations in obs[i].idl. + 478 """ + 479 if self.N != 1: + 480 raise Exception("Reweighting only implemented for one-dimensional correlators.") + 481 new_content = [] + 482 for t_slice in self.content: + 483 if _check_for_none(self, t_slice): + 484 new_content.append(None) + 485 else: + 486 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) + 487 return Corr(new_content) + 488 + 489 def T_symmetry(self, partner, parity=+1): + 490 """Return the time symmetry average of the correlator and its partner + 491 + 492 Parameters + 493 ---------- + 494 partner : Corr + 495 Time symmetry partner of the Corr + 496 partity : int + 497 Parity quantum number of the correlator, can be +1 or -1 + 498 """ + 499 if self.N != 1: + 500 raise Exception("T_symmetry only implemented for one-dimensional correlators.") + 501 if not isinstance(partner, Corr): + 502 raise Exception("T partner has to be a Corr object.") + 503 if parity not in [+1, -1]: + 504 raise Exception("Parity has to be +1 or -1.") + 505 T_partner = parity * partner.reverse() + 506 + 507 t_slices = [] + 508 test = (self - T_partner) + 509 test.gamma_method() + 510 for x0, t_slice in enumerate(test.content): + 511 if t_slice is not None: + 512 if not t_slice[0].is_zero_within_error(5): + 513 t_slices.append(x0) + 514 if t_slices: + 515 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) + 516 + 517 return (self + T_partner) / 2 + 518 + 519 def deriv(self, variant="symmetric"): + 520 """Return the first derivative of the correlator with respect to x0. + 521 + 522 Parameters + 523 ---------- + 524 variant : str + 525 decides which definition of the finite differences derivative is used. + 526 Available choice: symmetric, forward, backward, improved, default: symmetric + 527 """ + 528 if self.N != 1: + 529 raise Exception("deriv only implemented for one-dimensional correlators.") + 530 if variant == "symmetric": + 531 newcontent = [] + 532 for t in range(1, self.T - 1): + 533 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 534 newcontent.append(None) + 535 else: + 536 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) + 537 if(all([x is None for x in newcontent])): + 538 raise Exception('Derivative is undefined at all timeslices') + 539 return Corr(newcontent, padding=[1, 1]) + 540 elif variant == "forward": + 541 newcontent = [] + 542 for t in range(self.T - 1): + 543 if (self.content[t] is None) or (self.content[t + 1] is None): + 544 newcontent.append(None) + 545 else: + 546 newcontent.append(self.content[t + 1] - self.content[t]) + 547 if(all([x is None for x in newcontent])): + 548 raise Exception("Derivative is undefined at all timeslices") + 549 return Corr(newcontent, padding=[0, 1]) + 550 elif variant == "backward": + 551 newcontent = [] + 552 for t in range(1, self.T): + 553 if (self.content[t - 1] is None) or (self.content[t] is None): + 554 newcontent.append(None) + 555 else: + 556 newcontent.append(self.content[t] - self.content[t - 1]) + 557 if(all([x is None for x in newcontent])): + 558 raise Exception("Derivative is undefined at all timeslices") + 559 return Corr(newcontent, padding=[1, 0]) + 560 elif variant == "improved": + 561 newcontent = [] + 562 for t in range(2, self.T - 2): + 563 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): + 564 newcontent.append(None) + 565 else: + 566 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) + 567 if(all([x is None for x in newcontent])): + 568 raise Exception('Derivative is undefined at all timeslices') + 569 return Corr(newcontent, padding=[2, 2]) + 570 else: + 571 raise Exception("Unknown variant.") + 572 + 573 def second_deriv(self, variant="symmetric"): + 574 """Return the second derivative of the correlator with respect to x0. + 575 + 576 Parameters + 577 ---------- + 578 variant : str + 579 decides which definition of the finite differences derivative is used. + 580 Available choice: symmetric, improved, default: symmetric + 581 """ + 582 if self.N != 1: + 583 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 584 if variant == "symmetric": + 585 newcontent = [] + 586 for t in range(1, self.T - 1): + 587 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 588 newcontent.append(None) + 589 else: + 590 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 591 if(all([x is None for x in newcontent])): + 592 raise Exception("Derivative is undefined at all timeslices") + 593 return Corr(newcontent, padding=[1, 1]) + 594 elif variant == "improved": + 595 newcontent = [] + 596 for t in range(2, self.T - 2): + 597 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): + 598 newcontent.append(None) + 599 else: + 600 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])) + 601 if(all([x is None for x in newcontent])): + 602 raise Exception("Derivative is undefined at all timeslices") + 603 return Corr(newcontent, padding=[2, 2]) + 604 else: + 605 raise Exception("Unknown variant.") + 606 + 607 def m_eff(self, variant='log', guess=1.0): + 608 """Returns the effective mass of the correlator as correlator object + 609 + 610 Parameters + 611 ---------- + 612 variant : str + 613 log : uses the standard effective mass log(C(t) / C(t+1)) + 614 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. + 615 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. + 616 See, e.g., arXiv:1205.5380 + 617 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 618 guess : float + 619 guess for the root finder, only relevant for the root variant + 620 """ + 621 if self.N != 1: + 622 raise Exception('Correlator must be projected before getting m_eff') + 623 if variant == 'log': + 624 newcontent = [] + 625 for t in range(self.T - 1): + 626 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 627 newcontent.append(None) + 628 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 629 newcontent.append(None) + 630 else: + 631 newcontent.append(self.content[t] / self.content[t + 1]) + 632 if(all([x is None for x in newcontent])): + 633 raise Exception('m_eff is undefined at all timeslices') + 634 + 635 return np.log(Corr(newcontent, padding=[0, 1])) + 636 + 637 elif variant in ['periodic', 'cosh', 'sinh']: + 638 if variant in ['periodic', 'cosh']: + 639 func = anp.cosh + 640 else: + 641 func = anp.sinh + 642 + 643 def root_function(x, d): + 644 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 645 + 646 newcontent = [] + 647 for t in range(self.T - 1): + 648 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 649 newcontent.append(None) + 650 # Fill the two timeslices in the middle of the lattice with their predecessors + 651 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 652 newcontent.append(newcontent[-1]) + 653 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 654 newcontent.append(None) + 655 else: + 656 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) + 657 if(all([x is None for x in newcontent])): + 658 raise Exception('m_eff is undefined at all timeslices') + 659 + 660 return Corr(newcontent, padding=[0, 1]) + 661 + 662 elif variant == 'arccosh': + 663 newcontent = [] + 664 for t in range(1, self.T - 1): + 665 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): + 666 newcontent.append(None) + 667 else: + 668 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 669 if(all([x is None for x in newcontent])): + 670 raise Exception("m_eff is undefined at all timeslices") + 671 return np.arccosh(Corr(newcontent, padding=[1, 1])) 672 - 673 if fitrange is None: - 674 if self.prange: - 675 fitrange = self.prange - 676 else: - 677 fitrange = [0, self.T - 1] - 678 else: - 679 if not isinstance(fitrange, list): - 680 raise Exception("fitrange has to be a list with two elements") - 681 if len(fitrange) != 2: - 682 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 683 - 684 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 685 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 686 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 687 return result - 688 - 689 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 690 """ Extract a plateau value from a Corr object - 691 - 692 Parameters - 693 ---------- - 694 plateau_range : list - 695 list with two entries, indicating the first and the last timeslice - 696 of the plateau region. - 697 method : str - 698 method to extract the plateau. - 699 'fit' fits a constant to the plateau region - 700 'avg', 'average' or 'mean' just average over the given timeslices. - 701 auto_gamma : bool - 702 apply gamma_method with default parameters to the Corr. Defaults to None - 703 """ - 704 if not plateau_range: - 705 if self.prange: - 706 plateau_range = self.prange - 707 else: - 708 raise Exception("no plateau range provided") - 709 if self.N != 1: - 710 raise Exception("Correlator must be projected before getting a plateau.") - 711 if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 712 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 713 if auto_gamma: - 714 self.gamma_method() - 715 if method == "fit": - 716 def const_func(a, t): - 717 return a[0] - 718 return self.fit(const_func, plateau_range)[0] - 719 elif method in ["avg", "average", "mean"]: - 720 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 721 return returnvalue - 722 - 723 else: - 724 raise Exception("Unsupported plateau method: " + method) - 725 - 726 def set_prange(self, prange): - 727 """Sets the attribute prange of the Corr object.""" - 728 if not len(prange) == 2: - 729 raise Exception("prange must be a list or array with two values") - 730 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 731 raise Exception("Start and end point must be integers") - 732 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 733 raise Exception("Start and end point must define a range in the interval 0,T") - 734 - 735 self.prange = prange - 736 return - 737 - 738 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): - 739 """Plots the correlator using the tag of the correlator as label if available. - 740 - 741 Parameters - 742 ---------- - 743 x_range : list - 744 list of two values, determining the range of the x-axis e.g. [4, 8]. - 745 comp : Corr or list of Corr - 746 Correlator or list of correlators which are plotted for comparison. - 747 The tags of these correlators are used as labels if available. - 748 logscale : bool - 749 Sets y-axis to logscale. - 750 plateau : Obs - 751 Plateau value to be visualized in the figure. - 752 fit_res : Fit_result - 753 Fit_result object to be visualized. - 754 ylabel : str - 755 Label for the y-axis. - 756 save : str - 757 path to file in which the figure should be saved. - 758 auto_gamma : bool - 759 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 760 hide_sigma : float - 761 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 762 references : list - 763 List of floating point values that are displayed as horizontal lines for reference. - 764 title : string - 765 Optional title of the figure. - 766 """ - 767 if self.N != 1: - 768 raise Exception("Correlator must be projected before plotting") - 769 - 770 if auto_gamma: - 771 self.gamma_method() - 772 - 773 if x_range is None: - 774 x_range = [0, self.T - 1] - 775 - 776 fig = plt.figure() - 777 ax1 = fig.add_subplot(111) - 778 - 779 x, y, y_err = self.plottable() - 780 if hide_sigma: - 781 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 782 else: - 783 hide_from = None - 784 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 785 if logscale: - 786 ax1.set_yscale('log') - 787 else: - 788 if y_range is None: - 789 try: - 790 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)]) - 791 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)]) - 792 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 793 except Exception: - 794 pass - 795 else: - 796 ax1.set_ylim(y_range) - 797 if comp: - 798 if isinstance(comp, (Corr, list)): - 799 for corr in comp if isinstance(comp, list) else [comp]: - 800 if auto_gamma: - 801 corr.gamma_method() - 802 x, y, y_err = corr.plottable() - 803 if hide_sigma: - 804 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 805 else: - 806 hide_from = None - 807 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 808 else: - 809 raise Exception("'comp' must be a correlator or a list of correlators.") - 810 - 811 if plateau: - 812 if isinstance(plateau, Obs): - 813 if auto_gamma: - 814 plateau.gamma_method() - 815 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 816 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 817 else: - 818 raise Exception("'plateau' must be an Obs") - 819 - 820 if references: - 821 if isinstance(references, list): - 822 for ref in references: - 823 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 824 else: - 825 raise Exception("'references' must be a list of floating pint values.") - 826 - 827 if self.prange: - 828 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 829 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 830 - 831 if fit_res: - 832 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 833 ax1.plot(x_samples, - 834 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 835 ls='-', marker=',', lw=2) - 836 - 837 ax1.set_xlabel(r'$x_0 / a$') - 838 if ylabel: - 839 ax1.set_ylabel(ylabel) - 840 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 841 - 842 handles, labels = ax1.get_legend_handles_labels() - 843 if labels: - 844 ax1.legend() - 845 - 846 if title: - 847 plt.title(title) - 848 - 849 plt.draw() - 850 - 851 if save: - 852 if isinstance(save, str): - 853 fig.savefig(save, bbox_inches='tight') - 854 else: - 855 raise Exception("'save' has to be a string.") - 856 - 857 def spaghetti_plot(self, logscale=True): - 858 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 859 - 860 Parameters - 861 ---------- - 862 logscale : bool - 863 Determines whether the scale of the y-axis is logarithmic or standard. - 864 """ - 865 if self.N != 1: - 866 raise Exception("Correlator needs to be projected first.") - 867 - 868 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) - 869 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 870 - 871 for name in mc_names: - 872 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T - 873 - 874 fig = plt.figure() - 875 ax = fig.add_subplot(111) - 876 for dat in data: - 877 ax.plot(x0_vals, dat, ls='-', marker='') - 878 - 879 if logscale is True: - 880 ax.set_yscale('log') - 881 - 882 ax.set_xlabel(r'$x_0 / a$') - 883 plt.title(name) - 884 plt.draw() - 885 - 886 def dump(self, filename, datatype="json.gz", **kwargs): - 887 """Dumps the Corr into a file of chosen type - 888 Parameters - 889 ---------- - 890 filename : str - 891 Name of the file to be saved. - 892 datatype : str - 893 Format of the exported file. Supported formats include - 894 "json.gz" and "pickle" - 895 path : str - 896 specifies a custom path for the file (default '.') - 897 """ - 898 if datatype == "json.gz": - 899 from .input.json import dump_to_json - 900 if 'path' in kwargs: - 901 file_name = kwargs.get('path') + '/' + filename - 902 else: - 903 file_name = filename - 904 dump_to_json(self, file_name) - 905 elif datatype == "pickle": - 906 dump_object(self, filename, **kwargs) - 907 else: - 908 raise Exception("Unknown datatype " + str(datatype)) - 909 - 910 def print(self, print_range=None): - 911 print(self.__repr__(print_range)) - 912 - 913 def __repr__(self, print_range=None): - 914 if print_range is None: - 915 print_range = [0, None] - 916 - 917 content_string = "" - 918 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 - 919 - 920 if self.tag is not None: - 921 content_string += "Description: " + self.tag + "\n" - 922 if self.N != 1: - 923 return content_string - 924 - 925 if print_range[1]: - 926 print_range[1] += 1 - 927 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 928 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 929 if sub_corr is None: - 930 content_string += str(i + print_range[0]) + '\n' - 931 else: - 932 content_string += str(i + print_range[0]) - 933 for element in sub_corr: - 934 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 935 content_string += '\n' - 936 return content_string + 673 else: + 674 raise Exception('Unknown variant.') + 675 + 676 def fit(self, function, fitrange=None, silent=False, **kwargs): + 677 r'''Fits function to the data + 678 + 679 Parameters + 680 ---------- + 681 function : obj + 682 function to fit to the data. See fits.least_squares for details. + 683 fitrange : list + 684 Two element list containing the timeslices on which the fit is supposed to start and stop. + 685 Caution: This range is inclusive as opposed to standard python indexing. + 686 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 687 If not specified, self.prange or all timeslices are used. + 688 silent : bool + 689 Decides whether output is printed to the standard output. + 690 ''' + 691 if self.N != 1: + 692 raise Exception("Correlator must be projected before fitting") + 693 + 694 if fitrange is None: + 695 if self.prange: + 696 fitrange = self.prange + 697 else: + 698 fitrange = [0, self.T - 1] + 699 else: + 700 if not isinstance(fitrange, list): + 701 raise Exception("fitrange has to be a list with two elements") + 702 if len(fitrange) != 2: + 703 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 704 + 705 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 706 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 707 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 708 return result + 709 + 710 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 711 """ Extract a plateau value from a Corr object + 712 + 713 Parameters + 714 ---------- + 715 plateau_range : list + 716 list with two entries, indicating the first and the last timeslice + 717 of the plateau region. + 718 method : str + 719 method to extract the plateau. + 720 'fit' fits a constant to the plateau region + 721 'avg', 'average' or 'mean' just average over the given timeslices. + 722 auto_gamma : bool + 723 apply gamma_method with default parameters to the Corr. Defaults to None + 724 """ + 725 if not plateau_range: + 726 if self.prange: + 727 plateau_range = self.prange + 728 else: + 729 raise Exception("no plateau range provided") + 730 if self.N != 1: + 731 raise Exception("Correlator must be projected before getting a plateau.") + 732 if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 733 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 734 if auto_gamma: + 735 self.gamma_method() + 736 if method == "fit": + 737 def const_func(a, t): + 738 return a[0] + 739 return self.fit(const_func, plateau_range)[0] + 740 elif method in ["avg", "average", "mean"]: + 741 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 742 return returnvalue + 743 + 744 else: + 745 raise Exception("Unsupported plateau method: " + method) + 746 + 747 def set_prange(self, prange): + 748 """Sets the attribute prange of the Corr object.""" + 749 if not len(prange) == 2: + 750 raise Exception("prange must be a list or array with two values") + 751 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 752 raise Exception("Start and end point must be integers") + 753 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 754 raise Exception("Start and end point must define a range in the interval 0,T") + 755 + 756 self.prange = prange + 757 return + 758 + 759 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): + 760 """Plots the correlator using the tag of the correlator as label if available. + 761 + 762 Parameters + 763 ---------- + 764 x_range : list + 765 list of two values, determining the range of the x-axis e.g. [4, 8]. + 766 comp : Corr or list of Corr + 767 Correlator or list of correlators which are plotted for comparison. + 768 The tags of these correlators are used as labels if available. + 769 logscale : bool + 770 Sets y-axis to logscale. + 771 plateau : Obs + 772 Plateau value to be visualized in the figure. + 773 fit_res : Fit_result + 774 Fit_result object to be visualized. + 775 ylabel : str + 776 Label for the y-axis. + 777 save : str + 778 path to file in which the figure should be saved. + 779 auto_gamma : bool + 780 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 781 hide_sigma : float + 782 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 783 references : list + 784 List of floating point values that are displayed as horizontal lines for reference. + 785 title : string + 786 Optional title of the figure. + 787 """ + 788 if self.N != 1: + 789 raise Exception("Correlator must be projected before plotting") + 790 + 791 if auto_gamma: + 792 self.gamma_method() + 793 + 794 if x_range is None: + 795 x_range = [0, self.T - 1] + 796 + 797 fig = plt.figure() + 798 ax1 = fig.add_subplot(111) + 799 + 800 x, y, y_err = self.plottable() + 801 if hide_sigma: + 802 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 803 else: + 804 hide_from = None + 805 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 806 if logscale: + 807 ax1.set_yscale('log') + 808 else: + 809 if y_range is None: + 810 try: + 811 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)]) + 812 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)]) + 813 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 814 except Exception: + 815 pass + 816 else: + 817 ax1.set_ylim(y_range) + 818 if comp: + 819 if isinstance(comp, (Corr, list)): + 820 for corr in comp if isinstance(comp, list) else [comp]: + 821 if auto_gamma: + 822 corr.gamma_method() + 823 x, y, y_err = corr.plottable() + 824 if hide_sigma: + 825 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 826 else: + 827 hide_from = None + 828 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 829 else: + 830 raise Exception("'comp' must be a correlator or a list of correlators.") + 831 + 832 if plateau: + 833 if isinstance(plateau, Obs): + 834 if auto_gamma: + 835 plateau.gamma_method() + 836 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 837 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 838 else: + 839 raise Exception("'plateau' must be an Obs") + 840 + 841 if references: + 842 if isinstance(references, list): + 843 for ref in references: + 844 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 845 else: + 846 raise Exception("'references' must be a list of floating pint values.") + 847 + 848 if self.prange: + 849 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 850 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') + 851 + 852 if fit_res: + 853 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 854 ax1.plot(x_samples, + 855 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 856 ls='-', marker=',', lw=2) + 857 + 858 ax1.set_xlabel(r'$x_0 / a$') + 859 if ylabel: + 860 ax1.set_ylabel(ylabel) + 861 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 862 + 863 handles, labels = ax1.get_legend_handles_labels() + 864 if labels: + 865 ax1.legend() + 866 + 867 if title: + 868 plt.title(title) + 869 + 870 plt.draw() + 871 + 872 if save: + 873 if isinstance(save, str): + 874 fig.savefig(save, bbox_inches='tight') + 875 else: + 876 raise Exception("'save' has to be a string.") + 877 + 878 def spaghetti_plot(self, logscale=True): + 879 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 880 + 881 Parameters + 882 ---------- + 883 logscale : bool + 884 Determines whether the scale of the y-axis is logarithmic or standard. + 885 """ + 886 if self.N != 1: + 887 raise Exception("Correlator needs to be projected first.") + 888 + 889 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) + 890 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 891 + 892 for name in mc_names: + 893 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 894 + 895 fig = plt.figure() + 896 ax = fig.add_subplot(111) + 897 for dat in data: + 898 ax.plot(x0_vals, dat, ls='-', marker='') + 899 + 900 if logscale is True: + 901 ax.set_yscale('log') + 902 + 903 ax.set_xlabel(r'$x_0 / a$') + 904 plt.title(name) + 905 plt.draw() + 906 + 907 def dump(self, filename, datatype="json.gz", **kwargs): + 908 """Dumps the Corr into a file of chosen type + 909 Parameters + 910 ---------- + 911 filename : str + 912 Name of the file to be saved. + 913 datatype : str + 914 Format of the exported file. Supported formats include + 915 "json.gz" and "pickle" + 916 path : str + 917 specifies a custom path for the file (default '.') + 918 """ + 919 if datatype == "json.gz": + 920 from .input.json import dump_to_json + 921 if 'path' in kwargs: + 922 file_name = kwargs.get('path') + '/' + filename + 923 else: + 924 file_name = filename + 925 dump_to_json(self, file_name) + 926 elif datatype == "pickle": + 927 dump_object(self, filename, **kwargs) + 928 else: + 929 raise Exception("Unknown datatype " + str(datatype)) + 930 + 931 def print(self, print_range=None): + 932 print(self.__repr__(print_range)) + 933 + 934 def __repr__(self, print_range=None): + 935 if print_range is None: + 936 print_range = [0, None] 937 - 938 def __str__(self): - 939 return self.__repr__() + 938 content_string = "" + 939 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 940 - 941 # We define the basic operations, that can be performed with correlators. - 942 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 943 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 944 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 941 if self.tag is not None: + 942 content_string += "Description: " + self.tag + "\n" + 943 if self.N != 1: + 944 return content_string 945 - 946 def __add__(self, y): - 947 if isinstance(y, Corr): - 948 if ((self.N != y.N) or (self.T != y.T)): - 949 raise Exception("Addition of Corrs with different shape") - 950 newcontent = [] - 951 for t in range(self.T): - 952 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 953 newcontent.append(None) - 954 else: - 955 newcontent.append(self.content[t] + y.content[t]) - 956 return Corr(newcontent) - 957 - 958 elif isinstance(y, (Obs, int, float, CObs)): - 959 newcontent = [] - 960 for t in range(self.T): - 961 if _check_for_none(self, self.content[t]): - 962 newcontent.append(None) - 963 else: - 964 newcontent.append(self.content[t] + y) - 965 return Corr(newcontent, prange=self.prange) - 966 elif isinstance(y, np.ndarray): - 967 if y.shape == (self.T,): - 968 return Corr(list((np.array(self.content).T + y).T)) - 969 else: - 970 raise ValueError("operands could not be broadcast together") - 971 else: - 972 raise TypeError("Corr + wrong type") - 973 - 974 def __mul__(self, y): - 975 if isinstance(y, Corr): - 976 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 977 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") - 978 newcontent = [] - 979 for t in range(self.T): - 980 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 981 newcontent.append(None) - 982 else: - 983 newcontent.append(self.content[t] * y.content[t]) - 984 return Corr(newcontent) - 985 - 986 elif isinstance(y, (Obs, int, float, CObs)): - 987 newcontent = [] - 988 for t in range(self.T): - 989 if _check_for_none(self, self.content[t]): - 990 newcontent.append(None) - 991 else: - 992 newcontent.append(self.content[t] * y) - 993 return Corr(newcontent, prange=self.prange) - 994 elif isinstance(y, np.ndarray): - 995 if y.shape == (self.T,): - 996 return Corr(list((np.array(self.content).T * y).T)) - 997 else: - 998 raise ValueError("operands could not be broadcast together") - 999 else: -1000 raise TypeError("Corr * wrong type") -1001 -1002 def __truediv__(self, y): -1003 if isinstance(y, Corr): -1004 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1005 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1006 newcontent = [] -1007 for t in range(self.T): -1008 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1009 newcontent.append(None) -1010 else: -1011 newcontent.append(self.content[t] / y.content[t]) -1012 for t in range(self.T): -1013 if _check_for_none(self, newcontent[t]): -1014 continue -1015 if np.isnan(np.sum(newcontent[t]).value): -1016 newcontent[t] = None -1017 -1018 if all([item is None for item in newcontent]): -1019 raise Exception("Division returns completely undefined correlator") -1020 return Corr(newcontent) -1021 -1022 elif isinstance(y, (Obs, CObs)): -1023 if isinstance(y, Obs): -1024 if y.value == 0: -1025 raise Exception('Division by zero will return undefined correlator') -1026 if isinstance(y, CObs): -1027 if y.is_zero(): -1028 raise Exception('Division by zero will return undefined correlator') -1029 -1030 newcontent = [] -1031 for t in range(self.T): -1032 if _check_for_none(self, self.content[t]): -1033 newcontent.append(None) -1034 else: -1035 newcontent.append(self.content[t] / y) -1036 return Corr(newcontent, prange=self.prange) -1037 -1038 elif isinstance(y, (int, float)): -1039 if y == 0: -1040 raise Exception('Division by zero will return undefined correlator') -1041 newcontent = [] -1042 for t in range(self.T): -1043 if _check_for_none(self, self.content[t]): -1044 newcontent.append(None) -1045 else: -1046 newcontent.append(self.content[t] / y) -1047 return Corr(newcontent, prange=self.prange) -1048 elif isinstance(y, np.ndarray): -1049 if y.shape == (self.T,): -1050 return Corr(list((np.array(self.content).T / y).T)) -1051 else: -1052 raise ValueError("operands could not be broadcast together") -1053 else: -1054 raise TypeError('Corr / wrong type') -1055 -1056 def __neg__(self): -1057 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1058 return Corr(newcontent, prange=self.prange) -1059 -1060 def __sub__(self, y): -1061 return self + (-y) -1062 -1063 def __pow__(self, y): -1064 if isinstance(y, (Obs, int, float, CObs)): -1065 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1066 return Corr(newcontent, prange=self.prange) -1067 else: -1068 raise TypeError('Type of exponent not supported') -1069 -1070 def __abs__(self): -1071 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1072 return Corr(newcontent, prange=self.prange) -1073 -1074 # The numpy functions: -1075 def sqrt(self): -1076 return self ** 0.5 -1077 -1078 def log(self): -1079 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1080 return Corr(newcontent, prange=self.prange) -1081 -1082 def exp(self): -1083 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1084 return Corr(newcontent, prange=self.prange) -1085 -1086 def _apply_func_to_corr(self, func): -1087 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1088 for t in range(self.T): -1089 if _check_for_none(self, newcontent[t]): -1090 continue -1091 if np.isnan(np.sum(newcontent[t]).value): -1092 newcontent[t] = None -1093 if all([item is None for item in newcontent]): -1094 raise Exception('Operation returns undefined correlator') -1095 return Corr(newcontent) -1096 -1097 def sin(self): -1098 return self._apply_func_to_corr(np.sin) -1099 -1100 def cos(self): -1101 return self._apply_func_to_corr(np.cos) + 946 if print_range[1]: + 947 print_range[1] += 1 + 948 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 949 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 950 if sub_corr is None: + 951 content_string += str(i + print_range[0]) + '\n' + 952 else: + 953 content_string += str(i + print_range[0]) + 954 for element in sub_corr: + 955 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 956 content_string += '\n' + 957 return content_string + 958 + 959 def __str__(self): + 960 return self.__repr__() + 961 + 962 # We define the basic operations, that can be performed with correlators. + 963 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. + 964 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. + 965 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 966 + 967 def __add__(self, y): + 968 if isinstance(y, Corr): + 969 if ((self.N != y.N) or (self.T != y.T)): + 970 raise Exception("Addition of Corrs with different shape") + 971 newcontent = [] + 972 for t in range(self.T): + 973 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): + 974 newcontent.append(None) + 975 else: + 976 newcontent.append(self.content[t] + y.content[t]) + 977 return Corr(newcontent) + 978 + 979 elif isinstance(y, (Obs, int, float, CObs)): + 980 newcontent = [] + 981 for t in range(self.T): + 982 if _check_for_none(self, self.content[t]): + 983 newcontent.append(None) + 984 else: + 985 newcontent.append(self.content[t] + y) + 986 return Corr(newcontent, prange=self.prange) + 987 elif isinstance(y, np.ndarray): + 988 if y.shape == (self.T,): + 989 return Corr(list((np.array(self.content).T + y).T)) + 990 else: + 991 raise ValueError("operands could not be broadcast together") + 992 else: + 993 raise TypeError("Corr + wrong type") + 994 + 995 def __mul__(self, y): + 996 if isinstance(y, Corr): + 997 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): + 998 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") + 999 newcontent = [] +1000 for t in range(self.T): +1001 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1002 newcontent.append(None) +1003 else: +1004 newcontent.append(self.content[t] * y.content[t]) +1005 return Corr(newcontent) +1006 +1007 elif isinstance(y, (Obs, int, float, CObs)): +1008 newcontent = [] +1009 for t in range(self.T): +1010 if _check_for_none(self, self.content[t]): +1011 newcontent.append(None) +1012 else: +1013 newcontent.append(self.content[t] * y) +1014 return Corr(newcontent, prange=self.prange) +1015 elif isinstance(y, np.ndarray): +1016 if y.shape == (self.T,): +1017 return Corr(list((np.array(self.content).T * y).T)) +1018 else: +1019 raise ValueError("operands could not be broadcast together") +1020 else: +1021 raise TypeError("Corr * wrong type") +1022 +1023 def __truediv__(self, y): +1024 if isinstance(y, Corr): +1025 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1026 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1027 newcontent = [] +1028 for t in range(self.T): +1029 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1030 newcontent.append(None) +1031 else: +1032 newcontent.append(self.content[t] / y.content[t]) +1033 for t in range(self.T): +1034 if _check_for_none(self, newcontent[t]): +1035 continue +1036 if np.isnan(np.sum(newcontent[t]).value): +1037 newcontent[t] = None +1038 +1039 if all([item is None for item in newcontent]): +1040 raise Exception("Division returns completely undefined correlator") +1041 return Corr(newcontent) +1042 +1043 elif isinstance(y, (Obs, CObs)): +1044 if isinstance(y, Obs): +1045 if y.value == 0: +1046 raise Exception('Division by zero will return undefined correlator') +1047 if isinstance(y, CObs): +1048 if y.is_zero(): +1049 raise Exception('Division by zero will return undefined correlator') +1050 +1051 newcontent = [] +1052 for t in range(self.T): +1053 if _check_for_none(self, self.content[t]): +1054 newcontent.append(None) +1055 else: +1056 newcontent.append(self.content[t] / y) +1057 return Corr(newcontent, prange=self.prange) +1058 +1059 elif isinstance(y, (int, float)): +1060 if y == 0: +1061 raise Exception('Division by zero will return undefined correlator') +1062 newcontent = [] +1063 for t in range(self.T): +1064 if _check_for_none(self, self.content[t]): +1065 newcontent.append(None) +1066 else: +1067 newcontent.append(self.content[t] / y) +1068 return Corr(newcontent, prange=self.prange) +1069 elif isinstance(y, np.ndarray): +1070 if y.shape == (self.T,): +1071 return Corr(list((np.array(self.content).T / y).T)) +1072 else: +1073 raise ValueError("operands could not be broadcast together") +1074 else: +1075 raise TypeError('Corr / wrong type') +1076 +1077 def __neg__(self): +1078 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1079 return Corr(newcontent, prange=self.prange) +1080 +1081 def __sub__(self, y): +1082 return self + (-y) +1083 +1084 def __pow__(self, y): +1085 if isinstance(y, (Obs, int, float, CObs)): +1086 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1087 return Corr(newcontent, prange=self.prange) +1088 else: +1089 raise TypeError('Type of exponent not supported') +1090 +1091 def __abs__(self): +1092 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1093 return Corr(newcontent, prange=self.prange) +1094 +1095 # The numpy functions: +1096 def sqrt(self): +1097 return self ** 0.5 +1098 +1099 def log(self): +1100 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1101 return Corr(newcontent, prange=self.prange) 1102 -1103 def tan(self): -1104 return self._apply_func_to_corr(np.tan) -1105 -1106 def sinh(self): -1107 return self._apply_func_to_corr(np.sinh) -1108 -1109 def cosh(self): -1110 return self._apply_func_to_corr(np.cosh) -1111 -1112 def tanh(self): -1113 return self._apply_func_to_corr(np.tanh) -1114 -1115 def arcsin(self): -1116 return self._apply_func_to_corr(np.arcsin) +1103 def exp(self): +1104 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1105 return Corr(newcontent, prange=self.prange) +1106 +1107 def _apply_func_to_corr(self, func): +1108 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1109 for t in range(self.T): +1110 if _check_for_none(self, newcontent[t]): +1111 continue +1112 if np.isnan(np.sum(newcontent[t]).value): +1113 newcontent[t] = None +1114 if all([item is None for item in newcontent]): +1115 raise Exception('Operation returns undefined correlator') +1116 return Corr(newcontent) 1117 -1118 def arccos(self): -1119 return self._apply_func_to_corr(np.arccos) +1118 def sin(self): +1119 return self._apply_func_to_corr(np.sin) 1120 -1121 def arctan(self): -1122 return self._apply_func_to_corr(np.arctan) +1121 def cos(self): +1122 return self._apply_func_to_corr(np.cos) 1123 -1124 def arcsinh(self): -1125 return self._apply_func_to_corr(np.arcsinh) +1124 def tan(self): +1125 return self._apply_func_to_corr(np.tan) 1126 -1127 def arccosh(self): -1128 return self._apply_func_to_corr(np.arccosh) +1127 def sinh(self): +1128 return self._apply_func_to_corr(np.sinh) 1129 -1130 def arctanh(self): -1131 return self._apply_func_to_corr(np.arctanh) +1130 def cosh(self): +1131 return self._apply_func_to_corr(np.cosh) 1132 -1133 # Right hand side operations (require tweak in main module to work) -1134 def __radd__(self, y): -1135 return self + y -1136 -1137 def __rsub__(self, y): -1138 return -self + y -1139 -1140 def __rmul__(self, y): -1141 return self * y -1142 -1143 def __rtruediv__(self, y): -1144 return (self / y) ** (-1) -1145 -1146 @property -1147 def real(self): -1148 def return_real(obs_OR_cobs): -1149 if isinstance(obs_OR_cobs, CObs): -1150 return obs_OR_cobs.real -1151 else: -1152 return obs_OR_cobs +1133 def tanh(self): +1134 return self._apply_func_to_corr(np.tanh) +1135 +1136 def arcsin(self): +1137 return self._apply_func_to_corr(np.arcsin) +1138 +1139 def arccos(self): +1140 return self._apply_func_to_corr(np.arccos) +1141 +1142 def arctan(self): +1143 return self._apply_func_to_corr(np.arctan) +1144 +1145 def arcsinh(self): +1146 return self._apply_func_to_corr(np.arcsinh) +1147 +1148 def arccosh(self): +1149 return self._apply_func_to_corr(np.arccosh) +1150 +1151 def arctanh(self): +1152 return self._apply_func_to_corr(np.arctanh) 1153 -1154 return self._apply_func_to_corr(return_real) -1155 -1156 @property -1157 def imag(self): -1158 def return_imag(obs_OR_cobs): -1159 if isinstance(obs_OR_cobs, CObs): -1160 return obs_OR_cobs.imag -1161 else: -1162 return obs_OR_cobs * 0 # So it stays the right type +1154 # Right hand side operations (require tweak in main module to work) +1155 def __radd__(self, y): +1156 return self + y +1157 +1158 def __rsub__(self, y): +1159 return -self + y +1160 +1161 def __rmul__(self, y): +1162 return self * y 1163 -1164 return self._apply_func_to_corr(return_imag) -1165 -1166 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1167 r''' Project large correlation matrix to lowest states -1168 -1169 This method can be used to reduce the size of an (N x N) correlation matrix -1170 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1171 is still small. -1172 -1173 Parameters -1174 ---------- -1175 Ntrunc: int -1176 Rank of the target matrix. -1177 tproj: int -1178 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1179 The default value is 3. -1180 t0proj: int -1181 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1182 discouraged for O(a) improved theories, since the correctness of the procedure -1183 cannot be granted in this case. The default value is 2. -1184 basematrix : Corr -1185 Correlation matrix that is used to determine the eigenvectors of the -1186 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1187 is is not specified. -1188 -1189 Notes -1190 ----- -1191 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1192 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1193 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1194 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1195 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1196 correlation matrix and to remove some noise that is added by irrelevant operators. -1197 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1198 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1199 ''' -1200 -1201 if self.N == 1: -1202 raise Exception('Method cannot be applied to one-dimensional correlators.') -1203 if basematrix is None: -1204 basematrix = self -1205 if Ntrunc >= basematrix.N: -1206 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1207 if basematrix.N != self.N: -1208 raise Exception('basematrix and targetmatrix have to be of the same size.') +1164 def __rtruediv__(self, y): +1165 return (self / y) ** (-1) +1166 +1167 @property +1168 def real(self): +1169 def return_real(obs_OR_cobs): +1170 if isinstance(obs_OR_cobs, CObs): +1171 return obs_OR_cobs.real +1172 else: +1173 return obs_OR_cobs +1174 +1175 return self._apply_func_to_corr(return_real) +1176 +1177 @property +1178 def imag(self): +1179 def return_imag(obs_OR_cobs): +1180 if isinstance(obs_OR_cobs, CObs): +1181 return obs_OR_cobs.imag +1182 else: +1183 return obs_OR_cobs * 0 # So it stays the right type +1184 +1185 return self._apply_func_to_corr(return_imag) +1186 +1187 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1188 r''' Project large correlation matrix to lowest states +1189 +1190 This method can be used to reduce the size of an (N x N) correlation matrix +1191 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1192 is still small. +1193 +1194 Parameters +1195 ---------- +1196 Ntrunc: int +1197 Rank of the target matrix. +1198 tproj: int +1199 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1200 The default value is 3. +1201 t0proj: int +1202 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1203 discouraged for O(a) improved theories, since the correctness of the procedure +1204 cannot be granted in this case. The default value is 2. +1205 basematrix : Corr +1206 Correlation matrix that is used to determine the eigenvectors of the +1207 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1208 is is not specified. 1209 -1210 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1211 -1212 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1213 rmat = [] -1214 for t in range(basematrix.T): -1215 for i in range(Ntrunc): -1216 for j in range(Ntrunc): -1217 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1218 rmat.append(np.copy(tmpmat)) -1219 -1220 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1221 return Corr(newcontent) -1222 -1223 -1224def _sort_vectors(vec_set, ts): -1225 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" -1226 reference_sorting = np.array(vec_set[ts]) -1227 N = reference_sorting.shape[0] -1228 sorted_vec_set = [] -1229 for t in range(len(vec_set)): -1230 if vec_set[t] is None: -1231 sorted_vec_set.append(None) -1232 elif not t == ts: -1233 perms = [list(o) for o in permutations([i for i in range(N)], N)] -1234 best_score = 0 -1235 for perm in perms: -1236 current_score = 1 -1237 for k in range(N): -1238 new_sorting = reference_sorting.copy() -1239 new_sorting[perm[k], :] = vec_set[t][k] -1240 current_score *= abs(np.linalg.det(new_sorting)) -1241 if current_score > best_score: -1242 best_score = current_score -1243 best_perm = perm -1244 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) -1245 else: -1246 sorted_vec_set.append(vec_set[t]) -1247 -1248 return sorted_vec_set -1249 -1250 -1251def _check_for_none(corr, entry): -1252 """Checks if entry for correlator corr is None""" -1253 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 -1254 -1255 -1256def _GEVP_solver(Gt, G0): -1257 """Helper function for solving the GEVP and sorting the eigenvectors. -1258 -1259 The helper function assumes that both provided matrices are symmetric and -1260 only processes the lower triangular part of both matrices. In case the matrices -1261 are not symmetric the upper triangular parts are effectively discarded.""" -1262 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] +1210 Notes +1211 ----- +1212 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1213 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1214 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1215 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1216 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1217 correlation matrix and to remove some noise that is added by irrelevant operators. +1218 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1219 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1220 ''' +1221 +1222 if self.N == 1: +1223 raise Exception('Method cannot be applied to one-dimensional correlators.') +1224 if basematrix is None: +1225 basematrix = self +1226 if Ntrunc >= basematrix.N: +1227 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1228 if basematrix.N != self.N: +1229 raise Exception('basematrix and targetmatrix have to be of the same size.') +1230 +1231 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1232 +1233 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1234 rmat = [] +1235 for t in range(basematrix.T): +1236 for i in range(Ntrunc): +1237 for j in range(Ntrunc): +1238 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1239 rmat.append(np.copy(tmpmat)) +1240 +1241 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1242 return Corr(newcontent) +1243 +1244 +1245def _sort_vectors(vec_set, ts): +1246 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" +1247 reference_sorting = np.array(vec_set[ts]) +1248 N = reference_sorting.shape[0] +1249 sorted_vec_set = [] +1250 for t in range(len(vec_set)): +1251 if vec_set[t] is None: +1252 sorted_vec_set.append(None) +1253 elif not t == ts: +1254 perms = [list(o) for o in permutations([i for i in range(N)], N)] +1255 best_score = 0 +1256 for perm in perms: +1257 current_score = 1 +1258 for k in range(N): +1259 new_sorting = reference_sorting.copy() +1260 new_sorting[perm[k], :] = vec_set[t][k] +1261 current_score *= abs(np.linalg.det(new_sorting)) +1262 if current_score > best_score: +1263 best_score = current_score +1264 best_perm = perm +1265 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) +1266 else: +1267 sorted_vec_set.append(vec_set[t]) +1268 +1269 return sorted_vec_set +1270 +1271 +1272def _check_for_none(corr, entry): +1273 """Checks if entry for correlator corr is None""" +1274 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1275 +1276 +1277def _GEVP_solver(Gt, G0): +1278 """Helper function for solving the GEVP and sorting the eigenvectors. +1279 +1280 The helper function assumes that both provided matrices are symmetric and +1281 only processes the lower triangular part of both matrices. In case the matrices +1282 are not symmetric the upper triangular parts are effectively discarded.""" +1283 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] @@ -1716,988 +1740,1009 @@ 238 raise Exception("Corr could not be symmetrized: No redundant values") 239 return Corr(newcontent, prange=self.prange) 240 - 241 def matrix_symmetric(self): - 242 """Symmetrizes the correlator matrices on every timeslice.""" - 243 if self.N > 1: - 244 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 245 return 0.5 * (Corr(transposed) + self) - 246 if self.N == 1: - 247 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 248 - 249 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 250 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 251 - 252 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 253 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 254 ```python - 255 C.GEVP(t0=2)[0] # Ground state vector(s) - 256 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 257 ``` - 258 - 259 Parameters - 260 ---------- - 261 t0 : int - 262 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 263 ts : int - 264 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 265 If sort="Eigenvector" it gives a reference point for the sorting method. - 266 sort : string - 267 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. - 268 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 269 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 270 The reference state is identified by its eigenvalue at $t=t_s$. - 271 - 272 Other Parameters - 273 ---------------- - 274 state : int - 275 Returns only the vector(s) for a specified state. The lowest state is zero. - 276 ''' - 277 - 278 if self.N == 1: - 279 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 280 if ts is not None: - 281 if (ts <= t0): - 282 raise Exception("ts has to be larger than t0.") - 283 - 284 if "sorted_list" in kwargs: - 285 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 286 sort = kwargs.get("sorted_list") - 287 - 288 symmetric_corr = self.matrix_symmetric() - 289 if sort is None: - 290 if (ts is None): - 291 raise Exception("ts is required if sort=None.") - 292 if (self.content[t0] is None) or (self.content[ts] is None): - 293 raise Exception("Corr not defined at t0/ts.") - 294 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") - 295 for i in range(self.N): - 296 for j in range(self.N): - 297 G0[i, j] = symmetric_corr[t0][i, j].value - 298 Gt[i, j] = symmetric_corr[ts][i, j].value - 299 - 300 reordered_vecs = _GEVP_solver(Gt, G0) - 301 - 302 elif sort in ["Eigenvalue", "Eigenvector"]: - 303 if sort == "Eigenvalue" and ts is not None: - 304 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) - 305 all_vecs = [None] * (t0 + 1) - 306 for t in range(t0 + 1, self.T): - 307 try: - 308 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") - 309 for i in range(self.N): - 310 for j in range(self.N): - 311 G0[i, j] = symmetric_corr[t0][i, j].value - 312 Gt[i, j] = symmetric_corr[t][i, j].value - 313 - 314 all_vecs.append(_GEVP_solver(Gt, G0)) - 315 except Exception: - 316 all_vecs.append(None) - 317 if sort == "Eigenvector": - 318 if (ts is None): - 319 raise Exception("ts is required for the Eigenvector sorting method.") - 320 all_vecs = _sort_vectors(all_vecs, ts) - 321 - 322 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 323 else: - 324 raise Exception("Unkown value for 'sort'.") - 325 - 326 if "state" in kwargs: - 327 return reordered_vecs[kwargs.get("state")] - 328 else: - 329 return reordered_vecs - 330 - 331 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 332 """Determines the eigenvalue of the GEVP by solving and projecting the correlator - 333 - 334 Parameters - 335 ---------- - 336 state : int - 337 The state one is interested in ordered by energy. The lowest state is zero. - 338 - 339 All other parameters are identical to the ones of Corr.GEVP. - 340 """ - 341 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 342 return self.projected(vec) - 343 - 344 def Hankel(self, N, periodic=False): - 345 """Constructs an NxN Hankel matrix + 241 def is_matrix_symmetric(self): + 242 """Checks whether a correlator matrices is symmetric on every timeslice.""" + 243 if self.N == 1: + 244 raise Exception("Only works for correlator matrices.") + 245 for t in range(self.T): + 246 if self[t] is None: + 247 continue + 248 for i in range(self.N): + 249 for j in range(i + 1, self.N): + 250 if self[t][i, j] is self[t][j, i]: + 251 continue + 252 if hash(self[t][i, j]) != hash(self[t][j, i]): + 253 return False + 254 return True + 255 + 256 def matrix_symmetric(self): + 257 """Symmetrizes the correlator matrices on every timeslice.""" + 258 if self.N == 1: + 259 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") + 260 if self.is_matrix_symmetric(): + 261 return 1.0 * self + 262 else: + 263 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] + 264 return 0.5 * (Corr(transposed) + self) + 265 + 266 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): + 267 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. + 268 + 269 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the + 270 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing + 271 ```python + 272 C.GEVP(t0=2)[0] # Ground state vector(s) + 273 C.GEVP(t0=2)[:3] # Vectors for the lowest three states + 274 ``` + 275 + 276 Parameters + 277 ---------- + 278 t0 : int + 279 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ + 280 ts : int + 281 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. + 282 If sort="Eigenvector" it gives a reference point for the sorting method. + 283 sort : string + 284 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. + 285 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. + 286 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. + 287 The reference state is identified by its eigenvalue at $t=t_s$. + 288 + 289 Other Parameters + 290 ---------------- + 291 state : int + 292 Returns only the vector(s) for a specified state. The lowest state is zero. + 293 ''' + 294 + 295 if self.N == 1: + 296 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") + 297 if ts is not None: + 298 if (ts <= t0): + 299 raise Exception("ts has to be larger than t0.") + 300 + 301 if "sorted_list" in kwargs: + 302 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) + 303 sort = kwargs.get("sorted_list") + 304 + 305 if self.is_matrix_symmetric(): + 306 symmetric_corr = self + 307 else: + 308 symmetric_corr = self.matrix_symmetric() + 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 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") + 316 for i in range(self.N): + 317 for j in range(self.N): + 318 G0[i, j] = symmetric_corr[t0][i, j].value + 319 Gt[i, j] = symmetric_corr[ts][i, j].value + 320 + 321 reordered_vecs = _GEVP_solver(Gt, G0) + 322 + 323 elif sort in ["Eigenvalue", "Eigenvector"]: + 324 if sort == "Eigenvalue" and ts is not None: + 325 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) + 326 all_vecs = [None] * (t0 + 1) + 327 for t in range(t0 + 1, self.T): + 328 try: + 329 G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double") + 330 for i in range(self.N): + 331 for j in range(self.N): + 332 G0[i, j] = symmetric_corr[t0][i, j].value + 333 Gt[i, j] = symmetric_corr[t][i, j].value + 334 + 335 all_vecs.append(_GEVP_solver(Gt, G0)) + 336 except Exception: + 337 all_vecs.append(None) + 338 if sort == "Eigenvector": + 339 if (ts is None): + 340 raise Exception("ts is required for the Eigenvector sorting method.") + 341 all_vecs = _sort_vectors(all_vecs, ts) + 342 + 343 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] + 344 else: + 345 raise Exception("Unkown value for 'sort'.") 346 - 347 C(t) c(t+1) ... c(t+n-1) - 348 C(t+1) c(t+2) ... c(t+n) - 349 ................. - 350 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) + 347 if "state" in kwargs: + 348 return reordered_vecs[kwargs.get("state")] + 349 else: + 350 return reordered_vecs 351 - 352 Parameters - 353 ---------- - 354 N : int - 355 Dimension of the Hankel matrix - 356 periodic : bool, optional - 357 determines whether the matrix is extended periodically - 358 """ + 352 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): + 353 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 354 + 355 Parameters + 356 ---------- + 357 state : int + 358 The state one is interested in ordered by energy. The lowest state is zero. 359 - 360 if self.N != 1: - 361 raise Exception("Multi-operator Prony not implemented!") - 362 - 363 array = np.empty([N, N], dtype="object") - 364 new_content = [] - 365 for t in range(self.T): - 366 new_content.append(array.copy()) + 360 All other parameters are identical to the ones of Corr.GEVP. + 361 """ + 362 vec = self.GEVP(t0, ts=ts, sort=sort)[state] + 363 return self.projected(vec) + 364 + 365 def Hankel(self, N, periodic=False): + 366 """Constructs an NxN Hankel matrix 367 - 368 def wrap(i): - 369 while i >= self.T: - 370 i -= self.T - 371 return i + 368 C(t) c(t+1) ... c(t+n-1) + 369 C(t+1) c(t+2) ... c(t+n) + 370 ................. + 371 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) 372 - 373 for t in range(self.T): - 374 for i in range(N): - 375 for j in range(N): - 376 if periodic: - 377 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 378 elif (t + i + j) >= self.T: - 379 new_content[t] = None - 380 else: - 381 new_content[t][i, j] = self.content[t + i + j][0] - 382 - 383 return Corr(new_content) - 384 - 385 def roll(self, dt): - 386 """Periodically shift the correlator by dt timeslices - 387 - 388 Parameters - 389 ---------- - 390 dt : int - 391 number of timeslices - 392 """ - 393 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) - 394 - 395 def reverse(self): - 396 """Reverse the time ordering of the Corr""" - 397 return Corr(self.content[:: -1]) - 398 - 399 def thin(self, spacing=2, offset=0): - 400 """Thin out a correlator to suppress correlations - 401 - 402 Parameters - 403 ---------- - 404 spacing : int - 405 Keep only every 'spacing'th entry of the correlator - 406 offset : int - 407 Offset the equal spacing - 408 """ - 409 new_content = [] - 410 for t in range(self.T): - 411 if (offset + t) % spacing != 0: - 412 new_content.append(None) - 413 else: - 414 new_content.append(self.content[t]) - 415 return Corr(new_content) - 416 - 417 def correlate(self, partner): - 418 """Correlate the correlator with another correlator or Obs + 373 Parameters + 374 ---------- + 375 N : int + 376 Dimension of the Hankel matrix + 377 periodic : bool, optional + 378 determines whether the matrix is extended periodically + 379 """ + 380 + 381 if self.N != 1: + 382 raise Exception("Multi-operator Prony not implemented!") + 383 + 384 array = np.empty([N, N], dtype="object") + 385 new_content = [] + 386 for t in range(self.T): + 387 new_content.append(array.copy()) + 388 + 389 def wrap(i): + 390 while i >= self.T: + 391 i -= self.T + 392 return i + 393 + 394 for t in range(self.T): + 395 for i in range(N): + 396 for j in range(N): + 397 if periodic: + 398 new_content[t][i, j] = self.content[wrap(t + i + j)][0] + 399 elif (t + i + j) >= self.T: + 400 new_content[t] = None + 401 else: + 402 new_content[t][i, j] = self.content[t + i + j][0] + 403 + 404 return Corr(new_content) + 405 + 406 def roll(self, dt): + 407 """Periodically shift the correlator by dt timeslices + 408 + 409 Parameters + 410 ---------- + 411 dt : int + 412 number of timeslices + 413 """ + 414 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) + 415 + 416 def reverse(self): + 417 """Reverse the time ordering of the Corr""" + 418 return Corr(self.content[:: -1]) 419 - 420 Parameters - 421 ---------- - 422 partner : Obs or Corr - 423 partner to correlate the correlator with. - 424 Can either be an Obs which is correlated with all entries of the - 425 correlator or a Corr of same length. - 426 """ - 427 if self.N != 1: - 428 raise Exception("Only one-dimensional correlators can be safely correlated.") - 429 new_content = [] - 430 for x0, t_slice in enumerate(self.content): - 431 if _check_for_none(self, t_slice): - 432 new_content.append(None) - 433 else: - 434 if isinstance(partner, Corr): - 435 if _check_for_none(partner, partner.content[x0]): - 436 new_content.append(None) - 437 else: - 438 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 439 elif isinstance(partner, Obs): # Should this include CObs? - 440 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 441 else: - 442 raise Exception("Can only correlate with an Obs or a Corr.") - 443 - 444 return Corr(new_content) - 445 - 446 def reweight(self, weight, **kwargs): - 447 """Reweight the correlator. - 448 - 449 Parameters - 450 ---------- - 451 weight : Obs - 452 Reweighting factor. An Observable that has to be defined on a superset of the - 453 configurations in obs[i].idl for all i. - 454 all_configs : bool - 455 if True, the reweighted observables are normalized by the average of - 456 the reweighting factor on all configurations in weight.idl and not - 457 on the configurations in obs[i].idl. - 458 """ - 459 if self.N != 1: - 460 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 461 new_content = [] - 462 for t_slice in self.content: - 463 if _check_for_none(self, t_slice): - 464 new_content.append(None) - 465 else: - 466 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 467 return Corr(new_content) - 468 - 469 def T_symmetry(self, partner, parity=+1): - 470 """Return the time symmetry average of the correlator and its partner - 471 - 472 Parameters - 473 ---------- - 474 partner : Corr - 475 Time symmetry partner of the Corr - 476 partity : int - 477 Parity quantum number of the correlator, can be +1 or -1 - 478 """ - 479 if self.N != 1: - 480 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 481 if not isinstance(partner, Corr): - 482 raise Exception("T partner has to be a Corr object.") - 483 if parity not in [+1, -1]: - 484 raise Exception("Parity has to be +1 or -1.") - 485 T_partner = parity * partner.reverse() - 486 - 487 t_slices = [] - 488 test = (self - T_partner) - 489 test.gamma_method() - 490 for x0, t_slice in enumerate(test.content): - 491 if t_slice is not None: - 492 if not t_slice[0].is_zero_within_error(5): - 493 t_slices.append(x0) - 494 if t_slices: - 495 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) - 496 - 497 return (self + T_partner) / 2 - 498 - 499 def deriv(self, variant="symmetric"): - 500 """Return the first derivative of the correlator with respect to x0. - 501 - 502 Parameters - 503 ---------- - 504 variant : str - 505 decides which definition of the finite differences derivative is used. - 506 Available choice: symmetric, forward, backward, improved, default: symmetric - 507 """ - 508 if self.N != 1: - 509 raise Exception("deriv only implemented for one-dimensional correlators.") - 510 if variant == "symmetric": - 511 newcontent = [] - 512 for t in range(1, self.T - 1): - 513 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 514 newcontent.append(None) - 515 else: - 516 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 517 if(all([x is None for x in newcontent])): - 518 raise Exception('Derivative is undefined at all timeslices') - 519 return Corr(newcontent, padding=[1, 1]) - 520 elif variant == "forward": - 521 newcontent = [] - 522 for t in range(self.T - 1): - 523 if (self.content[t] is None) or (self.content[t + 1] is None): - 524 newcontent.append(None) - 525 else: - 526 newcontent.append(self.content[t + 1] - self.content[t]) - 527 if(all([x is None for x in newcontent])): - 528 raise Exception("Derivative is undefined at all timeslices") - 529 return Corr(newcontent, padding=[0, 1]) - 530 elif variant == "backward": - 531 newcontent = [] - 532 for t in range(1, self.T): - 533 if (self.content[t - 1] is None) or (self.content[t] is None): - 534 newcontent.append(None) - 535 else: - 536 newcontent.append(self.content[t] - self.content[t - 1]) - 537 if(all([x is None for x in newcontent])): - 538 raise Exception("Derivative is undefined at all timeslices") - 539 return Corr(newcontent, padding=[1, 0]) - 540 elif variant == "improved": - 541 newcontent = [] - 542 for t in range(2, self.T - 2): - 543 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): - 544 newcontent.append(None) - 545 else: - 546 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 547 if(all([x is None for x in newcontent])): - 548 raise Exception('Derivative is undefined at all timeslices') - 549 return Corr(newcontent, padding=[2, 2]) - 550 else: - 551 raise Exception("Unknown variant.") - 552 - 553 def second_deriv(self, variant="symmetric"): - 554 """Return the second derivative of the correlator with respect to x0. - 555 - 556 Parameters - 557 ---------- - 558 variant : str - 559 decides which definition of the finite differences derivative is used. - 560 Available choice: symmetric, improved, default: symmetric - 561 """ - 562 if self.N != 1: - 563 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 564 if variant == "symmetric": - 565 newcontent = [] - 566 for t in range(1, self.T - 1): - 567 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 568 newcontent.append(None) - 569 else: - 570 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 571 if(all([x is None for x in newcontent])): - 572 raise Exception("Derivative is undefined at all timeslices") - 573 return Corr(newcontent, padding=[1, 1]) - 574 elif variant == "improved": - 575 newcontent = [] - 576 for t in range(2, self.T - 2): - 577 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): - 578 newcontent.append(None) - 579 else: - 580 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])) - 581 if(all([x is None for x in newcontent])): - 582 raise Exception("Derivative is undefined at all timeslices") - 583 return Corr(newcontent, padding=[2, 2]) - 584 else: - 585 raise Exception("Unknown variant.") - 586 - 587 def m_eff(self, variant='log', guess=1.0): - 588 """Returns the effective mass of the correlator as correlator object - 589 - 590 Parameters - 591 ---------- - 592 variant : str - 593 log : uses the standard effective mass log(C(t) / C(t+1)) - 594 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. - 595 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. - 596 See, e.g., arXiv:1205.5380 - 597 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 598 guess : float - 599 guess for the root finder, only relevant for the root variant - 600 """ - 601 if self.N != 1: - 602 raise Exception('Correlator must be projected before getting m_eff') - 603 if variant == 'log': - 604 newcontent = [] - 605 for t in range(self.T - 1): - 606 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 607 newcontent.append(None) - 608 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 609 newcontent.append(None) - 610 else: - 611 newcontent.append(self.content[t] / self.content[t + 1]) - 612 if(all([x is None for x in newcontent])): - 613 raise Exception('m_eff is undefined at all timeslices') - 614 - 615 return np.log(Corr(newcontent, padding=[0, 1])) - 616 - 617 elif variant in ['periodic', 'cosh', 'sinh']: - 618 if variant in ['periodic', 'cosh']: - 619 func = anp.cosh - 620 else: - 621 func = anp.sinh - 622 - 623 def root_function(x, d): - 624 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 625 - 626 newcontent = [] - 627 for t in range(self.T - 1): - 628 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 629 newcontent.append(None) - 630 # Fill the two timeslices in the middle of the lattice with their predecessors - 631 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 632 newcontent.append(newcontent[-1]) - 633 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 634 newcontent.append(None) - 635 else: - 636 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 637 if(all([x is None for x in newcontent])): - 638 raise Exception('m_eff is undefined at all timeslices') - 639 - 640 return Corr(newcontent, padding=[0, 1]) - 641 - 642 elif variant == 'arccosh': - 643 newcontent = [] - 644 for t in range(1, self.T - 1): - 645 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): - 646 newcontent.append(None) - 647 else: - 648 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) - 649 if(all([x is None for x in newcontent])): - 650 raise Exception("m_eff is undefined at all timeslices") - 651 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 652 - 653 else: - 654 raise Exception('Unknown variant.') - 655 - 656 def fit(self, function, fitrange=None, silent=False, **kwargs): - 657 r'''Fits function to the data - 658 - 659 Parameters - 660 ---------- - 661 function : obj - 662 function to fit to the data. See fits.least_squares for details. - 663 fitrange : list - 664 Two element list containing the timeslices on which the fit is supposed to start and stop. - 665 Caution: This range is inclusive as opposed to standard python indexing. - 666 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 667 If not specified, self.prange or all timeslices are used. - 668 silent : bool - 669 Decides whether output is printed to the standard output. - 670 ''' - 671 if self.N != 1: - 672 raise Exception("Correlator must be projected before fitting") + 420 def thin(self, spacing=2, offset=0): + 421 """Thin out a correlator to suppress correlations + 422 + 423 Parameters + 424 ---------- + 425 spacing : int + 426 Keep only every 'spacing'th entry of the correlator + 427 offset : int + 428 Offset the equal spacing + 429 """ + 430 new_content = [] + 431 for t in range(self.T): + 432 if (offset + t) % spacing != 0: + 433 new_content.append(None) + 434 else: + 435 new_content.append(self.content[t]) + 436 return Corr(new_content) + 437 + 438 def correlate(self, partner): + 439 """Correlate the correlator with another correlator or Obs + 440 + 441 Parameters + 442 ---------- + 443 partner : Obs or Corr + 444 partner to correlate the correlator with. + 445 Can either be an Obs which is correlated with all entries of the + 446 correlator or a Corr of same length. + 447 """ + 448 if self.N != 1: + 449 raise Exception("Only one-dimensional correlators can be safely correlated.") + 450 new_content = [] + 451 for x0, t_slice in enumerate(self.content): + 452 if _check_for_none(self, t_slice): + 453 new_content.append(None) + 454 else: + 455 if isinstance(partner, Corr): + 456 if _check_for_none(partner, partner.content[x0]): + 457 new_content.append(None) + 458 else: + 459 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) + 460 elif isinstance(partner, Obs): # Should this include CObs? + 461 new_content.append(np.array([correlate(o, partner) for o in t_slice])) + 462 else: + 463 raise Exception("Can only correlate with an Obs or a Corr.") + 464 + 465 return Corr(new_content) + 466 + 467 def reweight(self, weight, **kwargs): + 468 """Reweight the correlator. + 469 + 470 Parameters + 471 ---------- + 472 weight : Obs + 473 Reweighting factor. An Observable that has to be defined on a superset of the + 474 configurations in obs[i].idl for all i. + 475 all_configs : bool + 476 if True, the reweighted observables are normalized by the average of + 477 the reweighting factor on all configurations in weight.idl and not + 478 on the configurations in obs[i].idl. + 479 """ + 480 if self.N != 1: + 481 raise Exception("Reweighting only implemented for one-dimensional correlators.") + 482 new_content = [] + 483 for t_slice in self.content: + 484 if _check_for_none(self, t_slice): + 485 new_content.append(None) + 486 else: + 487 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) + 488 return Corr(new_content) + 489 + 490 def T_symmetry(self, partner, parity=+1): + 491 """Return the time symmetry average of the correlator and its partner + 492 + 493 Parameters + 494 ---------- + 495 partner : Corr + 496 Time symmetry partner of the Corr + 497 partity : int + 498 Parity quantum number of the correlator, can be +1 or -1 + 499 """ + 500 if self.N != 1: + 501 raise Exception("T_symmetry only implemented for one-dimensional correlators.") + 502 if not isinstance(partner, Corr): + 503 raise Exception("T partner has to be a Corr object.") + 504 if parity not in [+1, -1]: + 505 raise Exception("Parity has to be +1 or -1.") + 506 T_partner = parity * partner.reverse() + 507 + 508 t_slices = [] + 509 test = (self - T_partner) + 510 test.gamma_method() + 511 for x0, t_slice in enumerate(test.content): + 512 if t_slice is not None: + 513 if not t_slice[0].is_zero_within_error(5): + 514 t_slices.append(x0) + 515 if t_slices: + 516 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) + 517 + 518 return (self + T_partner) / 2 + 519 + 520 def deriv(self, variant="symmetric"): + 521 """Return the first derivative of the correlator with respect to x0. + 522 + 523 Parameters + 524 ---------- + 525 variant : str + 526 decides which definition of the finite differences derivative is used. + 527 Available choice: symmetric, forward, backward, improved, default: symmetric + 528 """ + 529 if self.N != 1: + 530 raise Exception("deriv only implemented for one-dimensional correlators.") + 531 if variant == "symmetric": + 532 newcontent = [] + 533 for t in range(1, self.T - 1): + 534 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 535 newcontent.append(None) + 536 else: + 537 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) + 538 if(all([x is None for x in newcontent])): + 539 raise Exception('Derivative is undefined at all timeslices') + 540 return Corr(newcontent, padding=[1, 1]) + 541 elif variant == "forward": + 542 newcontent = [] + 543 for t in range(self.T - 1): + 544 if (self.content[t] is None) or (self.content[t + 1] is None): + 545 newcontent.append(None) + 546 else: + 547 newcontent.append(self.content[t + 1] - self.content[t]) + 548 if(all([x is None for x in newcontent])): + 549 raise Exception("Derivative is undefined at all timeslices") + 550 return Corr(newcontent, padding=[0, 1]) + 551 elif variant == "backward": + 552 newcontent = [] + 553 for t in range(1, self.T): + 554 if (self.content[t - 1] is None) or (self.content[t] is None): + 555 newcontent.append(None) + 556 else: + 557 newcontent.append(self.content[t] - self.content[t - 1]) + 558 if(all([x is None for x in newcontent])): + 559 raise Exception("Derivative is undefined at all timeslices") + 560 return Corr(newcontent, padding=[1, 0]) + 561 elif variant == "improved": + 562 newcontent = [] + 563 for t in range(2, self.T - 2): + 564 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): + 565 newcontent.append(None) + 566 else: + 567 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) + 568 if(all([x is None for x in newcontent])): + 569 raise Exception('Derivative is undefined at all timeslices') + 570 return Corr(newcontent, padding=[2, 2]) + 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, 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 else: + 606 raise Exception("Unknown variant.") + 607 + 608 def m_eff(self, variant='log', guess=1.0): + 609 """Returns the effective mass of the correlator as correlator object + 610 + 611 Parameters + 612 ---------- + 613 variant : str + 614 log : uses the standard effective mass log(C(t) / C(t+1)) + 615 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. + 616 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. + 617 See, e.g., arXiv:1205.5380 + 618 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 619 guess : float + 620 guess for the root finder, only relevant for the root variant + 621 """ + 622 if self.N != 1: + 623 raise Exception('Correlator must be projected before getting m_eff') + 624 if variant == 'log': + 625 newcontent = [] + 626 for t in range(self.T - 1): + 627 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 628 newcontent.append(None) + 629 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 630 newcontent.append(None) + 631 else: + 632 newcontent.append(self.content[t] / self.content[t + 1]) + 633 if(all([x is None for x in newcontent])): + 634 raise Exception('m_eff is undefined at all timeslices') + 635 + 636 return np.log(Corr(newcontent, padding=[0, 1])) + 637 + 638 elif variant in ['periodic', 'cosh', 'sinh']: + 639 if variant in ['periodic', 'cosh']: + 640 func = anp.cosh + 641 else: + 642 func = anp.sinh + 643 + 644 def root_function(x, d): + 645 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 646 + 647 newcontent = [] + 648 for t in range(self.T - 1): + 649 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 650 newcontent.append(None) + 651 # Fill the two timeslices in the middle of the lattice with their predecessors + 652 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 653 newcontent.append(newcontent[-1]) + 654 elif self.content[t][0].value / self.content[t + 1][0].value < 0: + 655 newcontent.append(None) + 656 else: + 657 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) + 658 if(all([x is None for x in newcontent])): + 659 raise Exception('m_eff is undefined at all timeslices') + 660 + 661 return Corr(newcontent, padding=[0, 1]) + 662 + 663 elif variant == 'arccosh': + 664 newcontent = [] + 665 for t in range(1, self.T - 1): + 666 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): + 667 newcontent.append(None) + 668 else: + 669 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 670 if(all([x is None for x in newcontent])): + 671 raise Exception("m_eff is undefined at all timeslices") + 672 return np.arccosh(Corr(newcontent, padding=[1, 1])) 673 - 674 if fitrange is None: - 675 if self.prange: - 676 fitrange = self.prange - 677 else: - 678 fitrange = [0, self.T - 1] - 679 else: - 680 if not isinstance(fitrange, list): - 681 raise Exception("fitrange has to be a list with two elements") - 682 if len(fitrange) != 2: - 683 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 684 - 685 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 686 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] - 687 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 688 return result - 689 - 690 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 691 """ Extract a plateau value from a Corr object - 692 - 693 Parameters - 694 ---------- - 695 plateau_range : list - 696 list with two entries, indicating the first and the last timeslice - 697 of the plateau region. - 698 method : str - 699 method to extract the plateau. - 700 'fit' fits a constant to the plateau region - 701 'avg', 'average' or 'mean' just average over the given timeslices. - 702 auto_gamma : bool - 703 apply gamma_method with default parameters to the Corr. Defaults to None - 704 """ - 705 if not plateau_range: - 706 if self.prange: - 707 plateau_range = self.prange - 708 else: - 709 raise Exception("no plateau range provided") - 710 if self.N != 1: - 711 raise Exception("Correlator must be projected before getting a plateau.") - 712 if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 713 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 714 if auto_gamma: - 715 self.gamma_method() - 716 if method == "fit": - 717 def const_func(a, t): - 718 return a[0] - 719 return self.fit(const_func, plateau_range)[0] - 720 elif method in ["avg", "average", "mean"]: - 721 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 722 return returnvalue - 723 - 724 else: - 725 raise Exception("Unsupported plateau method: " + method) - 726 - 727 def set_prange(self, prange): - 728 """Sets the attribute prange of the Corr object.""" - 729 if not len(prange) == 2: - 730 raise Exception("prange must be a list or array with two values") - 731 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 732 raise Exception("Start and end point must be integers") - 733 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 734 raise Exception("Start and end point must define a range in the interval 0,T") - 735 - 736 self.prange = prange - 737 return - 738 - 739 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): - 740 """Plots the correlator using the tag of the correlator as label if available. - 741 - 742 Parameters - 743 ---------- - 744 x_range : list - 745 list of two values, determining the range of the x-axis e.g. [4, 8]. - 746 comp : Corr or list of Corr - 747 Correlator or list of correlators which are plotted for comparison. - 748 The tags of these correlators are used as labels if available. - 749 logscale : bool - 750 Sets y-axis to logscale. - 751 plateau : Obs - 752 Plateau value to be visualized in the figure. - 753 fit_res : Fit_result - 754 Fit_result object to be visualized. - 755 ylabel : str - 756 Label for the y-axis. - 757 save : str - 758 path to file in which the figure should be saved. - 759 auto_gamma : bool - 760 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 761 hide_sigma : float - 762 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 763 references : list - 764 List of floating point values that are displayed as horizontal lines for reference. - 765 title : string - 766 Optional title of the figure. - 767 """ - 768 if self.N != 1: - 769 raise Exception("Correlator must be projected before plotting") - 770 - 771 if auto_gamma: - 772 self.gamma_method() - 773 - 774 if x_range is None: - 775 x_range = [0, self.T - 1] - 776 - 777 fig = plt.figure() - 778 ax1 = fig.add_subplot(111) - 779 - 780 x, y, y_err = self.plottable() - 781 if hide_sigma: - 782 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 783 else: - 784 hide_from = None - 785 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 786 if logscale: - 787 ax1.set_yscale('log') - 788 else: - 789 if y_range is None: - 790 try: - 791 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)]) - 792 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)]) - 793 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 794 except Exception: - 795 pass - 796 else: - 797 ax1.set_ylim(y_range) - 798 if comp: - 799 if isinstance(comp, (Corr, list)): - 800 for corr in comp if isinstance(comp, list) else [comp]: - 801 if auto_gamma: - 802 corr.gamma_method() - 803 x, y, y_err = corr.plottable() - 804 if hide_sigma: - 805 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 806 else: - 807 hide_from = None - 808 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 809 else: - 810 raise Exception("'comp' must be a correlator or a list of correlators.") - 811 - 812 if plateau: - 813 if isinstance(plateau, Obs): - 814 if auto_gamma: - 815 plateau.gamma_method() - 816 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 817 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 818 else: - 819 raise Exception("'plateau' must be an Obs") - 820 - 821 if references: - 822 if isinstance(references, list): - 823 for ref in references: - 824 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 825 else: - 826 raise Exception("'references' must be a list of floating pint values.") - 827 - 828 if self.prange: - 829 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') - 830 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') - 831 - 832 if fit_res: - 833 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 834 ax1.plot(x_samples, - 835 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), - 836 ls='-', marker=',', lw=2) - 837 - 838 ax1.set_xlabel(r'$x_0 / a$') - 839 if ylabel: - 840 ax1.set_ylabel(ylabel) - 841 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 842 - 843 handles, labels = ax1.get_legend_handles_labels() - 844 if labels: - 845 ax1.legend() - 846 - 847 if title: - 848 plt.title(title) - 849 - 850 plt.draw() - 851 - 852 if save: - 853 if isinstance(save, str): - 854 fig.savefig(save, bbox_inches='tight') - 855 else: - 856 raise Exception("'save' has to be a string.") - 857 - 858 def spaghetti_plot(self, logscale=True): - 859 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 860 - 861 Parameters - 862 ---------- - 863 logscale : bool - 864 Determines whether the scale of the y-axis is logarithmic or standard. - 865 """ - 866 if self.N != 1: - 867 raise Exception("Correlator needs to be projected first.") - 868 - 869 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) - 870 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 871 - 872 for name in mc_names: - 873 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T - 874 - 875 fig = plt.figure() - 876 ax = fig.add_subplot(111) - 877 for dat in data: - 878 ax.plot(x0_vals, dat, ls='-', marker='') - 879 - 880 if logscale is True: - 881 ax.set_yscale('log') - 882 - 883 ax.set_xlabel(r'$x_0 / a$') - 884 plt.title(name) - 885 plt.draw() - 886 - 887 def dump(self, filename, datatype="json.gz", **kwargs): - 888 """Dumps the Corr into a file of chosen type - 889 Parameters - 890 ---------- - 891 filename : str - 892 Name of the file to be saved. - 893 datatype : str - 894 Format of the exported file. Supported formats include - 895 "json.gz" and "pickle" - 896 path : str - 897 specifies a custom path for the file (default '.') - 898 """ - 899 if datatype == "json.gz": - 900 from .input.json import dump_to_json - 901 if 'path' in kwargs: - 902 file_name = kwargs.get('path') + '/' + filename - 903 else: - 904 file_name = filename - 905 dump_to_json(self, file_name) - 906 elif datatype == "pickle": - 907 dump_object(self, filename, **kwargs) - 908 else: - 909 raise Exception("Unknown datatype " + str(datatype)) - 910 - 911 def print(self, print_range=None): - 912 print(self.__repr__(print_range)) - 913 - 914 def __repr__(self, print_range=None): - 915 if print_range is None: - 916 print_range = [0, None] - 917 - 918 content_string = "" - 919 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 - 920 - 921 if self.tag is not None: - 922 content_string += "Description: " + self.tag + "\n" - 923 if self.N != 1: - 924 return content_string - 925 - 926 if print_range[1]: - 927 print_range[1] += 1 - 928 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' - 929 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): - 930 if sub_corr is None: - 931 content_string += str(i + print_range[0]) + '\n' - 932 else: - 933 content_string += str(i + print_range[0]) - 934 for element in sub_corr: - 935 content_string += '\t' + ' ' * int(element >= 0) + str(element) - 936 content_string += '\n' - 937 return content_string + 674 else: + 675 raise Exception('Unknown variant.') + 676 + 677 def fit(self, function, fitrange=None, silent=False, **kwargs): + 678 r'''Fits function to the data + 679 + 680 Parameters + 681 ---------- + 682 function : obj + 683 function to fit to the data. See fits.least_squares for details. + 684 fitrange : list + 685 Two element list containing the timeslices on which the fit is supposed to start and stop. + 686 Caution: This range is inclusive as opposed to standard python indexing. + 687 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 688 If not specified, self.prange or all timeslices are used. + 689 silent : bool + 690 Decides whether output is printed to the standard output. + 691 ''' + 692 if self.N != 1: + 693 raise Exception("Correlator must be projected before fitting") + 694 + 695 if fitrange is None: + 696 if self.prange: + 697 fitrange = self.prange + 698 else: + 699 fitrange = [0, self.T - 1] + 700 else: + 701 if not isinstance(fitrange, list): + 702 raise Exception("fitrange has to be a list with two elements") + 703 if len(fitrange) != 2: + 704 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 705 + 706 xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 707 ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None] + 708 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 709 return result + 710 + 711 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 712 """ Extract a plateau value from a Corr object + 713 + 714 Parameters + 715 ---------- + 716 plateau_range : list + 717 list with two entries, indicating the first and the last timeslice + 718 of the plateau region. + 719 method : str + 720 method to extract the plateau. + 721 'fit' fits a constant to the plateau region + 722 'avg', 'average' or 'mean' just average over the given timeslices. + 723 auto_gamma : bool + 724 apply gamma_method with default parameters to the Corr. Defaults to None + 725 """ + 726 if not plateau_range: + 727 if self.prange: + 728 plateau_range = self.prange + 729 else: + 730 raise Exception("no plateau range provided") + 731 if self.N != 1: + 732 raise Exception("Correlator must be projected before getting a plateau.") + 733 if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 734 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 735 if auto_gamma: + 736 self.gamma_method() + 737 if method == "fit": + 738 def const_func(a, t): + 739 return a[0] + 740 return self.fit(const_func, plateau_range)[0] + 741 elif method in ["avg", "average", "mean"]: + 742 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 743 return returnvalue + 744 + 745 else: + 746 raise Exception("Unsupported plateau method: " + method) + 747 + 748 def set_prange(self, prange): + 749 """Sets the attribute prange of the Corr object.""" + 750 if not len(prange) == 2: + 751 raise Exception("prange must be a list or array with two values") + 752 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 753 raise Exception("Start and end point must be integers") + 754 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 755 raise Exception("Start and end point must define a range in the interval 0,T") + 756 + 757 self.prange = prange + 758 return + 759 + 760 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): + 761 """Plots the correlator using the tag of the correlator as label if available. + 762 + 763 Parameters + 764 ---------- + 765 x_range : list + 766 list of two values, determining the range of the x-axis e.g. [4, 8]. + 767 comp : Corr or list of Corr + 768 Correlator or list of correlators which are plotted for comparison. + 769 The tags of these correlators are used as labels if available. + 770 logscale : bool + 771 Sets y-axis to logscale. + 772 plateau : Obs + 773 Plateau value to be visualized in the figure. + 774 fit_res : Fit_result + 775 Fit_result object to be visualized. + 776 ylabel : str + 777 Label for the y-axis. + 778 save : str + 779 path to file in which the figure should be saved. + 780 auto_gamma : bool + 781 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 782 hide_sigma : float + 783 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 784 references : list + 785 List of floating point values that are displayed as horizontal lines for reference. + 786 title : string + 787 Optional title of the figure. + 788 """ + 789 if self.N != 1: + 790 raise Exception("Correlator must be projected before plotting") + 791 + 792 if auto_gamma: + 793 self.gamma_method() + 794 + 795 if x_range is None: + 796 x_range = [0, self.T - 1] + 797 + 798 fig = plt.figure() + 799 ax1 = fig.add_subplot(111) + 800 + 801 x, y, y_err = self.plottable() + 802 if hide_sigma: + 803 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 804 else: + 805 hide_from = None + 806 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 807 if logscale: + 808 ax1.set_yscale('log') + 809 else: + 810 if y_range is None: + 811 try: + 812 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)]) + 813 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)]) + 814 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 815 except Exception: + 816 pass + 817 else: + 818 ax1.set_ylim(y_range) + 819 if comp: + 820 if isinstance(comp, (Corr, list)): + 821 for corr in comp if isinstance(comp, list) else [comp]: + 822 if auto_gamma: + 823 corr.gamma_method() + 824 x, y, y_err = corr.plottable() + 825 if hide_sigma: + 826 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 827 else: + 828 hide_from = None + 829 plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 830 else: + 831 raise Exception("'comp' must be a correlator or a list of correlators.") + 832 + 833 if plateau: + 834 if isinstance(plateau, Obs): + 835 if auto_gamma: + 836 plateau.gamma_method() + 837 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 838 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 839 else: + 840 raise Exception("'plateau' must be an Obs") + 841 + 842 if references: + 843 if isinstance(references, list): + 844 for ref in references: + 845 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 846 else: + 847 raise Exception("'references' must be a list of floating pint values.") + 848 + 849 if self.prange: + 850 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',') + 851 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',') + 852 + 853 if fit_res: + 854 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 855 ax1.plot(x_samples, + 856 fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), + 857 ls='-', marker=',', lw=2) + 858 + 859 ax1.set_xlabel(r'$x_0 / a$') + 860 if ylabel: + 861 ax1.set_ylabel(ylabel) + 862 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 863 + 864 handles, labels = ax1.get_legend_handles_labels() + 865 if labels: + 866 ax1.legend() + 867 + 868 if title: + 869 plt.title(title) + 870 + 871 plt.draw() + 872 + 873 if save: + 874 if isinstance(save, str): + 875 fig.savefig(save, bbox_inches='tight') + 876 else: + 877 raise Exception("'save' has to be a string.") + 878 + 879 def spaghetti_plot(self, logscale=True): + 880 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 881 + 882 Parameters + 883 ---------- + 884 logscale : bool + 885 Determines whether the scale of the y-axis is logarithmic or standard. + 886 """ + 887 if self.N != 1: + 888 raise Exception("Correlator needs to be projected first.") + 889 + 890 mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist])) + 891 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 892 + 893 for name in mc_names: + 894 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T + 895 + 896 fig = plt.figure() + 897 ax = fig.add_subplot(111) + 898 for dat in data: + 899 ax.plot(x0_vals, dat, ls='-', marker='') + 900 + 901 if logscale is True: + 902 ax.set_yscale('log') + 903 + 904 ax.set_xlabel(r'$x_0 / a$') + 905 plt.title(name) + 906 plt.draw() + 907 + 908 def dump(self, filename, datatype="json.gz", **kwargs): + 909 """Dumps the Corr into a file of chosen type + 910 Parameters + 911 ---------- + 912 filename : str + 913 Name of the file to be saved. + 914 datatype : str + 915 Format of the exported file. Supported formats include + 916 "json.gz" and "pickle" + 917 path : str + 918 specifies a custom path for the file (default '.') + 919 """ + 920 if datatype == "json.gz": + 921 from .input.json import dump_to_json + 922 if 'path' in kwargs: + 923 file_name = kwargs.get('path') + '/' + filename + 924 else: + 925 file_name = filename + 926 dump_to_json(self, file_name) + 927 elif datatype == "pickle": + 928 dump_object(self, filename, **kwargs) + 929 else: + 930 raise Exception("Unknown datatype " + str(datatype)) + 931 + 932 def print(self, print_range=None): + 933 print(self.__repr__(print_range)) + 934 + 935 def __repr__(self, print_range=None): + 936 if print_range is None: + 937 print_range = [0, None] 938 - 939 def __str__(self): - 940 return self.__repr__() + 939 content_string = "" + 940 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 941 - 942 # We define the basic operations, that can be performed with correlators. - 943 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. - 944 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. - 945 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 942 if self.tag is not None: + 943 content_string += "Description: " + self.tag + "\n" + 944 if self.N != 1: + 945 return content_string 946 - 947 def __add__(self, y): - 948 if isinstance(y, Corr): - 949 if ((self.N != y.N) or (self.T != y.T)): - 950 raise Exception("Addition of Corrs with different shape") - 951 newcontent = [] - 952 for t in range(self.T): - 953 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 954 newcontent.append(None) - 955 else: - 956 newcontent.append(self.content[t] + y.content[t]) - 957 return Corr(newcontent) - 958 - 959 elif isinstance(y, (Obs, int, float, CObs)): - 960 newcontent = [] - 961 for t in range(self.T): - 962 if _check_for_none(self, self.content[t]): - 963 newcontent.append(None) - 964 else: - 965 newcontent.append(self.content[t] + y) - 966 return Corr(newcontent, prange=self.prange) - 967 elif isinstance(y, np.ndarray): - 968 if y.shape == (self.T,): - 969 return Corr(list((np.array(self.content).T + y).T)) - 970 else: - 971 raise ValueError("operands could not be broadcast together") - 972 else: - 973 raise TypeError("Corr + wrong type") - 974 - 975 def __mul__(self, y): - 976 if isinstance(y, Corr): - 977 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): - 978 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") - 979 newcontent = [] - 980 for t in range(self.T): - 981 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): - 982 newcontent.append(None) - 983 else: - 984 newcontent.append(self.content[t] * y.content[t]) - 985 return Corr(newcontent) - 986 - 987 elif isinstance(y, (Obs, int, float, CObs)): - 988 newcontent = [] - 989 for t in range(self.T): - 990 if _check_for_none(self, self.content[t]): - 991 newcontent.append(None) - 992 else: - 993 newcontent.append(self.content[t] * y) - 994 return Corr(newcontent, prange=self.prange) - 995 elif isinstance(y, np.ndarray): - 996 if y.shape == (self.T,): - 997 return Corr(list((np.array(self.content).T * y).T)) - 998 else: - 999 raise ValueError("operands could not be broadcast together") -1000 else: -1001 raise TypeError("Corr * wrong type") -1002 -1003 def __truediv__(self, y): -1004 if isinstance(y, Corr): -1005 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1006 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1007 newcontent = [] -1008 for t in range(self.T): -1009 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1010 newcontent.append(None) -1011 else: -1012 newcontent.append(self.content[t] / y.content[t]) -1013 for t in range(self.T): -1014 if _check_for_none(self, newcontent[t]): -1015 continue -1016 if np.isnan(np.sum(newcontent[t]).value): -1017 newcontent[t] = None -1018 -1019 if all([item is None for item in newcontent]): -1020 raise Exception("Division returns completely undefined correlator") -1021 return Corr(newcontent) -1022 -1023 elif isinstance(y, (Obs, CObs)): -1024 if isinstance(y, Obs): -1025 if y.value == 0: -1026 raise Exception('Division by zero will return undefined correlator') -1027 if isinstance(y, CObs): -1028 if y.is_zero(): -1029 raise Exception('Division by zero will return undefined correlator') -1030 -1031 newcontent = [] -1032 for t in range(self.T): -1033 if _check_for_none(self, self.content[t]): -1034 newcontent.append(None) -1035 else: -1036 newcontent.append(self.content[t] / y) -1037 return Corr(newcontent, prange=self.prange) -1038 -1039 elif isinstance(y, (int, float)): -1040 if y == 0: -1041 raise Exception('Division by zero will return undefined correlator') -1042 newcontent = [] -1043 for t in range(self.T): -1044 if _check_for_none(self, self.content[t]): -1045 newcontent.append(None) -1046 else: -1047 newcontent.append(self.content[t] / y) -1048 return Corr(newcontent, prange=self.prange) -1049 elif isinstance(y, np.ndarray): -1050 if y.shape == (self.T,): -1051 return Corr(list((np.array(self.content).T / y).T)) -1052 else: -1053 raise ValueError("operands could not be broadcast together") -1054 else: -1055 raise TypeError('Corr / wrong type') -1056 -1057 def __neg__(self): -1058 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1059 return Corr(newcontent, prange=self.prange) -1060 -1061 def __sub__(self, y): -1062 return self + (-y) -1063 -1064 def __pow__(self, y): -1065 if isinstance(y, (Obs, int, float, CObs)): -1066 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1067 return Corr(newcontent, prange=self.prange) -1068 else: -1069 raise TypeError('Type of exponent not supported') -1070 -1071 def __abs__(self): -1072 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1073 return Corr(newcontent, prange=self.prange) -1074 -1075 # The numpy functions: -1076 def sqrt(self): -1077 return self ** 0.5 -1078 -1079 def log(self): -1080 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1081 return Corr(newcontent, prange=self.prange) -1082 -1083 def exp(self): -1084 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1085 return Corr(newcontent, prange=self.prange) -1086 -1087 def _apply_func_to_corr(self, func): -1088 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1089 for t in range(self.T): -1090 if _check_for_none(self, newcontent[t]): -1091 continue -1092 if np.isnan(np.sum(newcontent[t]).value): -1093 newcontent[t] = None -1094 if all([item is None for item in newcontent]): -1095 raise Exception('Operation returns undefined correlator') -1096 return Corr(newcontent) -1097 -1098 def sin(self): -1099 return self._apply_func_to_corr(np.sin) -1100 -1101 def cos(self): -1102 return self._apply_func_to_corr(np.cos) + 947 if print_range[1]: + 948 print_range[1] += 1 + 949 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' + 950 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): + 951 if sub_corr is None: + 952 content_string += str(i + print_range[0]) + '\n' + 953 else: + 954 content_string += str(i + print_range[0]) + 955 for element in sub_corr: + 956 content_string += '\t' + ' ' * int(element >= 0) + str(element) + 957 content_string += '\n' + 958 return content_string + 959 + 960 def __str__(self): + 961 return self.__repr__() + 962 + 963 # We define the basic operations, that can be performed with correlators. + 964 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. + 965 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. + 966 # One could try and tell Obs to check if the y in __mul__ is a Corr and + 967 + 968 def __add__(self, y): + 969 if isinstance(y, Corr): + 970 if ((self.N != y.N) or (self.T != y.T)): + 971 raise Exception("Addition of Corrs with different shape") + 972 newcontent = [] + 973 for t in range(self.T): + 974 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): + 975 newcontent.append(None) + 976 else: + 977 newcontent.append(self.content[t] + y.content[t]) + 978 return Corr(newcontent) + 979 + 980 elif isinstance(y, (Obs, int, float, CObs)): + 981 newcontent = [] + 982 for t in range(self.T): + 983 if _check_for_none(self, self.content[t]): + 984 newcontent.append(None) + 985 else: + 986 newcontent.append(self.content[t] + y) + 987 return Corr(newcontent, prange=self.prange) + 988 elif isinstance(y, np.ndarray): + 989 if y.shape == (self.T,): + 990 return Corr(list((np.array(self.content).T + y).T)) + 991 else: + 992 raise ValueError("operands could not be broadcast together") + 993 else: + 994 raise TypeError("Corr + wrong type") + 995 + 996 def __mul__(self, y): + 997 if isinstance(y, Corr): + 998 if not((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): + 999 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +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 __truediv__(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 for t in range(self.T): +1035 if _check_for_none(self, newcontent[t]): +1036 continue +1037 if np.isnan(np.sum(newcontent[t]).value): +1038 newcontent[t] = None +1039 +1040 if all([item is None for item in newcontent]): +1041 raise Exception("Division returns completely undefined correlator") +1042 return Corr(newcontent) +1043 +1044 elif isinstance(y, (Obs, CObs)): +1045 if isinstance(y, Obs): +1046 if y.value == 0: +1047 raise Exception('Division by zero will return undefined correlator') +1048 if isinstance(y, CObs): +1049 if y.is_zero(): +1050 raise Exception('Division by zero will return undefined correlator') +1051 +1052 newcontent = [] +1053 for t in range(self.T): +1054 if _check_for_none(self, self.content[t]): +1055 newcontent.append(None) +1056 else: +1057 newcontent.append(self.content[t] / y) +1058 return Corr(newcontent, prange=self.prange) +1059 +1060 elif isinstance(y, (int, float)): +1061 if y == 0: +1062 raise Exception('Division by zero will return undefined correlator') +1063 newcontent = [] +1064 for t in range(self.T): +1065 if _check_for_none(self, self.content[t]): +1066 newcontent.append(None) +1067 else: +1068 newcontent.append(self.content[t] / y) +1069 return Corr(newcontent, prange=self.prange) +1070 elif isinstance(y, np.ndarray): +1071 if y.shape == (self.T,): +1072 return Corr(list((np.array(self.content).T / y).T)) +1073 else: +1074 raise ValueError("operands could not be broadcast together") +1075 else: +1076 raise TypeError('Corr / wrong type') +1077 +1078 def __neg__(self): +1079 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1080 return Corr(newcontent, prange=self.prange) +1081 +1082 def __sub__(self, y): +1083 return self + (-y) +1084 +1085 def __pow__(self, y): +1086 if isinstance(y, (Obs, int, float, CObs)): +1087 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1088 return Corr(newcontent, prange=self.prange) +1089 else: +1090 raise TypeError('Type of exponent not supported') +1091 +1092 def __abs__(self): +1093 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1094 return Corr(newcontent, prange=self.prange) +1095 +1096 # The numpy functions: +1097 def sqrt(self): +1098 return self ** 0.5 +1099 +1100 def log(self): +1101 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1102 return Corr(newcontent, prange=self.prange) 1103 -1104 def tan(self): -1105 return self._apply_func_to_corr(np.tan) -1106 -1107 def sinh(self): -1108 return self._apply_func_to_corr(np.sinh) -1109 -1110 def cosh(self): -1111 return self._apply_func_to_corr(np.cosh) -1112 -1113 def tanh(self): -1114 return self._apply_func_to_corr(np.tanh) -1115 -1116 def arcsin(self): -1117 return self._apply_func_to_corr(np.arcsin) +1104 def exp(self): +1105 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1106 return Corr(newcontent, prange=self.prange) +1107 +1108 def _apply_func_to_corr(self, func): +1109 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1110 for t in range(self.T): +1111 if _check_for_none(self, newcontent[t]): +1112 continue +1113 if np.isnan(np.sum(newcontent[t]).value): +1114 newcontent[t] = None +1115 if all([item is None for item in newcontent]): +1116 raise Exception('Operation returns undefined correlator') +1117 return Corr(newcontent) 1118 -1119 def arccos(self): -1120 return self._apply_func_to_corr(np.arccos) +1119 def sin(self): +1120 return self._apply_func_to_corr(np.sin) 1121 -1122 def arctan(self): -1123 return self._apply_func_to_corr(np.arctan) +1122 def cos(self): +1123 return self._apply_func_to_corr(np.cos) 1124 -1125 def arcsinh(self): -1126 return self._apply_func_to_corr(np.arcsinh) +1125 def tan(self): +1126 return self._apply_func_to_corr(np.tan) 1127 -1128 def arccosh(self): -1129 return self._apply_func_to_corr(np.arccosh) +1128 def sinh(self): +1129 return self._apply_func_to_corr(np.sinh) 1130 -1131 def arctanh(self): -1132 return self._apply_func_to_corr(np.arctanh) +1131 def cosh(self): +1132 return self._apply_func_to_corr(np.cosh) 1133 -1134 # Right hand side operations (require tweak in main module to work) -1135 def __radd__(self, y): -1136 return self + y -1137 -1138 def __rsub__(self, y): -1139 return -self + y -1140 -1141 def __rmul__(self, y): -1142 return self * y -1143 -1144 def __rtruediv__(self, y): -1145 return (self / y) ** (-1) -1146 -1147 @property -1148 def real(self): -1149 def return_real(obs_OR_cobs): -1150 if isinstance(obs_OR_cobs, CObs): -1151 return obs_OR_cobs.real -1152 else: -1153 return obs_OR_cobs +1134 def tanh(self): +1135 return self._apply_func_to_corr(np.tanh) +1136 +1137 def arcsin(self): +1138 return self._apply_func_to_corr(np.arcsin) +1139 +1140 def arccos(self): +1141 return self._apply_func_to_corr(np.arccos) +1142 +1143 def arctan(self): +1144 return self._apply_func_to_corr(np.arctan) +1145 +1146 def arcsinh(self): +1147 return self._apply_func_to_corr(np.arcsinh) +1148 +1149 def arccosh(self): +1150 return self._apply_func_to_corr(np.arccosh) +1151 +1152 def arctanh(self): +1153 return self._apply_func_to_corr(np.arctanh) 1154 -1155 return self._apply_func_to_corr(return_real) -1156 -1157 @property -1158 def imag(self): -1159 def return_imag(obs_OR_cobs): -1160 if isinstance(obs_OR_cobs, CObs): -1161 return obs_OR_cobs.imag -1162 else: -1163 return obs_OR_cobs * 0 # So it stays the right type +1155 # Right hand side operations (require tweak in main module to work) +1156 def __radd__(self, y): +1157 return self + y +1158 +1159 def __rsub__(self, y): +1160 return -self + y +1161 +1162 def __rmul__(self, y): +1163 return self * y 1164 -1165 return self._apply_func_to_corr(return_imag) -1166 -1167 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1168 r''' Project large correlation matrix to lowest states -1169 -1170 This method can be used to reduce the size of an (N x N) correlation matrix -1171 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1172 is still small. -1173 -1174 Parameters -1175 ---------- -1176 Ntrunc: int -1177 Rank of the target matrix. -1178 tproj: int -1179 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1180 The default value is 3. -1181 t0proj: int -1182 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1183 discouraged for O(a) improved theories, since the correctness of the procedure -1184 cannot be granted in this case. The default value is 2. -1185 basematrix : Corr -1186 Correlation matrix that is used to determine the eigenvectors of the -1187 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1188 is is not specified. -1189 -1190 Notes -1191 ----- -1192 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1193 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1194 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1195 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1196 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1197 correlation matrix and to remove some noise that is added by irrelevant operators. -1198 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1199 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1200 ''' -1201 -1202 if self.N == 1: -1203 raise Exception('Method cannot be applied to one-dimensional correlators.') -1204 if basematrix is None: -1205 basematrix = self -1206 if Ntrunc >= basematrix.N: -1207 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1208 if basematrix.N != self.N: -1209 raise Exception('basematrix and targetmatrix have to be of the same size.') +1165 def __rtruediv__(self, y): +1166 return (self / y) ** (-1) +1167 +1168 @property +1169 def real(self): +1170 def return_real(obs_OR_cobs): +1171 if isinstance(obs_OR_cobs, CObs): +1172 return obs_OR_cobs.real +1173 else: +1174 return obs_OR_cobs +1175 +1176 return self._apply_func_to_corr(return_real) +1177 +1178 @property +1179 def imag(self): +1180 def return_imag(obs_OR_cobs): +1181 if isinstance(obs_OR_cobs, CObs): +1182 return obs_OR_cobs.imag +1183 else: +1184 return obs_OR_cobs * 0 # So it stays the right type +1185 +1186 return self._apply_func_to_corr(return_imag) +1187 +1188 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1189 r''' Project large correlation matrix to lowest states +1190 +1191 This method can be used to reduce the size of an (N x N) correlation matrix +1192 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1193 is still small. +1194 +1195 Parameters +1196 ---------- +1197 Ntrunc: int +1198 Rank of the target matrix. +1199 tproj: int +1200 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1201 The default value is 3. +1202 t0proj: int +1203 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1204 discouraged for O(a) improved theories, since the correctness of the procedure +1205 cannot be granted in this case. The default value is 2. +1206 basematrix : Corr +1207 Correlation matrix that is used to determine the eigenvectors of the +1208 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1209 is is not specified. 1210 -1211 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1212 -1213 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1214 rmat = [] -1215 for t in range(basematrix.T): -1216 for i in range(Ntrunc): -1217 for j in range(Ntrunc): -1218 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1219 rmat.append(np.copy(tmpmat)) -1220 -1221 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1222 return Corr(newcontent) +1211 Notes +1212 ----- +1213 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1214 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1215 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1216 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1217 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1218 correlation matrix and to remove some noise that is added by irrelevant operators. +1219 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1220 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1221 ''' +1222 +1223 if self.N == 1: +1224 raise Exception('Method cannot be applied to one-dimensional correlators.') +1225 if basematrix is None: +1226 basematrix = self +1227 if Ntrunc >= basematrix.N: +1228 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1229 if basematrix.N != self.N: +1230 raise Exception('basematrix and targetmatrix have to be of the same size.') +1231 +1232 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1233 +1234 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1235 rmat = [] +1236 for t in range(basematrix.T): +1237 for i in range(Ntrunc): +1238 for j in range(Ntrunc): +1239 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1240 rmat.append(np.copy(tmpmat)) +1241 +1242 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1243 return Corr(newcontent) @@ -3073,6 +3118,39 @@ timeslice and the error on each timeslice.

    + +
    + +
    + + def + is_matrix_symmetric(self) + + + +
    + + 
    241    def is_matrix_symmetric(self):
+242        """Checks whether a correlator matrices is symmetric on every timeslice."""
+243        if self.N == 1:
+244            raise Exception("Only works for correlator matrices.")
+245        for t in range(self.T):
+246            if self[t] is None:
+247                continue
+248            for i in range(self.N):
+249                for j in range(i + 1, self.N):
+250                    if self[t][i, j] is self[t][j, i]:
+251                        continue
+252                    if hash(self[t][i, j]) != hash(self[t][j, i]):
+253                        return False
+254        return True
+
    + + +

    Checks whether a correlator matrices is symmetric on every timeslice.

    +
    + +
    @@ -3085,13 +3163,15 @@ timeslice and the error on each timeslice.

    - 
    241    def matrix_symmetric(self):
-242        """Symmetrizes the correlator matrices on every timeslice."""
-243        if self.N > 1:
-244            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
-245            return 0.5 * (Corr(transposed) + self)
-246        if self.N == 1:
-247            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
+            
    256    def matrix_symmetric(self):
+257        """Symmetrizes the correlator matrices on every timeslice."""
+258        if self.N == 1:
+259            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
+260        if self.is_matrix_symmetric():
+261            return 1.0 * self
+262        else:
+263            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
+264            return 0.5 * (Corr(transposed) + self)
 
    
 
 
@@ -3111,87 +3191,91 @@ timeslice and the error on each timeslice.
    - 
    249    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
-250        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
-251
-252        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
-253        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
-254        ```python
-255        C.GEVP(t0=2)[0]  # Ground state vector(s)
-256        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
-257        ```
-258
-259        Parameters
-260        ----------
-261        t0 : int
-262            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
-263        ts : int
-264            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
-265            If sort="Eigenvector" it gives a reference point for the sorting method.
-266        sort : string
-267            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.
-268            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-269            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
-270              The reference state is identified by its eigenvalue at $t=t_s$.
-271
-272        Other Parameters
-273        ----------------
-274        state : int
-275           Returns only the vector(s) for a specified state. The lowest state is zero.
-276        '''
-277
-278        if self.N == 1:
-279            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
-280        if ts is not None:
-281            if (ts <= t0):
-282                raise Exception("ts has to be larger than t0.")
-283
-284        if "sorted_list" in kwargs:
-285            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
-286            sort = kwargs.get("sorted_list")
-287
-288        symmetric_corr = self.matrix_symmetric()
-289        if sort is None:
-290            if (ts is None):
-291                raise Exception("ts is required if sort=None.")
-292            if (self.content[t0] is None) or (self.content[ts] is None):
-293                raise Exception("Corr not defined at t0/ts.")
-294            G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
-295            for i in range(self.N):
-296                for j in range(self.N):
-297                    G0[i, j] = symmetric_corr[t0][i, j].value
-298                    Gt[i, j] = symmetric_corr[ts][i, j].value
-299
-300            reordered_vecs = _GEVP_solver(Gt, G0)
-301
-302        elif sort in ["Eigenvalue", "Eigenvector"]:
-303            if sort == "Eigenvalue" and ts is not None:
-304                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
-305            all_vecs = [None] * (t0 + 1)
-306            for t in range(t0 + 1, self.T):
-307                try:
-308                    G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
-309                    for i in range(self.N):
-310                        for j in range(self.N):
-311                            G0[i, j] = symmetric_corr[t0][i, j].value
-312                            Gt[i, j] = symmetric_corr[t][i, j].value
-313
-314                    all_vecs.append(_GEVP_solver(Gt, G0))
-315                except Exception:
-316                    all_vecs.append(None)
-317            if sort == "Eigenvector":
-318                if (ts is None):
-319                    raise Exception("ts is required for the Eigenvector sorting method.")
-320                all_vecs = _sort_vectors(all_vecs, ts)
-321
-322            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
-323        else:
-324            raise Exception("Unkown value for 'sort'.")
-325
-326        if "state" in kwargs:
-327            return reordered_vecs[kwargs.get("state")]
-328        else:
-329            return reordered_vecs
+            
    266    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
+267        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
+268
+269        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
+270        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
+271        ```python
+272        C.GEVP(t0=2)[0]  # Ground state vector(s)
+273        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
+274        ```
+275
+276        Parameters
+277        ----------
+278        t0 : int
+279            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
+280        ts : int
+281            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
+282            If sort="Eigenvector" it gives a reference point for the sorting method.
+283        sort : string
+284            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.
+285            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
+286            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
+287              The reference state is identified by its eigenvalue at $t=t_s$.
+288
+289        Other Parameters
+290        ----------------
+291        state : int
+292           Returns only the vector(s) for a specified state. The lowest state is zero.
+293        '''
+294
+295        if self.N == 1:
+296            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
+297        if ts is not None:
+298            if (ts <= t0):
+299                raise Exception("ts has to be larger than t0.")
+300
+301        if "sorted_list" in kwargs:
+302            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
+303            sort = kwargs.get("sorted_list")
+304
+305        if self.is_matrix_symmetric():
+306            symmetric_corr = self
+307        else:
+308            symmetric_corr = self.matrix_symmetric()
+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            G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
+316            for i in range(self.N):
+317                for j in range(self.N):
+318                    G0[i, j] = symmetric_corr[t0][i, j].value
+319                    Gt[i, j] = symmetric_corr[ts][i, j].value
+320
+321            reordered_vecs = _GEVP_solver(Gt, G0)
+322
+323        elif sort in ["Eigenvalue", "Eigenvector"]:
+324            if sort == "Eigenvalue" and ts is not None:
+325                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
+326            all_vecs = [None] * (t0 + 1)
+327            for t in range(t0 + 1, self.T):
+328                try:
+329                    G0, Gt = np.empty([self.N, self.N], dtype="double"), np.empty([self.N, self.N], dtype="double")
+330                    for i in range(self.N):
+331                        for j in range(self.N):
+332                            G0[i, j] = symmetric_corr[t0][i, j].value
+333                            Gt[i, j] = symmetric_corr[t][i, j].value
+334
+335                    all_vecs.append(_GEVP_solver(Gt, G0))
+336                except Exception:
+337                    all_vecs.append(None)
+338            if sort == "Eigenvector":
+339                if (ts is None):
+340                    raise Exception("ts is required for the Eigenvector sorting method.")
+341                all_vecs = _sort_vectors(all_vecs, ts)
+342
+343            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
+344        else:
+345            raise Exception("Unkown value for 'sort'.")
+346
+347        if "state" in kwargs:
+348            return reordered_vecs[kwargs.get("state")]
+349        else:
+350            return reordered_vecs
 
    
 
 
@@ -3242,18 +3326,18 @@ Returns only the vector(s) for a specified state. The lowest state is zero.
    - 
    331    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
-332        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
-333
-334        Parameters
-335        ----------
-336        state : int
-337            The state one is interested in ordered by energy. The lowest state is zero.
-338
-339        All other parameters are identical to the ones of Corr.GEVP.
-340        """
-341        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
-342        return self.projected(vec)
+            
    352    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
+353        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
+354
+355        Parameters
+356        ----------
+357        state : int
+358            The state one is interested in ordered by energy. The lowest state is zero.
+359
+360        All other parameters are identical to the ones of Corr.GEVP.
+361        """
+362        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
+363        return self.projected(vec)
 
    
 
 
@@ -3281,46 +3365,46 @@ The state one is interested in ordered by energy. The lowest state is zero.
    - 
    344    def Hankel(self, N, periodic=False):
-345        """Constructs an NxN Hankel matrix
-346
-347        C(t) c(t+1) ... c(t+n-1)
-348        C(t+1) c(t+2) ... c(t+n)
-349        .................
-350        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
-351
-352        Parameters
-353        ----------
-354        N : int
-355            Dimension of the Hankel matrix
-356        periodic : bool, optional
-357            determines whether the matrix is extended periodically
-358        """
-359
-360        if self.N != 1:
-361            raise Exception("Multi-operator Prony not implemented!")
-362
-363        array = np.empty([N, N], dtype="object")
-364        new_content = []
-365        for t in range(self.T):
-366            new_content.append(array.copy())
+            
    365    def Hankel(self, N, periodic=False):
+366        """Constructs an NxN Hankel matrix
 367
-368        def wrap(i):
-369            while i >= self.T:
-370                i -= self.T
-371            return i
+368        C(t) c(t+1) ... c(t+n-1)
+369        C(t+1) c(t+2) ... c(t+n)
+370        .................
+371        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
 372
-373        for t in range(self.T):
-374            for i in range(N):
-375                for j in range(N):
-376                    if periodic:
-377                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
-378                    elif (t + i + j) >= self.T:
-379                        new_content[t] = None
-380                    else:
-381                        new_content[t][i, j] = self.content[t + i + j][0]
-382
-383        return Corr(new_content)
+373        Parameters
+374        ----------
+375        N : int
+376            Dimension of the Hankel matrix
+377        periodic : bool, optional
+378            determines whether the matrix is extended periodically
+379        """
+380
+381        if self.N != 1:
+382            raise Exception("Multi-operator Prony not implemented!")
+383
+384        array = np.empty([N, N], dtype="object")
+385        new_content = []
+386        for t in range(self.T):
+387            new_content.append(array.copy())
+388
+389        def wrap(i):
+390            while i >= self.T:
+391                i -= self.T
+392            return i
+393
+394        for t in range(self.T):
+395            for i in range(N):
+396                for j in range(N):
+397                    if periodic:
+398                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
+399                    elif (t + i + j) >= self.T:
+400                        new_content[t] = None
+401                    else:
+402                        new_content[t][i, j] = self.content[t + i + j][0]
+403
+404        return Corr(new_content)
 
    
 
 
@@ -3354,15 +3438,15 @@ determines whether the matrix is extended periodically
    - 
    385    def roll(self, dt):
-386        """Periodically shift the correlator by dt timeslices
-387
-388        Parameters
-389        ----------
-390        dt : int
-391            number of timeslices
-392        """
-393        return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))
+            
    406    def roll(self, dt):
+407        """Periodically shift the correlator by dt timeslices
+408
+409        Parameters
+410        ----------
+411        dt : int
+412            number of timeslices
+413        """
+414        return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))
 
    
 
 
@@ -3389,9 +3473,9 @@ number of timeslices
    - 
    395    def reverse(self):
-396        """Reverse the time ordering of the Corr"""
-397        return Corr(self.content[:: -1])
+            
    416    def reverse(self):
+417        """Reverse the time ordering of the Corr"""
+418        return Corr(self.content[:: -1])
 
    
 
 
@@ -3411,23 +3495,23 @@ number of timeslices
    - 
    399    def thin(self, spacing=2, offset=0):
-400        """Thin out a correlator to suppress correlations
-401
-402        Parameters
-403        ----------
-404        spacing : int
-405            Keep only every 'spacing'th entry of the correlator
-406        offset : int
-407            Offset the equal spacing
-408        """
-409        new_content = []
-410        for t in range(self.T):
-411            if (offset + t) % spacing != 0:
-412                new_content.append(None)
-413            else:
-414                new_content.append(self.content[t])
-415        return Corr(new_content)
+            
    420    def thin(self, spacing=2, offset=0):
+421        """Thin out a correlator to suppress correlations
+422
+423        Parameters
+424        ----------
+425        spacing : int
+426            Keep only every 'spacing'th entry of the correlator
+427        offset : int
+428            Offset the equal spacing
+429        """
+430        new_content = []
+431        for t in range(self.T):
+432            if (offset + t) % spacing != 0:
+433                new_content.append(None)
+434            else:
+435                new_content.append(self.content[t])
+436        return Corr(new_content)
 
    
 
 
@@ -3456,34 +3540,34 @@ Offset the equal spacing
    - 
    417    def correlate(self, partner):
-418        """Correlate the correlator with another correlator or Obs
-419
-420        Parameters
-421        ----------
-422        partner : Obs or Corr
-423            partner to correlate the correlator with.
-424            Can either be an Obs which is correlated with all entries of the
-425            correlator or a Corr of same length.
-426        """
-427        if self.N != 1:
-428            raise Exception("Only one-dimensional correlators can be safely correlated.")
-429        new_content = []
-430        for x0, t_slice in enumerate(self.content):
-431            if _check_for_none(self, t_slice):
-432                new_content.append(None)
-433            else:
-434                if isinstance(partner, Corr):
-435                    if _check_for_none(partner, partner.content[x0]):
-436                        new_content.append(None)
-437                    else:
-438                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
-439                elif isinstance(partner, Obs):  # Should this include CObs?
-440                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
-441                else:
-442                    raise Exception("Can only correlate with an Obs or a Corr.")
-443
-444        return Corr(new_content)
+            
    438    def correlate(self, partner):
+439        """Correlate the correlator with another correlator or Obs
+440
+441        Parameters
+442        ----------
+443        partner : Obs or Corr
+444            partner to correlate the correlator with.
+445            Can either be an Obs which is correlated with all entries of the
+446            correlator or a Corr of same length.
+447        """
+448        if self.N != 1:
+449            raise Exception("Only one-dimensional correlators can be safely correlated.")
+450        new_content = []
+451        for x0, t_slice in enumerate(self.content):
+452            if _check_for_none(self, t_slice):
+453                new_content.append(None)
+454            else:
+455                if isinstance(partner, Corr):
+456                    if _check_for_none(partner, partner.content[x0]):
+457                        new_content.append(None)
+458                    else:
+459                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
+460                elif isinstance(partner, Obs):  # Should this include CObs?
+461                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
+462                else:
+463                    raise Exception("Can only correlate with an Obs or a Corr.")
+464
+465        return Corr(new_content)
 
    
 
 
@@ -3512,28 +3596,28 @@ correlator or a Corr of same length.
    - 
    446    def reweight(self, weight, **kwargs):
-447        """Reweight the correlator.
-448
-449        Parameters
-450        ----------
-451        weight : Obs
-452            Reweighting factor. An Observable that has to be defined on a superset of the
-453            configurations in obs[i].idl for all i.
-454        all_configs : bool
-455            if True, the reweighted observables are normalized by the average of
-456            the reweighting factor on all configurations in weight.idl and not
-457            on the configurations in obs[i].idl.
-458        """
-459        if self.N != 1:
-460            raise Exception("Reweighting only implemented for one-dimensional correlators.")
-461        new_content = []
-462        for t_slice in self.content:
-463            if _check_for_none(self, t_slice):
-464                new_content.append(None)
-465            else:
-466                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
-467        return Corr(new_content)
+            
    467    def reweight(self, weight, **kwargs):
+468        """Reweight the correlator.
+469
+470        Parameters
+471        ----------
+472        weight : Obs
+473            Reweighting factor. An Observable that has to be defined on a superset of the
+474            configurations in obs[i].idl for all i.
+475        all_configs : bool
+476            if True, the reweighted observables are normalized by the average of
+477            the reweighting factor on all configurations in weight.idl and not
+478            on the configurations in obs[i].idl.
+479        """
+480        if self.N != 1:
+481            raise Exception("Reweighting only implemented for one-dimensional correlators.")
+482        new_content = []
+483        for t_slice in self.content:
+484            if _check_for_none(self, t_slice):
+485                new_content.append(None)
+486            else:
+487                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
+488        return Corr(new_content)
 
    
 
 
@@ -3565,35 +3649,35 @@ on the configurations in obs[i].idl.
    - 
    469    def T_symmetry(self, partner, parity=+1):
-470        """Return the time symmetry average of the correlator and its partner
-471
-472        Parameters
-473        ----------
-474        partner : Corr
-475            Time symmetry partner of the Corr
-476        partity : int
-477            Parity quantum number of the correlator, can be +1 or -1
-478        """
-479        if self.N != 1:
-480            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
-481        if not isinstance(partner, Corr):
-482            raise Exception("T partner has to be a Corr object.")
-483        if parity not in [+1, -1]:
-484            raise Exception("Parity has to be +1 or -1.")
-485        T_partner = parity * partner.reverse()
-486
-487        t_slices = []
-488        test = (self - T_partner)
-489        test.gamma_method()
-490        for x0, t_slice in enumerate(test.content):
-491            if t_slice is not None:
-492                if not t_slice[0].is_zero_within_error(5):
-493                    t_slices.append(x0)
-494        if t_slices:
-495            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
-496
-497        return (self + T_partner) / 2
+            
    490    def T_symmetry(self, partner, parity=+1):
+491        """Return the time symmetry average of the correlator and its partner
+492
+493        Parameters
+494        ----------
+495        partner : Corr
+496            Time symmetry partner of the Corr
+497        partity : int
+498            Parity quantum number of the correlator, can be +1 or -1
+499        """
+500        if self.N != 1:
+501            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
+502        if not isinstance(partner, Corr):
+503            raise Exception("T partner has to be a Corr object.")
+504        if parity not in [+1, -1]:
+505            raise Exception("Parity has to be +1 or -1.")
+506        T_partner = parity * partner.reverse()
+507
+508        t_slices = []
+509        test = (self - T_partner)
+510        test.gamma_method()
+511        for x0, t_slice in enumerate(test.content):
+512            if t_slice is not None:
+513                if not t_slice[0].is_zero_within_error(5):
+514                    t_slices.append(x0)
+515        if t_slices:
+516            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
+517
+518        return (self + T_partner) / 2
 
    
 
 
@@ -3622,59 +3706,59 @@ Parity quantum number of the correlator, can be +1 or -1
    - 
    499    def deriv(self, variant="symmetric"):
-500        """Return the first derivative of the correlator with respect to x0.
-501
-502        Parameters
-503        ----------
-504        variant : str
-505            decides which definition of the finite differences derivative is used.
-506            Available choice: symmetric, forward, backward, improved, default: symmetric
-507        """
-508        if self.N != 1:
-509            raise Exception("deriv only implemented for one-dimensional correlators.")
-510        if variant == "symmetric":
-511            newcontent = []
-512            for t in range(1, self.T - 1):
-513                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-514                    newcontent.append(None)
-515                else:
-516                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
-517            if(all([x is None for x in newcontent])):
-518                raise Exception('Derivative is undefined at all timeslices')
-519            return Corr(newcontent, padding=[1, 1])
-520        elif variant == "forward":
-521            newcontent = []
-522            for t in range(self.T - 1):
-523                if (self.content[t] is None) or (self.content[t + 1] is None):
-524                    newcontent.append(None)
-525                else:
-526                    newcontent.append(self.content[t + 1] - self.content[t])
-527            if(all([x is None for x in newcontent])):
-528                raise Exception("Derivative is undefined at all timeslices")
-529            return Corr(newcontent, padding=[0, 1])
-530        elif variant == "backward":
-531            newcontent = []
-532            for t in range(1, self.T):
-533                if (self.content[t - 1] is None) or (self.content[t] is None):
-534                    newcontent.append(None)
-535                else:
-536                    newcontent.append(self.content[t] - self.content[t - 1])
-537            if(all([x is None for x in newcontent])):
-538                raise Exception("Derivative is undefined at all timeslices")
-539            return Corr(newcontent, padding=[1, 0])
-540        elif variant == "improved":
-541            newcontent = []
-542            for t in range(2, self.T - 2):
-543                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):
-544                    newcontent.append(None)
-545                else:
-546                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
-547            if(all([x is None for x in newcontent])):
-548                raise Exception('Derivative is undefined at all timeslices')
-549            return Corr(newcontent, padding=[2, 2])
-550        else:
-551            raise Exception("Unknown variant.")
+            
    520    def deriv(self, variant="symmetric"):
+521        """Return the first derivative of the correlator with respect to x0.
+522
+523        Parameters
+524        ----------
+525        variant : str
+526            decides which definition of the finite differences derivative is used.
+527            Available choice: symmetric, forward, backward, improved, default: symmetric
+528        """
+529        if self.N != 1:
+530            raise Exception("deriv only implemented for one-dimensional correlators.")
+531        if variant == "symmetric":
+532            newcontent = []
+533            for t in range(1, self.T - 1):
+534                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+535                    newcontent.append(None)
+536                else:
+537                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
+538            if(all([x is None for x in newcontent])):
+539                raise Exception('Derivative is undefined at all timeslices')
+540            return Corr(newcontent, padding=[1, 1])
+541        elif variant == "forward":
+542            newcontent = []
+543            for t in range(self.T - 1):
+544                if (self.content[t] is None) or (self.content[t + 1] is None):
+545                    newcontent.append(None)
+546                else:
+547                    newcontent.append(self.content[t + 1] - self.content[t])
+548            if(all([x is None for x in newcontent])):
+549                raise Exception("Derivative is undefined at all timeslices")
+550            return Corr(newcontent, padding=[0, 1])
+551        elif variant == "backward":
+552            newcontent = []
+553            for t in range(1, self.T):
+554                if (self.content[t - 1] is None) or (self.content[t] is None):
+555                    newcontent.append(None)
+556                else:
+557                    newcontent.append(self.content[t] - self.content[t - 1])
+558            if(all([x is None for x in newcontent])):
+559                raise Exception("Derivative is undefined at all timeslices")
+560            return Corr(newcontent, padding=[1, 0])
+561        elif variant == "improved":
+562            newcontent = []
+563            for t in range(2, self.T - 2):
+564                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):
+565                    newcontent.append(None)
+566                else:
+567                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
+568            if(all([x is None for x in newcontent])):
+569                raise Exception('Derivative is undefined at all timeslices')
+570            return Corr(newcontent, padding=[2, 2])
+571        else:
+572            raise Exception("Unknown variant.")
 
    
 
 
@@ -3702,39 +3786,39 @@ Available choice: symmetric, forward, backward, improved, default: symmetric
     
-            
    553    def second_deriv(self, variant="symmetric"):
-554        """Return the second derivative of the correlator with respect to x0.
-555
-556        Parameters
-557        ----------
-558        variant : str
-559            decides which definition of the finite differences derivative is used.
-560            Available choice: symmetric, improved, default: symmetric
-561        """
-562        if self.N != 1:
-563            raise Exception("second_deriv only implemented for one-dimensional correlators.")
-564        if variant == "symmetric":
-565            newcontent = []
-566            for t in range(1, self.T - 1):
-567                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-568                    newcontent.append(None)
-569                else:
-570                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
-571            if(all([x is None for x in newcontent])):
-572                raise Exception("Derivative is undefined at all timeslices")
-573            return Corr(newcontent, padding=[1, 1])
-574        elif variant == "improved":
-575            newcontent = []
-576            for t in range(2, self.T - 2):
-577                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):
-578                    newcontent.append(None)
-579                else:
-580                    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]))
-581            if(all([x is None for x in newcontent])):
-582                raise Exception("Derivative is undefined at all timeslices")
-583            return Corr(newcontent, padding=[2, 2])
-584        else:
-585            raise Exception("Unknown variant.")
+            
    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, 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        else:
+606            raise Exception("Unknown variant.")
 
    
 
 
@@ -3762,74 +3846,74 @@ Available choice: symmetric, improved, default: symmetric
 
     
    
     
-            
    587    def m_eff(self, variant='log', guess=1.0):
-588        """Returns the effective mass of the correlator as correlator object
-589
-590        Parameters
-591        ----------
-592        variant : str
-593            log : uses the standard effective mass log(C(t) / C(t+1))
-594            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.
-595            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.
-596            See, e.g., arXiv:1205.5380
-597            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
-598        guess : float
-599            guess for the root finder, only relevant for the root variant
-600        """
-601        if self.N != 1:
-602            raise Exception('Correlator must be projected before getting m_eff')
-603        if variant == 'log':
-604            newcontent = []
-605            for t in range(self.T - 1):
-606                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-607                    newcontent.append(None)
-608                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-609                    newcontent.append(None)
-610                else:
-611                    newcontent.append(self.content[t] / self.content[t + 1])
-612            if(all([x is None for x in newcontent])):
-613                raise Exception('m_eff is undefined at all timeslices')
-614
-615            return np.log(Corr(newcontent, padding=[0, 1]))
-616
-617        elif variant in ['periodic', 'cosh', 'sinh']:
-618            if variant in ['periodic', 'cosh']:
-619                func = anp.cosh
-620            else:
-621                func = anp.sinh
-622
-623            def root_function(x, d):
-624                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
-625
-626            newcontent = []
-627            for t in range(self.T - 1):
-628                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
-629                    newcontent.append(None)
-630                # Fill the two timeslices in the middle of the lattice with their predecessors
-631                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
-632                    newcontent.append(newcontent[-1])
-633                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-634                    newcontent.append(None)
-635                else:
-636                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
-637            if(all([x is None for x in newcontent])):
-638                raise Exception('m_eff is undefined at all timeslices')
-639
-640            return Corr(newcontent, padding=[0, 1])
-641
-642        elif variant == 'arccosh':
-643            newcontent = []
-644            for t in range(1, self.T - 1):
-645                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):
-646                    newcontent.append(None)
-647                else:
-648                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
-649            if(all([x is None for x in newcontent])):
-650                raise Exception("m_eff is undefined at all timeslices")
-651            return np.arccosh(Corr(newcontent, padding=[1, 1]))
-652
-653        else:
-654            raise Exception('Unknown variant.')
+            
    608    def m_eff(self, variant='log', guess=1.0):
+609        """Returns the effective mass of the correlator as correlator object
+610
+611        Parameters
+612        ----------
+613        variant : str
+614            log : uses the standard effective mass log(C(t) / C(t+1))
+615            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.
+616            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.
+617            See, e.g., arXiv:1205.5380
+618            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+619        guess : float
+620            guess for the root finder, only relevant for the root variant
+621        """
+622        if self.N != 1:
+623            raise Exception('Correlator must be projected before getting m_eff')
+624        if variant == 'log':
+625            newcontent = []
+626            for t in range(self.T - 1):
+627                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+628                    newcontent.append(None)
+629                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+630                    newcontent.append(None)
+631                else:
+632                    newcontent.append(self.content[t] / self.content[t + 1])
+633            if(all([x is None for x in newcontent])):
+634                raise Exception('m_eff is undefined at all timeslices')
+635
+636            return np.log(Corr(newcontent, padding=[0, 1]))
+637
+638        elif variant in ['periodic', 'cosh', 'sinh']:
+639            if variant in ['periodic', 'cosh']:
+640                func = anp.cosh
+641            else:
+642                func = anp.sinh
+643
+644            def root_function(x, d):
+645                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
+646
+647            newcontent = []
+648            for t in range(self.T - 1):
+649                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+650                    newcontent.append(None)
+651                # Fill the two timeslices in the middle of the lattice with their predecessors
+652                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
+653                    newcontent.append(newcontent[-1])
+654                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
+655                    newcontent.append(None)
+656                else:
+657                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
+658            if(all([x is None for x in newcontent])):
+659                raise Exception('m_eff is undefined at all timeslices')
+660
+661            return Corr(newcontent, padding=[0, 1])
+662
+663        elif variant == 'arccosh':
+664            newcontent = []
+665            for t in range(1, self.T - 1):
+666                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):
+667                    newcontent.append(None)
+668                else:
+669                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+670            if(all([x is None for x in newcontent])):
+671                raise Exception("m_eff is undefined at all timeslices")
+672            return np.arccosh(Corr(newcontent, padding=[1, 1]))
+673
+674        else:
+675            raise Exception('Unknown variant.')
 
    
 
 
@@ -3862,39 +3946,39 @@ guess for the root finder, only relevant for the root variant
 
     
    
     
-            
    656    def fit(self, function, fitrange=None, silent=False, **kwargs):
-657        r'''Fits function to the data
-658
-659        Parameters
-660        ----------
-661        function : obj
-662            function to fit to the data. See fits.least_squares for details.
-663        fitrange : list
-664            Two element list containing the timeslices on which the fit is supposed to start and stop.
-665            Caution: This range is inclusive as opposed to standard python indexing.
-666            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
-667            If not specified, self.prange or all timeslices are used.
-668        silent : bool
-669            Decides whether output is printed to the standard output.
-670        '''
-671        if self.N != 1:
-672            raise Exception("Correlator must be projected before fitting")
-673
-674        if fitrange is None:
-675            if self.prange:
-676                fitrange = self.prange
-677            else:
-678                fitrange = [0, self.T - 1]
-679        else:
-680            if not isinstance(fitrange, list):
-681                raise Exception("fitrange has to be a list with two elements")
-682            if len(fitrange) != 2:
-683                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
-684
-685        xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
-686        ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
-687        result = least_squares(xs, ys, function, silent=silent, **kwargs)
-688        return result
+            
    677    def fit(self, function, fitrange=None, silent=False, **kwargs):
+678        r'''Fits function to the data
+679
+680        Parameters
+681        ----------
+682        function : obj
+683            function to fit to the data. See fits.least_squares for details.
+684        fitrange : list
+685            Two element list containing the timeslices on which the fit is supposed to start and stop.
+686            Caution: This range is inclusive as opposed to standard python indexing.
+687            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
+688            If not specified, self.prange or all timeslices are used.
+689        silent : bool
+690            Decides whether output is printed to the standard output.
+691        '''
+692        if self.N != 1:
+693            raise Exception("Correlator must be projected before fitting")
+694
+695        if fitrange is None:
+696            if self.prange:
+697                fitrange = self.prange
+698            else:
+699                fitrange = [0, self.T - 1]
+700        else:
+701            if not isinstance(fitrange, list):
+702                raise Exception("fitrange has to be a list with two elements")
+703            if len(fitrange) != 2:
+704                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
+705
+706        xs = [x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
+707        ys = [self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]
+708        result = least_squares(xs, ys, function, silent=silent, **kwargs)
+709        return result
 
    
 
 
@@ -3928,42 +4012,42 @@ Decides whether output is printed to the standard output.
 
     
    
     
-            
    690    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
-691        """ Extract a plateau value from a Corr object
-692
-693        Parameters
-694        ----------
-695        plateau_range : list
-696            list with two entries, indicating the first and the last timeslice
-697            of the plateau region.
-698        method : str
-699            method to extract the plateau.
-700                'fit' fits a constant to the plateau region
-701                'avg', 'average' or 'mean' just average over the given timeslices.
-702        auto_gamma : bool
-703            apply gamma_method with default parameters to the Corr. Defaults to None
-704        """
-705        if not plateau_range:
-706            if self.prange:
-707                plateau_range = self.prange
-708            else:
-709                raise Exception("no plateau range provided")
-710        if self.N != 1:
-711            raise Exception("Correlator must be projected before getting a plateau.")
-712        if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
-713            raise Exception("plateau is undefined at all timeslices in plateaurange.")
-714        if auto_gamma:
-715            self.gamma_method()
-716        if method == "fit":
-717            def const_func(a, t):
-718                return a[0]
-719            return self.fit(const_func, plateau_range)[0]
-720        elif method in ["avg", "average", "mean"]:
-721            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
-722            return returnvalue
-723
-724        else:
-725            raise Exception("Unsupported plateau method: " + method)
+            
    711    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+712        """ Extract a plateau value from a Corr object
+713
+714        Parameters
+715        ----------
+716        plateau_range : list
+717            list with two entries, indicating the first and the last timeslice
+718            of the plateau region.
+719        method : str
+720            method to extract the plateau.
+721                'fit' fits a constant to the plateau region
+722                'avg', 'average' or 'mean' just average over the given timeslices.
+723        auto_gamma : bool
+724            apply gamma_method with default parameters to the Corr. Defaults to None
+725        """
+726        if not plateau_range:
+727            if self.prange:
+728                plateau_range = self.prange
+729            else:
+730                raise Exception("no plateau range provided")
+731        if self.N != 1:
+732            raise Exception("Correlator must be projected before getting a plateau.")
+733        if(all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
+734            raise Exception("plateau is undefined at all timeslices in plateaurange.")
+735        if auto_gamma:
+736            self.gamma_method()
+737        if method == "fit":
+738            def const_func(a, t):
+739                return a[0]
+740            return self.fit(const_func, plateau_range)[0]
+741        elif method in ["avg", "average", "mean"]:
+742            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
+743            return returnvalue
+744
+745        else:
+746            raise Exception("Unsupported plateau method: " + method)
 
    
 
 
@@ -3997,17 +4081,17 @@ apply gamma_method with default parameters to the Corr. Defaults to None
 
     
    
     
-            
    727    def set_prange(self, prange):
-728        """Sets the attribute prange of the Corr object."""
-729        if not len(prange) == 2:
-730            raise Exception("prange must be a list or array with two values")
-731        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
-732            raise Exception("Start and end point must be integers")
-733        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
-734            raise Exception("Start and end point must define a range in the interval 0,T")
-735
-736        self.prange = prange
-737        return
+            
    748    def set_prange(self, prange):
+749        """Sets the attribute prange of the Corr object."""
+750        if not len(prange) == 2:
+751            raise Exception("prange must be a list or array with two values")
+752        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
+753            raise Exception("Start and end point must be integers")
+754        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
+755            raise Exception("Start and end point must define a range in the interval 0,T")
+756
+757        self.prange = prange
+758        return
 
    
 
 
@@ -4027,124 +4111,124 @@ apply gamma_method with default parameters to the Corr. Defaults to None
 
     
    
     
-            
    739    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):
-740        """Plots the correlator using the tag of the correlator as label if available.
-741
-742        Parameters
-743        ----------
-744        x_range : list
-745            list of two values, determining the range of the x-axis e.g. [4, 8].
-746        comp : Corr or list of Corr
-747            Correlator or list of correlators which are plotted for comparison.
-748            The tags of these correlators are used as labels if available.
-749        logscale : bool
-750            Sets y-axis to logscale.
-751        plateau : Obs
-752            Plateau value to be visualized in the figure.
-753        fit_res : Fit_result
-754            Fit_result object to be visualized.
-755        ylabel : str
-756            Label for the y-axis.
-757        save : str
-758            path to file in which the figure should be saved.
-759        auto_gamma : bool
-760            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
-761        hide_sigma : float
-762            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
-763        references : list
-764            List of floating point values that are displayed as horizontal lines for reference.
-765        title : string
-766            Optional title of the figure.
-767        """
-768        if self.N != 1:
-769            raise Exception("Correlator must be projected before plotting")
-770
-771        if auto_gamma:
-772            self.gamma_method()
-773
-774        if x_range is None:
-775            x_range = [0, self.T - 1]
-776
-777        fig = plt.figure()
-778        ax1 = fig.add_subplot(111)
-779
-780        x, y, y_err = self.plottable()
-781        if hide_sigma:
-782            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-783        else:
-784            hide_from = None
-785        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
-786        if logscale:
-787            ax1.set_yscale('log')
-788        else:
-789            if y_range is None:
-790                try:
-791                    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)])
-792                    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)])
-793                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
-794                except Exception:
-795                    pass
-796            else:
-797                ax1.set_ylim(y_range)
-798        if comp:
-799            if isinstance(comp, (Corr, list)):
-800                for corr in comp if isinstance(comp, list) else [comp]:
-801                    if auto_gamma:
-802                        corr.gamma_method()
-803                    x, y, y_err = corr.plottable()
-804                    if hide_sigma:
-805                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-806                    else:
-807                        hide_from = None
-808                    plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
-809            else:
-810                raise Exception("'comp' must be a correlator or a list of correlators.")
-811
-812        if plateau:
-813            if isinstance(plateau, Obs):
-814                if auto_gamma:
-815                    plateau.gamma_method()
-816                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
-817                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
-818            else:
-819                raise Exception("'plateau' must be an Obs")
-820
-821        if references:
-822            if isinstance(references, list):
-823                for ref in references:
-824                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
-825            else:
-826                raise Exception("'references' must be a list of floating pint values.")
-827
-828        if self.prange:
-829            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
-830            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
-831
-832        if fit_res:
-833            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
-834            ax1.plot(x_samples,
-835                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
-836                     ls='-', marker=',', lw=2)
-837
-838        ax1.set_xlabel(r'$x_0 / a$')
-839        if ylabel:
-840            ax1.set_ylabel(ylabel)
-841        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
-842
-843        handles, labels = ax1.get_legend_handles_labels()
-844        if labels:
-845            ax1.legend()
-846
-847        if title:
-848            plt.title(title)
-849
-850        plt.draw()
-851
-852        if save:
-853            if isinstance(save, str):
-854                fig.savefig(save, bbox_inches='tight')
-855            else:
-856                raise Exception("'save' has to be a string.")
+            
    760    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):
+761        """Plots the correlator using the tag of the correlator as label if available.
+762
+763        Parameters
+764        ----------
+765        x_range : list
+766            list of two values, determining the range of the x-axis e.g. [4, 8].
+767        comp : Corr or list of Corr
+768            Correlator or list of correlators which are plotted for comparison.
+769            The tags of these correlators are used as labels if available.
+770        logscale : bool
+771            Sets y-axis to logscale.
+772        plateau : Obs
+773            Plateau value to be visualized in the figure.
+774        fit_res : Fit_result
+775            Fit_result object to be visualized.
+776        ylabel : str
+777            Label for the y-axis.
+778        save : str
+779            path to file in which the figure should be saved.
+780        auto_gamma : bool
+781            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
+782        hide_sigma : float
+783            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
+784        references : list
+785            List of floating point values that are displayed as horizontal lines for reference.
+786        title : string
+787            Optional title of the figure.
+788        """
+789        if self.N != 1:
+790            raise Exception("Correlator must be projected before plotting")
+791
+792        if auto_gamma:
+793            self.gamma_method()
+794
+795        if x_range is None:
+796            x_range = [0, self.T - 1]
+797
+798        fig = plt.figure()
+799        ax1 = fig.add_subplot(111)
+800
+801        x, y, y_err = self.plottable()
+802        if hide_sigma:
+803            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+804        else:
+805            hide_from = None
+806        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
+807        if logscale:
+808            ax1.set_yscale('log')
+809        else:
+810            if y_range is None:
+811                try:
+812                    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)])
+813                    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)])
+814                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
+815                except Exception:
+816                    pass
+817            else:
+818                ax1.set_ylim(y_range)
+819        if comp:
+820            if isinstance(comp, (Corr, list)):
+821                for corr in comp if isinstance(comp, list) else [comp]:
+822                    if auto_gamma:
+823                        corr.gamma_method()
+824                    x, y, y_err = corr.plottable()
+825                    if hide_sigma:
+826                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+827                    else:
+828                        hide_from = None
+829                    plt.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
+830            else:
+831                raise Exception("'comp' must be a correlator or a list of correlators.")
+832
+833        if plateau:
+834            if isinstance(plateau, Obs):
+835                if auto_gamma:
+836                    plateau.gamma_method()
+837                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
+838                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+839            else:
+840                raise Exception("'plateau' must be an Obs")
+841
+842        if references:
+843            if isinstance(references, list):
+844                for ref in references:
+845                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
+846            else:
+847                raise Exception("'references' must be a list of floating pint values.")
+848
+849        if self.prange:
+850            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',')
+851            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',')
+852
+853        if fit_res:
+854            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
+855            ax1.plot(x_samples,
+856                     fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples),
+857                     ls='-', marker=',', lw=2)
+858
+859        ax1.set_xlabel(r'$x_0 / a$')
+860        if ylabel:
+861            ax1.set_ylabel(ylabel)
+862        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
+863
+864        handles, labels = ax1.get_legend_handles_labels()
+865        if labels:
+866            ax1.legend()
+867
+868        if title:
+869            plt.title(title)
+870
+871        plt.draw()
+872
+873        if save:
+874            if isinstance(save, str):
+875                fig.savefig(save, bbox_inches='tight')
+876            else:
+877                raise Exception("'save' has to be a string.")
 
    
 
 
@@ -4192,34 +4276,34 @@ Optional title of the figure.
 
     
    
     
-            
    858    def spaghetti_plot(self, logscale=True):
-859        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-860
-861        Parameters
-862        ----------
-863        logscale : bool
-864            Determines whether the scale of the y-axis is logarithmic or standard.
-865        """
-866        if self.N != 1:
-867            raise Exception("Correlator needs to be projected first.")
-868
-869        mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist]))
-870        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
-871
-872        for name in mc_names:
-873            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
-874
-875            fig = plt.figure()
-876            ax = fig.add_subplot(111)
-877            for dat in data:
-878                ax.plot(x0_vals, dat, ls='-', marker='')
-879
-880            if logscale is True:
-881                ax.set_yscale('log')
-882
-883            ax.set_xlabel(r'$x_0 / a$')
-884            plt.title(name)
-885            plt.draw()
+            
    879    def spaghetti_plot(self, logscale=True):
+880        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+881
+882        Parameters
+883        ----------
+884        logscale : bool
+885            Determines whether the scale of the y-axis is logarithmic or standard.
+886        """
+887        if self.N != 1:
+888            raise Exception("Correlator needs to be projected first.")
+889
+890        mc_names = list(set([item for sublist in [o[0].mc_names for o in self.content if o is not None] for item in sublist]))
+891        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+892
+893        for name in mc_names:
+894            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+895
+896            fig = plt.figure()
+897            ax = fig.add_subplot(111)
+898            for dat in data:
+899                ax.plot(x0_vals, dat, ls='-', marker='')
+900
+901            if logscale is True:
+902                ax.set_yscale('log')
+903
+904            ax.set_xlabel(r'$x_0 / a$')
+905            plt.title(name)
+906            plt.draw()
 
    
 
 
@@ -4246,29 +4330,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.
 
     
    
     
-            
    887    def dump(self, filename, datatype="json.gz", **kwargs):
-888        """Dumps the Corr into a file of chosen type
-889        Parameters
-890        ----------
-891        filename : str
-892            Name of the file to be saved.
-893        datatype : str
-894            Format of the exported file. Supported formats include
-895            "json.gz" and "pickle"
-896        path : str
-897            specifies a custom path for the file (default '.')
-898        """
-899        if datatype == "json.gz":
-900            from .input.json import dump_to_json
-901            if 'path' in kwargs:
-902                file_name = kwargs.get('path') + '/' + filename
-903            else:
-904                file_name = filename
-905            dump_to_json(self, file_name)
-906        elif datatype == "pickle":
-907            dump_object(self, filename, **kwargs)
-908        else:
-909            raise Exception("Unknown datatype " + str(datatype))
+            
    908    def dump(self, filename, datatype="json.gz", **kwargs):
+909        """Dumps the Corr into a file of chosen type
+910        Parameters
+911        ----------
+912        filename : str
+913            Name of the file to be saved.
+914        datatype : str
+915            Format of the exported file. Supported formats include
+916            "json.gz" and "pickle"
+917        path : str
+918            specifies a custom path for the file (default '.')
+919        """
+920        if datatype == "json.gz":
+921            from .input.json import dump_to_json
+922            if 'path' in kwargs:
+923                file_name = kwargs.get('path') + '/' + filename
+924            else:
+925                file_name = filename
+926            dump_to_json(self, file_name)
+927        elif datatype == "pickle":
+928            dump_object(self, filename, **kwargs)
+929        else:
+930            raise Exception("Unknown datatype " + str(datatype))
 
    
 
 
@@ -4300,8 +4384,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    911    def print(self, print_range=None):
-912        print(self.__repr__(print_range))
+            
    932    def print(self, print_range=None):
+933        print(self.__repr__(print_range))
 
    
 
 
@@ -4319,8 +4403,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1076    def sqrt(self):
-1077        return self ** 0.5
+            
    1097    def sqrt(self):
+1098        return self ** 0.5
 
    
 
 
@@ -4338,9 +4422,9 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1079    def log(self):
-1080        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1081        return Corr(newcontent, prange=self.prange)
+            
    1100    def log(self):
+1101        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1102        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4358,9 +4442,9 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1083    def exp(self):
-1084        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1085        return Corr(newcontent, prange=self.prange)
+            
    1104    def exp(self):
+1105        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1106        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4378,8 +4462,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1098    def sin(self):
-1099        return self._apply_func_to_corr(np.sin)
+            
    1119    def sin(self):
+1120        return self._apply_func_to_corr(np.sin)
 
    
 
 
@@ -4397,8 +4481,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1101    def cos(self):
-1102        return self._apply_func_to_corr(np.cos)
+            
    1122    def cos(self):
+1123        return self._apply_func_to_corr(np.cos)
 
    
 
 
@@ -4416,8 +4500,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1104    def tan(self):
-1105        return self._apply_func_to_corr(np.tan)
+            
    1125    def tan(self):
+1126        return self._apply_func_to_corr(np.tan)
 
    
 
 
@@ -4435,8 +4519,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1107    def sinh(self):
-1108        return self._apply_func_to_corr(np.sinh)
+            
    1128    def sinh(self):
+1129        return self._apply_func_to_corr(np.sinh)
 
    
 
 
@@ -4454,8 +4538,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1110    def cosh(self):
-1111        return self._apply_func_to_corr(np.cosh)
+            
    1131    def cosh(self):
+1132        return self._apply_func_to_corr(np.cosh)
 
    
 
 
@@ -4473,8 +4557,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1113    def tanh(self):
-1114        return self._apply_func_to_corr(np.tanh)
+            
    1134    def tanh(self):
+1135        return self._apply_func_to_corr(np.tanh)
 
    
 
 
@@ -4492,8 +4576,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1116    def arcsin(self):
-1117        return self._apply_func_to_corr(np.arcsin)
+            
    1137    def arcsin(self):
+1138        return self._apply_func_to_corr(np.arcsin)
 
    
 
 
@@ -4511,8 +4595,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1119    def arccos(self):
-1120        return self._apply_func_to_corr(np.arccos)
+            
    1140    def arccos(self):
+1141        return self._apply_func_to_corr(np.arccos)
 
    
 
 
@@ -4530,8 +4614,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1122    def arctan(self):
-1123        return self._apply_func_to_corr(np.arctan)
+            
    1143    def arctan(self):
+1144        return self._apply_func_to_corr(np.arctan)
 
    
 
 
@@ -4549,8 +4633,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1125    def arcsinh(self):
-1126        return self._apply_func_to_corr(np.arcsinh)
+            
    1146    def arcsinh(self):
+1147        return self._apply_func_to_corr(np.arcsinh)
 
    
 
 
@@ -4568,8 +4652,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1128    def arccosh(self):
-1129        return self._apply_func_to_corr(np.arccosh)
+            
    1149    def arccosh(self):
+1150        return self._apply_func_to_corr(np.arccosh)
 
    
 
 
@@ -4587,8 +4671,8 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1131    def arctanh(self):
-1132        return self._apply_func_to_corr(np.arctanh)
+            
    1152    def arctanh(self):
+1153        return self._apply_func_to_corr(np.arctanh)
 
    
 
 
@@ -4628,62 +4712,62 @@ specifies a custom path for the file (default '.')
 
     
    
     
-            
    1167    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1168        r''' Project large correlation matrix to lowest states
-1169
-1170        This method can be used to reduce the size of an (N x N) correlation matrix
-1171        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1172        is still small.
-1173
-1174        Parameters
-1175        ----------
-1176        Ntrunc: int
-1177            Rank of the target matrix.
-1178        tproj: int
-1179            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1180            The default value is 3.
-1181        t0proj: int
-1182            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1183            discouraged for O(a) improved theories, since the correctness of the procedure
-1184            cannot be granted in this case. The default value is 2.
-1185        basematrix : Corr
-1186            Correlation matrix that is used to determine the eigenvectors of the
-1187            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1188            is is not specified.
-1189
-1190        Notes
-1191        -----
-1192        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1193        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1194        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1195        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1196        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1197        correlation matrix and to remove some noise that is added by irrelevant operators.
-1198        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1199        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1200        '''
-1201
-1202        if self.N == 1:
-1203            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1204        if basematrix is None:
-1205            basematrix = self
-1206        if Ntrunc >= basematrix.N:
-1207            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1208        if basematrix.N != self.N:
-1209            raise Exception('basematrix and targetmatrix have to be of the same size.')
+            
    1188    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1189        r''' Project large correlation matrix to lowest states
+1190
+1191        This method can be used to reduce the size of an (N x N) correlation matrix
+1192        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1193        is still small.
+1194
+1195        Parameters
+1196        ----------
+1197        Ntrunc: int
+1198            Rank of the target matrix.
+1199        tproj: int
+1200            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1201            The default value is 3.
+1202        t0proj: int
+1203            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1204            discouraged for O(a) improved theories, since the correctness of the procedure
+1205            cannot be granted in this case. The default value is 2.
+1206        basematrix : Corr
+1207            Correlation matrix that is used to determine the eigenvectors of the
+1208            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1209            is is not specified.
 1210
-1211        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1212
-1213        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1214        rmat = []
-1215        for t in range(basematrix.T):
-1216            for i in range(Ntrunc):
-1217                for j in range(Ntrunc):
-1218                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1219            rmat.append(np.copy(tmpmat))
-1220
-1221        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1222        return Corr(newcontent)
+1211        Notes
+1212        -----
+1213        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1214        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1215        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1216        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1217        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1218        correlation matrix and to remove some noise that is added by irrelevant operators.
+1219        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1220        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1221        '''
+1222
+1223        if self.N == 1:
+1224            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1225        if basematrix is None:
+1226            basematrix = self
+1227        if Ntrunc >= basematrix.N:
+1228            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1229        if basematrix.N != self.N:
+1230            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1231
+1232        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1233
+1234        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1235        rmat = []
+1236        for t in range(basematrix.T):
+1237            for i in range(Ntrunc):
+1238                for j in range(Ntrunc):
+1239                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1240            rmat.append(np.copy(tmpmat))
+1241
+1242        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1243        return Corr(newcontent)
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index ce36a096..eea4dfa9 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
    • 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
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the 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
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    print(my_corr[3])\n> 0.3227(33)\n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    o.covobs[k].grad\n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least 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
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only 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
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue')", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n   'fit' fits a constant to the plateau region\n   'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None,\n    title=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
    \n", "signature": "(self, print_range=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. 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
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n\n
    Second mode:
    \n\n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "type": "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 /\ncycles. 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
    • 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", "type": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "type": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "type": "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", "type": "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", "type": "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", "type": "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", "type": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
    \n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
    \n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
    \n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
    \n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "type": "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", "type": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
    \n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
    \n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 7930}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 108}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 94}, "pyerrors.correlators.Corr.reweighted": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.gamma_method": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 13}, "pyerrors.correlators.Corr.projected": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 64}, "pyerrors.correlators.Corr.item": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 53}, "pyerrors.correlators.Corr.plottable": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 31}, "pyerrors.correlators.Corr.symmetric": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 9}, "pyerrors.correlators.Corr.anti_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.matrix_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.GEVP": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 9, "bases": 0, "doc": 324}, "pyerrors.correlators.Corr.Eigenvalue": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 59}, "pyerrors.correlators.Corr.Hankel": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 6, "bases": 0, "doc": 67}, "pyerrors.correlators.Corr.roll": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 26}, "pyerrors.correlators.Corr.reverse": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 9}, "pyerrors.correlators.Corr.thin": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 7, "bases": 0, "doc": 43}, "pyerrors.correlators.Corr.correlate": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 53}, "pyerrors.correlators.Corr.reweight": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 79}, "pyerrors.correlators.Corr.T_symmetry": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 6, "bases": 0, "doc": 51}, "pyerrors.correlators.Corr.deriv": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 46}, "pyerrors.correlators.Corr.second_deriv": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 44}, "pyerrors.correlators.Corr.m_eff": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 8, "bases": 0, "doc": 135}, "pyerrors.correlators.Corr.fit": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 9, "bases": 0, "doc": 110}, "pyerrors.correlators.Corr.plateau": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 92}, "pyerrors.correlators.Corr.set_prange": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 11}, "pyerrors.correlators.Corr.show": {"qualname": 2, "fullname": 4, 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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "type": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact 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
    • 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
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the 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
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    print(my_corr[3])\n> 0.3227(33)\n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    o.covobs[k].grad\n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least 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
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only 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
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "type": "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", "type": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue')", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n   'fit' fits a constant to the plateau region\n   'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None,\n    title=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
    \n", "signature": "(self, print_range=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. 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
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n\n
    Second mode:
    \n\n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "type": "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 /\ncycles. 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
    • 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", "type": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "type": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "type": "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", "type": "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", "type": "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", "type": "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", "type": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
    \n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
    \n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
    \n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
    \n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "type": "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", "type": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
    \n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
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