From fca014ed5cde862ef60149ed8de0671a46c45125 Mon Sep 17 00:00:00 2001 From: fjosw Date: Mon, 17 Jul 2023 10:50:02 +0000 Subject: [PATCH] Documentation updated --- docs/pyerrors/correlators.html | 5901 ++++++++++++++++---------------- docs/search.js | 2 +- 2 files changed, 3025 insertions(+), 2878 deletions(-) diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html index c9c25c2e..a5a75ed2 100644 --- a/docs/pyerrors/correlators.html +++ b/docs/pyerrors/correlators.html @@ -97,6 +97,9 @@
  • is_matrix_symmetric
    • +
  • + trace +
  • matrix_symmetric
    • @@ -460,7 +463,7 @@ 220 def anti_symmetric(self): 221 """Anti-symmetrize the correlator around x0=0.""" 222 if self.N != 1: - 223 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') + 223 raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.') 224 if self.T % 2 != 0: 225 raise Exception("Can not symmetrize odd T") 226 @@ -482,7 +485,7 @@ 242 def is_matrix_symmetric(self): 243 """Checks whether a correlator matrices is symmetric on every timeslice.""" 244 if self.N == 1: - 245 raise Exception("Only works for correlator matrices.") + 245 raise TypeError("Only works for correlator matrices.") 246 for t in range(self.T): 247 if self[t] is None: 248 continue @@ -494,1091 +497,1148 @@ 254 return False 255 return True 256 - 257 def matrix_symmetric(self): - 258 """Symmetrizes the correlator matrices on every timeslice.""" + 257 def trace(self): + 258 """Calculates the per-timeslice trace of a correlator matrix.""" 259 if self.N == 1: - 260 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 261 if self.is_matrix_symmetric(): - 262 return 1.0 * self - 263 else: - 264 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 265 return 0.5 * (Corr(transposed) + self) - 266 - 267 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 268 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 269 - 270 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 271 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 272 ```python - 273 C.GEVP(t0=2)[0] # Ground state vector(s) - 274 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 275 ``` - 276 - 277 Parameters - 278 ---------- - 279 t0 : int - 280 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 281 ts : int - 282 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 283 If sort="Eigenvector" it gives a reference point for the sorting method. - 284 sort : string - 285 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. - 286 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 287 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 288 The reference state is identified by its eigenvalue at $t=t_s$. - 289 - 290 Other Parameters - 291 ---------------- - 292 state : int - 293 Returns only the vector(s) for a specified state. The lowest state is zero. - 294 ''' - 295 - 296 if self.N == 1: - 297 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 298 if ts is not None: - 299 if (ts <= t0): - 300 raise Exception("ts has to be larger than t0.") + 260 raise ValueError("Only works for correlator matrices.") + 261 newcontent = [] + 262 for t in range(self.T): + 263 if _check_for_none(self, self.content[t]): + 264 newcontent.append(None) + 265 else: + 266 newcontent.append(np.trace(self.content[t])) + 267 return Corr(newcontent) + 268 + 269 def matrix_symmetric(self): + 270 """Symmetrizes the correlator matrices on every timeslice.""" + 271 if self.N == 1: + 272 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") + 273 if self.is_matrix_symmetric(): + 274 return 1.0 * self + 275 else: + 276 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] + 277 return 0.5 * (Corr(transposed) + self) + 278 + 279 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): + 280 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. + 281 + 282 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the + 283 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing + 284 ```python + 285 C.GEVP(t0=2)[0] # Ground state vector(s) + 286 C.GEVP(t0=2)[:3] # Vectors for the lowest three states + 287 ``` + 288 + 289 Parameters + 290 ---------- + 291 t0 : int + 292 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ + 293 ts : int + 294 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. + 295 If sort="Eigenvector" it gives a reference point for the sorting method. + 296 sort : string + 297 If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned. + 298 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. + 299 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. + 300 The reference state is identified by its eigenvalue at $t=t_s$. 301 - 302 if "sorted_list" in kwargs: - 303 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 304 sort = kwargs.get("sorted_list") - 305 - 306 if self.is_matrix_symmetric(): - 307 symmetric_corr = self - 308 else: - 309 symmetric_corr = self.matrix_symmetric() - 310 - 311 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) - 312 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. + 302 Other Parameters + 303 ---------------- + 304 state : int + 305 Returns only the vector(s) for a specified state. The lowest state is zero. + 306 ''' + 307 + 308 if self.N == 1: + 309 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") + 310 if ts is not None: + 311 if (ts <= t0): + 312 raise Exception("ts has to be larger than t0.") 313 - 314 if sort is None: - 315 if (ts is None): - 316 raise Exception("ts is required if sort=None.") - 317 if (self.content[t0] is None) or (self.content[ts] is None): - 318 raise Exception("Corr not defined at t0/ts.") - 319 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) - 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 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) - 329 all_vecs.append(_GEVP_solver(Gt, G0)) - 330 except Exception: - 331 all_vecs.append(None) - 332 if sort == "Eigenvector": - 333 if ts is None: - 334 raise Exception("ts is required for the Eigenvector sorting method.") - 335 all_vecs = _sort_vectors(all_vecs, ts) - 336 - 337 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 338 else: - 339 raise Exception("Unkown value for 'sort'.") - 340 - 341 if "state" in kwargs: - 342 return reordered_vecs[kwargs.get("state")] - 343 else: - 344 return reordered_vecs - 345 - 346 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 347 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 314 if "sorted_list" in kwargs: + 315 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) + 316 sort = kwargs.get("sorted_list") + 317 + 318 if self.is_matrix_symmetric(): + 319 symmetric_corr = self + 320 else: + 321 symmetric_corr = self.matrix_symmetric() + 322 + 323 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) + 324 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. + 325 + 326 if sort is None: + 327 if (ts is None): + 328 raise Exception("ts is required if sort=None.") + 329 if (self.content[t0] is None) or (self.content[ts] is None): + 330 raise Exception("Corr not defined at t0/ts.") + 331 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) + 332 reordered_vecs = _GEVP_solver(Gt, G0) + 333 + 334 elif sort in ["Eigenvalue", "Eigenvector"]: + 335 if sort == "Eigenvalue" and ts is not None: + 336 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) + 337 all_vecs = [None] * (t0 + 1) + 338 for t in range(t0 + 1, self.T): + 339 try: + 340 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) + 341 all_vecs.append(_GEVP_solver(Gt, G0)) + 342 except Exception: + 343 all_vecs.append(None) + 344 if sort == "Eigenvector": + 345 if ts is None: + 346 raise Exception("ts is required for the Eigenvector sorting method.") + 347 all_vecs = _sort_vectors(all_vecs, ts) 348 - 349 Parameters - 350 ---------- - 351 state : int - 352 The state one is interested in ordered by energy. The lowest state is zero. - 353 - 354 All other parameters are identical to the ones of Corr.GEVP. - 355 """ - 356 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 357 return self.projected(vec) - 358 - 359 def Hankel(self, N, periodic=False): - 360 """Constructs an NxN Hankel matrix - 361 - 362 C(t) c(t+1) ... c(t+n-1) - 363 C(t+1) c(t+2) ... c(t+n) - 364 ................. - 365 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) - 366 - 367 Parameters - 368 ---------- - 369 N : int - 370 Dimension of the Hankel matrix - 371 periodic : bool, optional - 372 determines whether the matrix is extended periodically - 373 """ - 374 - 375 if self.N != 1: - 376 raise Exception("Multi-operator Prony not implemented!") - 377 - 378 array = np.empty([N, N], dtype="object") - 379 new_content = [] - 380 for t in range(self.T): - 381 new_content.append(array.copy()) - 382 - 383 def wrap(i): - 384 while i >= self.T: - 385 i -= self.T - 386 return i - 387 - 388 for t in range(self.T): - 389 for i in range(N): - 390 for j in range(N): - 391 if periodic: - 392 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 393 elif (t + i + j) >= self.T: - 394 new_content[t] = None - 395 else: - 396 new_content[t][i, j] = self.content[t + i + j][0] - 397 - 398 return Corr(new_content) + 349 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] + 350 else: + 351 raise Exception("Unkown value for 'sort'.") + 352 + 353 if "state" in kwargs: + 354 return reordered_vecs[kwargs.get("state")] + 355 else: + 356 return reordered_vecs + 357 + 358 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): + 359 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 360 + 361 Parameters + 362 ---------- + 363 state : int + 364 The state one is interested in ordered by energy. The lowest state is zero. + 365 + 366 All other parameters are identical to the ones of Corr.GEVP. + 367 """ + 368 vec = self.GEVP(t0, ts=ts, sort=sort)[state] + 369 return self.projected(vec) + 370 + 371 def Hankel(self, N, periodic=False): + 372 """Constructs an NxN Hankel matrix + 373 + 374 C(t) c(t+1) ... c(t+n-1) + 375 C(t+1) c(t+2) ... c(t+n) + 376 ................. + 377 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) + 378 + 379 Parameters + 380 ---------- + 381 N : int + 382 Dimension of the Hankel matrix + 383 periodic : bool, optional + 384 determines whether the matrix is extended periodically + 385 """ + 386 + 387 if self.N != 1: + 388 raise Exception("Multi-operator Prony not implemented!") + 389 + 390 array = np.empty([N, N], dtype="object") + 391 new_content = [] + 392 for t in range(self.T): + 393 new_content.append(array.copy()) + 394 + 395 def wrap(i): + 396 while i >= self.T: + 397 i -= self.T + 398 return i 399 - 400 def roll(self, dt): - 401 """Periodically shift the correlator by dt timeslices - 402 - 403 Parameters - 404 ---------- - 405 dt : int - 406 number of timeslices - 407 """ - 408 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) + 400 for t in range(self.T): + 401 for i in range(N): + 402 for j in range(N): + 403 if periodic: + 404 new_content[t][i, j] = self.content[wrap(t + i + j)][0] + 405 elif (t + i + j) >= self.T: + 406 new_content[t] = None + 407 else: + 408 new_content[t][i, j] = self.content[t + i + j][0] 409 - 410 def reverse(self): - 411 """Reverse the time ordering of the Corr""" - 412 return Corr(self.content[:: -1]) - 413 - 414 def thin(self, spacing=2, offset=0): - 415 """Thin out a correlator to suppress correlations - 416 - 417 Parameters - 418 ---------- - 419 spacing : int - 420 Keep only every 'spacing'th entry of the correlator - 421 offset : int - 422 Offset the equal spacing - 423 """ - 424 new_content = [] - 425 for t in range(self.T): - 426 if (offset + t) % spacing != 0: - 427 new_content.append(None) - 428 else: - 429 new_content.append(self.content[t]) - 430 return Corr(new_content) - 431 - 432 def correlate(self, partner): - 433 """Correlate the correlator with another correlator or Obs - 434 - 435 Parameters - 436 ---------- - 437 partner : Obs or Corr - 438 partner to correlate the correlator with. - 439 Can either be an Obs which is correlated with all entries of the - 440 correlator or a Corr of same length. - 441 """ - 442 if self.N != 1: - 443 raise Exception("Only one-dimensional correlators can be safely correlated.") - 444 new_content = [] - 445 for x0, t_slice in enumerate(self.content): - 446 if _check_for_none(self, t_slice): - 447 new_content.append(None) - 448 else: - 449 if isinstance(partner, Corr): - 450 if _check_for_none(partner, partner.content[x0]): - 451 new_content.append(None) - 452 else: - 453 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 454 elif isinstance(partner, Obs): # Should this include CObs? - 455 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 456 else: - 457 raise Exception("Can only correlate with an Obs or a Corr.") - 458 - 459 return Corr(new_content) - 460 - 461 def reweight(self, weight, **kwargs): - 462 """Reweight the correlator. - 463 - 464 Parameters - 465 ---------- - 466 weight : Obs - 467 Reweighting factor. An Observable that has to be defined on a superset of the - 468 configurations in obs[i].idl for all i. - 469 all_configs : bool - 470 if True, the reweighted observables are normalized by the average of - 471 the reweighting factor on all configurations in weight.idl and not - 472 on the configurations in obs[i].idl. - 473 """ - 474 if self.N != 1: - 475 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 476 new_content = [] - 477 for t_slice in self.content: - 478 if _check_for_none(self, t_slice): - 479 new_content.append(None) - 480 else: - 481 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 482 return Corr(new_content) - 483 - 484 def T_symmetry(self, partner, parity=+1): - 485 """Return the time symmetry average of the correlator and its partner - 486 - 487 Parameters - 488 ---------- - 489 partner : Corr - 490 Time symmetry partner of the Corr - 491 partity : int - 492 Parity quantum number of the correlator, can be +1 or -1 - 493 """ - 494 if self.N != 1: - 495 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 496 if not isinstance(partner, Corr): - 497 raise Exception("T partner has to be a Corr object.") - 498 if parity not in [+1, -1]: - 499 raise Exception("Parity has to be +1 or -1.") - 500 T_partner = parity * partner.reverse() - 501 - 502 t_slices = [] - 503 test = (self - T_partner) - 504 test.gamma_method() - 505 for x0, t_slice in enumerate(test.content): - 506 if t_slice is not None: - 507 if not t_slice[0].is_zero_within_error(5): - 508 t_slices.append(x0) - 509 if t_slices: - 510 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) - 511 - 512 return (self + T_partner) / 2 + 410 return Corr(new_content) + 411 + 412 def roll(self, dt): + 413 """Periodically shift the correlator by dt timeslices + 414 + 415 Parameters + 416 ---------- + 417 dt : int + 418 number of timeslices + 419 """ + 420 return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0))) + 421 + 422 def reverse(self): + 423 """Reverse the time ordering of the Corr""" + 424 return Corr(self.content[:: -1]) + 425 + 426 def thin(self, spacing=2, offset=0): + 427 """Thin out a correlator to suppress correlations + 428 + 429 Parameters + 430 ---------- + 431 spacing : int + 432 Keep only every 'spacing'th entry of the correlator + 433 offset : int + 434 Offset the equal spacing + 435 """ + 436 new_content = [] + 437 for t in range(self.T): + 438 if (offset + t) % spacing != 0: + 439 new_content.append(None) + 440 else: + 441 new_content.append(self.content[t]) + 442 return Corr(new_content) + 443 + 444 def correlate(self, partner): + 445 """Correlate the correlator with another correlator or Obs + 446 + 447 Parameters + 448 ---------- + 449 partner : Obs or Corr + 450 partner to correlate the correlator with. + 451 Can either be an Obs which is correlated with all entries of the + 452 correlator or a Corr of same length. + 453 """ + 454 if self.N != 1: + 455 raise Exception("Only one-dimensional correlators can be safely correlated.") + 456 new_content = [] + 457 for x0, t_slice in enumerate(self.content): + 458 if _check_for_none(self, t_slice): + 459 new_content.append(None) + 460 else: + 461 if isinstance(partner, Corr): + 462 if _check_for_none(partner, partner.content[x0]): + 463 new_content.append(None) + 464 else: + 465 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) + 466 elif isinstance(partner, Obs): # Should this include CObs? + 467 new_content.append(np.array([correlate(o, partner) for o in t_slice])) + 468 else: + 469 raise Exception("Can only correlate with an Obs or a Corr.") + 470 + 471 return Corr(new_content) + 472 + 473 def reweight(self, weight, **kwargs): + 474 """Reweight the correlator. + 475 + 476 Parameters + 477 ---------- + 478 weight : Obs + 479 Reweighting factor. An Observable that has to be defined on a superset of the + 480 configurations in obs[i].idl for all i. + 481 all_configs : bool + 482 if True, the reweighted observables are normalized by the average of + 483 the reweighting factor on all configurations in weight.idl and not + 484 on the configurations in obs[i].idl. + 485 """ + 486 if self.N != 1: + 487 raise Exception("Reweighting only implemented for one-dimensional correlators.") + 488 new_content = [] + 489 for t_slice in self.content: + 490 if _check_for_none(self, t_slice): + 491 new_content.append(None) + 492 else: + 493 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) + 494 return Corr(new_content) + 495 + 496 def T_symmetry(self, partner, parity=+1): + 497 """Return the time symmetry average of the correlator and its partner + 498 + 499 Parameters + 500 ---------- + 501 partner : Corr + 502 Time symmetry partner of the Corr + 503 partity : int + 504 Parity quantum number of the correlator, can be +1 or -1 + 505 """ + 506 if self.N != 1: + 507 raise Exception("T_symmetry only implemented for one-dimensional correlators.") + 508 if not isinstance(partner, Corr): + 509 raise Exception("T partner has to be a Corr object.") + 510 if parity not in [+1, -1]: + 511 raise Exception("Parity has to be +1 or -1.") + 512 T_partner = parity * partner.reverse() 513 - 514 def deriv(self, variant="symmetric"): - 515 """Return the first derivative of the correlator with respect to x0. - 516 - 517 Parameters - 518 ---------- - 519 variant : str - 520 decides which definition of the finite differences derivative is used. - 521 Available choice: symmetric, forward, backward, improved, log, default: symmetric - 522 """ - 523 if self.N != 1: - 524 raise Exception("deriv only implemented for one-dimensional correlators.") - 525 if variant == "symmetric": - 526 newcontent = [] - 527 for t in range(1, self.T - 1): - 528 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 529 newcontent.append(None) - 530 else: - 531 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 532 if (all([x is None for x in newcontent])): - 533 raise Exception('Derivative is undefined at all timeslices') - 534 return Corr(newcontent, padding=[1, 1]) - 535 elif variant == "forward": - 536 newcontent = [] - 537 for t in range(self.T - 1): - 538 if (self.content[t] is None) or (self.content[t + 1] is None): - 539 newcontent.append(None) - 540 else: - 541 newcontent.append(self.content[t + 1] - self.content[t]) - 542 if (all([x is None for x in newcontent])): - 543 raise Exception("Derivative is undefined at all timeslices") - 544 return Corr(newcontent, padding=[0, 1]) - 545 elif variant == "backward": - 546 newcontent = [] - 547 for t in range(1, self.T): - 548 if (self.content[t - 1] is None) or (self.content[t] is None): - 549 newcontent.append(None) - 550 else: - 551 newcontent.append(self.content[t] - self.content[t - 1]) - 552 if (all([x is None for x in newcontent])): - 553 raise Exception("Derivative is undefined at all timeslices") - 554 return Corr(newcontent, padding=[1, 0]) - 555 elif variant == "improved": - 556 newcontent = [] - 557 for t in range(2, self.T - 2): - 558 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): - 559 newcontent.append(None) - 560 else: - 561 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 562 if (all([x is None for x in newcontent])): - 563 raise Exception('Derivative is undefined at all timeslices') - 564 return Corr(newcontent, padding=[2, 2]) - 565 elif variant == 'log': - 566 newcontent = [] - 567 for t in range(self.T): - 568 if (self.content[t] is None) or (self.content[t] <= 0): - 569 newcontent.append(None) - 570 else: - 571 newcontent.append(np.log(self.content[t])) - 572 if (all([x is None for x in newcontent])): - 573 raise Exception("Log is undefined at all timeslices") - 574 logcorr = Corr(newcontent) - 575 return self * logcorr.deriv('symmetric') - 576 else: - 577 raise Exception("Unknown variant.") - 578 - 579 def second_deriv(self, variant="symmetric"): - 580 r"""Return the second derivative of the correlator with respect to x0. - 581 - 582 Parameters - 583 ---------- - 584 variant : str - 585 decides which definition of the finite differences derivative is used. - 586 Available choice: - 587 - symmetric (default) - 588 $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$ - 589 - big_symmetric - 590 $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$ - 591 - improved - 592 $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$ - 593 - log - 594 $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$ - 595 """ - 596 if self.N != 1: - 597 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 598 if variant == "symmetric": - 599 newcontent = [] - 600 for t in range(1, self.T - 1): - 601 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 602 newcontent.append(None) - 603 else: - 604 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 605 if (all([x is None for x in newcontent])): - 606 raise Exception("Derivative is undefined at all timeslices") - 607 return Corr(newcontent, padding=[1, 1]) - 608 elif variant == "big_symmetric": - 609 newcontent = [] - 610 for t in range(2, self.T - 2): - 611 if (self.content[t - 2] is None) or (self.content[t + 2] is None): - 612 newcontent.append(None) - 613 else: - 614 newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4) - 615 if (all([x is None for x in newcontent])): - 616 raise Exception("Derivative is undefined at all timeslices") - 617 return Corr(newcontent, padding=[2, 2]) - 618 elif variant == "improved": - 619 newcontent = [] - 620 for t in range(2, self.T - 2): - 621 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): - 622 newcontent.append(None) - 623 else: - 624 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) - 625 if (all([x is None for x in newcontent])): - 626 raise Exception("Derivative is undefined at all timeslices") - 627 return Corr(newcontent, padding=[2, 2]) - 628 elif variant == 'log': - 629 newcontent = [] - 630 for t in range(self.T): - 631 if (self.content[t] is None) or (self.content[t] <= 0): - 632 newcontent.append(None) - 633 else: - 634 newcontent.append(np.log(self.content[t])) - 635 if (all([x is None for x in newcontent])): - 636 raise Exception("Log is undefined at all timeslices") - 637 logcorr = Corr(newcontent) - 638 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) - 639 else: - 640 raise Exception("Unknown variant.") - 641 - 642 def m_eff(self, variant='log', guess=1.0): - 643 """Returns the effective mass of the correlator as correlator object - 644 - 645 Parameters - 646 ---------- - 647 variant : str - 648 log : uses the standard effective mass log(C(t) / C(t+1)) - 649 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. - 650 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. - 651 See, e.g., arXiv:1205.5380 - 652 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 653 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 - 654 guess : float - 655 guess for the root finder, only relevant for the root variant - 656 """ - 657 if self.N != 1: - 658 raise Exception('Correlator must be projected before getting m_eff') - 659 if variant == 'log': - 660 newcontent = [] - 661 for t in range(self.T - 1): - 662 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 663 newcontent.append(None) - 664 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 665 newcontent.append(None) - 666 else: - 667 newcontent.append(self.content[t] / self.content[t + 1]) - 668 if (all([x is None for x in newcontent])): - 669 raise Exception('m_eff is undefined at all timeslices') - 670 - 671 return np.log(Corr(newcontent, padding=[0, 1])) - 672 - 673 elif variant == 'logsym': - 674 newcontent = [] - 675 for t in range(1, self.T - 1): - 676 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 514 t_slices = [] + 515 test = (self - T_partner) + 516 test.gamma_method() + 517 for x0, t_slice in enumerate(test.content): + 518 if t_slice is not None: + 519 if not t_slice[0].is_zero_within_error(5): + 520 t_slices.append(x0) + 521 if t_slices: + 522 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) + 523 + 524 return (self + T_partner) / 2 + 525 + 526 def deriv(self, variant="symmetric"): + 527 """Return the first derivative of the correlator with respect to x0. + 528 + 529 Parameters + 530 ---------- + 531 variant : str + 532 decides which definition of the finite differences derivative is used. + 533 Available choice: symmetric, forward, backward, improved, log, default: symmetric + 534 """ + 535 if self.N != 1: + 536 raise Exception("deriv only implemented for one-dimensional correlators.") + 537 if variant == "symmetric": + 538 newcontent = [] + 539 for t in range(1, self.T - 1): + 540 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 541 newcontent.append(None) + 542 else: + 543 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) + 544 if (all([x is None for x in newcontent])): + 545 raise Exception('Derivative is undefined at all timeslices') + 546 return Corr(newcontent, padding=[1, 1]) + 547 elif variant == "forward": + 548 newcontent = [] + 549 for t in range(self.T - 1): + 550 if (self.content[t] is None) or (self.content[t + 1] is None): + 551 newcontent.append(None) + 552 else: + 553 newcontent.append(self.content[t + 1] - self.content[t]) + 554 if (all([x is None for x in newcontent])): + 555 raise Exception("Derivative is undefined at all timeslices") + 556 return Corr(newcontent, padding=[0, 1]) + 557 elif variant == "backward": + 558 newcontent = [] + 559 for t in range(1, self.T): + 560 if (self.content[t - 1] is None) or (self.content[t] is None): + 561 newcontent.append(None) + 562 else: + 563 newcontent.append(self.content[t] - self.content[t - 1]) + 564 if (all([x is None for x in newcontent])): + 565 raise Exception("Derivative is undefined at all timeslices") + 566 return Corr(newcontent, padding=[1, 0]) + 567 elif variant == "improved": + 568 newcontent = [] + 569 for t in range(2, self.T - 2): + 570 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 571 newcontent.append(None) + 572 else: + 573 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) + 574 if (all([x is None for x in newcontent])): + 575 raise Exception('Derivative is undefined at all timeslices') + 576 return Corr(newcontent, padding=[2, 2]) + 577 elif variant == 'log': + 578 newcontent = [] + 579 for t in range(self.T): + 580 if (self.content[t] is None) or (self.content[t] <= 0): + 581 newcontent.append(None) + 582 else: + 583 newcontent.append(np.log(self.content[t])) + 584 if (all([x is None for x in newcontent])): + 585 raise Exception("Log is undefined at all timeslices") + 586 logcorr = Corr(newcontent) + 587 return self * logcorr.deriv('symmetric') + 588 else: + 589 raise Exception("Unknown variant.") + 590 + 591 def second_deriv(self, variant="symmetric"): + 592 r"""Return the second derivative of the correlator with respect to x0. + 593 + 594 Parameters + 595 ---------- + 596 variant : str + 597 decides which definition of the finite differences derivative is used. + 598 Available choice: + 599 - symmetric (default) + 600 $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$ + 601 - big_symmetric + 602 $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$ + 603 - improved + 604 $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$ + 605 - log + 606 $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$ + 607 """ + 608 if self.N != 1: + 609 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 610 if variant == "symmetric": + 611 newcontent = [] + 612 for t in range(1, self.T - 1): + 613 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 614 newcontent.append(None) + 615 else: + 616 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 617 if (all([x is None for x in newcontent])): + 618 raise Exception("Derivative is undefined at all timeslices") + 619 return Corr(newcontent, padding=[1, 1]) + 620 elif variant == "big_symmetric": + 621 newcontent = [] + 622 for t in range(2, self.T - 2): + 623 if (self.content[t - 2] is None) or (self.content[t + 2] is None): + 624 newcontent.append(None) + 625 else: + 626 newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4) + 627 if (all([x is None for x in newcontent])): + 628 raise Exception("Derivative is undefined at all timeslices") + 629 return Corr(newcontent, padding=[2, 2]) + 630 elif variant == "improved": + 631 newcontent = [] + 632 for t in range(2, self.T - 2): + 633 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 634 newcontent.append(None) + 635 else: + 636 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) + 637 if (all([x is None for x in newcontent])): + 638 raise Exception("Derivative is undefined at all timeslices") + 639 return Corr(newcontent, padding=[2, 2]) + 640 elif variant == 'log': + 641 newcontent = [] + 642 for t in range(self.T): + 643 if (self.content[t] is None) or (self.content[t] <= 0): + 644 newcontent.append(None) + 645 else: + 646 newcontent.append(np.log(self.content[t])) + 647 if (all([x is None for x in newcontent])): + 648 raise Exception("Log is undefined at all timeslices") + 649 logcorr = Corr(newcontent) + 650 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) + 651 else: + 652 raise Exception("Unknown variant.") + 653 + 654 def m_eff(self, variant='log', guess=1.0): + 655 """Returns the effective mass of the correlator as correlator object + 656 + 657 Parameters + 658 ---------- + 659 variant : str + 660 log : uses the standard effective mass log(C(t) / C(t+1)) + 661 cosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. + 662 sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m. + 663 See, e.g., arXiv:1205.5380 + 664 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 665 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 + 666 guess : float + 667 guess for the root finder, only relevant for the root variant + 668 """ + 669 if self.N != 1: + 670 raise Exception('Correlator must be projected before getting m_eff') + 671 if variant == 'log': + 672 newcontent = [] + 673 for t in range(self.T - 1): + 674 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 675 newcontent.append(None) + 676 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 677 newcontent.append(None) - 678 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: - 679 newcontent.append(None) - 680 else: - 681 newcontent.append(self.content[t - 1] / self.content[t + 1]) - 682 if (all([x is None for x in newcontent])): - 683 raise Exception('m_eff is undefined at all timeslices') + 678 else: + 679 newcontent.append(self.content[t] / self.content[t + 1]) + 680 if (all([x is None for x in newcontent])): + 681 raise Exception('m_eff is undefined at all timeslices') + 682 + 683 return np.log(Corr(newcontent, padding=[0, 1])) 684 - 685 return np.log(Corr(newcontent, padding=[1, 1])) / 2 - 686 - 687 elif variant in ['periodic', 'cosh', 'sinh']: - 688 if variant in ['periodic', 'cosh']: - 689 func = anp.cosh - 690 else: - 691 func = anp.sinh - 692 - 693 def root_function(x, d): - 694 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 695 - 696 newcontent = [] - 697 for t in range(self.T - 1): - 698 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 699 newcontent.append(None) - 700 # Fill the two timeslices in the middle of the lattice with their predecessors - 701 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 702 newcontent.append(newcontent[-1]) - 703 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 704 newcontent.append(None) - 705 else: - 706 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 707 if (all([x is None for x in newcontent])): - 708 raise Exception('m_eff is undefined at all timeslices') - 709 - 710 return Corr(newcontent, padding=[0, 1]) - 711 - 712 elif variant == 'arccosh': - 713 newcontent = [] - 714 for t in range(1, self.T - 1): - 715 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): + 685 elif variant == 'logsym': + 686 newcontent = [] + 687 for t in range(1, self.T - 1): + 688 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 689 newcontent.append(None) + 690 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: + 691 newcontent.append(None) + 692 else: + 693 newcontent.append(self.content[t - 1] / self.content[t + 1]) + 694 if (all([x is None for x in newcontent])): + 695 raise Exception('m_eff is undefined at all timeslices') + 696 + 697 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 698 + 699 elif variant in ['periodic', 'cosh', 'sinh']: + 700 if variant in ['periodic', 'cosh']: + 701 func = anp.cosh + 702 else: + 703 func = anp.sinh + 704 + 705 def root_function(x, d): + 706 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 707 + 708 newcontent = [] + 709 for t in range(self.T - 1): + 710 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 711 newcontent.append(None) + 712 # Fill the two timeslices in the middle of the lattice with their predecessors + 713 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 714 newcontent.append(newcontent[-1]) + 715 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 716 newcontent.append(None) 717 else: - 718 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 718 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) 719 if (all([x is None for x in newcontent])): - 720 raise Exception("m_eff is undefined at all timeslices") - 721 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 722 - 723 else: - 724 raise Exception('Unknown variant.') - 725 - 726 def fit(self, function, fitrange=None, silent=False, **kwargs): - 727 r'''Fits function to the data - 728 - 729 Parameters - 730 ---------- - 731 function : obj - 732 function to fit to the data. See fits.least_squares for details. - 733 fitrange : list - 734 Two element list containing the timeslices on which the fit is supposed to start and stop. - 735 Caution: This range is inclusive as opposed to standard python indexing. - 736 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 737 If not specified, self.prange or all timeslices are used. - 738 silent : bool - 739 Decides whether output is printed to the standard output. - 740 ''' - 741 if self.N != 1: - 742 raise Exception("Correlator must be projected before fitting") - 743 - 744 if fitrange is None: - 745 if self.prange: - 746 fitrange = self.prange - 747 else: - 748 fitrange = [0, self.T - 1] - 749 else: - 750 if not isinstance(fitrange, list): - 751 raise Exception("fitrange has to be a list with two elements") - 752 if len(fitrange) != 2: - 753 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 754 - 755 xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 756 ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 757 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 758 return result - 759 - 760 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 761 """ Extract a plateau value from a Corr object - 762 - 763 Parameters - 764 ---------- - 765 plateau_range : list - 766 list with two entries, indicating the first and the last timeslice - 767 of the plateau region. - 768 method : str - 769 method to extract the plateau. - 770 'fit' fits a constant to the plateau region - 771 'avg', 'average' or 'mean' just average over the given timeslices. - 772 auto_gamma : bool - 773 apply gamma_method with default parameters to the Corr. Defaults to None - 774 """ - 775 if not plateau_range: - 776 if self.prange: - 777 plateau_range = self.prange - 778 else: - 779 raise Exception("no plateau range provided") - 780 if self.N != 1: - 781 raise Exception("Correlator must be projected before getting a plateau.") - 782 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 783 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 784 if auto_gamma: - 785 self.gamma_method() - 786 if method == "fit": - 787 def const_func(a, t): - 788 return a[0] - 789 return self.fit(const_func, plateau_range)[0] - 790 elif method in ["avg", "average", "mean"]: - 791 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 792 return returnvalue - 793 - 794 else: - 795 raise Exception("Unsupported plateau method: " + method) - 796 - 797 def set_prange(self, prange): - 798 """Sets the attribute prange of the Corr object.""" - 799 if not len(prange) == 2: - 800 raise Exception("prange must be a list or array with two values") - 801 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 802 raise Exception("Start and end point must be integers") - 803 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 804 raise Exception("Start and end point must define a range in the interval 0,T") + 720 raise Exception('m_eff is undefined at all timeslices') + 721 + 722 return Corr(newcontent, padding=[0, 1]) + 723 + 724 elif variant == 'arccosh': + 725 newcontent = [] + 726 for t in range(1, self.T - 1): + 727 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): + 728 newcontent.append(None) + 729 else: + 730 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 731 if (all([x is None for x in newcontent])): + 732 raise Exception("m_eff is undefined at all timeslices") + 733 return np.arccosh(Corr(newcontent, padding=[1, 1])) + 734 + 735 else: + 736 raise Exception('Unknown variant.') + 737 + 738 def fit(self, function, fitrange=None, silent=False, **kwargs): + 739 r'''Fits function to the data + 740 + 741 Parameters + 742 ---------- + 743 function : obj + 744 function to fit to the data. See fits.least_squares for details. + 745 fitrange : list + 746 Two element list containing the timeslices on which the fit is supposed to start and stop. + 747 Caution: This range is inclusive as opposed to standard python indexing. + 748 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 749 If not specified, self.prange or all timeslices are used. + 750 silent : bool + 751 Decides whether output is printed to the standard output. + 752 ''' + 753 if self.N != 1: + 754 raise Exception("Correlator must be projected before fitting") + 755 + 756 if fitrange is None: + 757 if self.prange: + 758 fitrange = self.prange + 759 else: + 760 fitrange = [0, self.T - 1] + 761 else: + 762 if not isinstance(fitrange, list): + 763 raise Exception("fitrange has to be a list with two elements") + 764 if len(fitrange) != 2: + 765 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 766 + 767 xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) + 768 ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) + 769 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 770 return result + 771 + 772 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 773 """ Extract a plateau value from a Corr object + 774 + 775 Parameters + 776 ---------- + 777 plateau_range : list + 778 list with two entries, indicating the first and the last timeslice + 779 of the plateau region. + 780 method : str + 781 method to extract the plateau. + 782 'fit' fits a constant to the plateau region + 783 'avg', 'average' or 'mean' just average over the given timeslices. + 784 auto_gamma : bool + 785 apply gamma_method with default parameters to the Corr. Defaults to None + 786 """ + 787 if not plateau_range: + 788 if self.prange: + 789 plateau_range = self.prange + 790 else: + 791 raise Exception("no plateau range provided") + 792 if self.N != 1: + 793 raise Exception("Correlator must be projected before getting a plateau.") + 794 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 795 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 796 if auto_gamma: + 797 self.gamma_method() + 798 if method == "fit": + 799 def const_func(a, t): + 800 return a[0] + 801 return self.fit(const_func, plateau_range)[0] + 802 elif method in ["avg", "average", "mean"]: + 803 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 804 return returnvalue 805 - 806 self.prange = prange - 807 return + 806 else: + 807 raise Exception("Unsupported plateau method: " + method) 808 - 809 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): - 810 """Plots the correlator using the tag of the correlator as label if available. - 811 - 812 Parameters - 813 ---------- - 814 x_range : list - 815 list of two values, determining the range of the x-axis e.g. [4, 8]. - 816 comp : Corr or list of Corr - 817 Correlator or list of correlators which are plotted for comparison. - 818 The tags of these correlators are used as labels if available. - 819 logscale : bool - 820 Sets y-axis to logscale. - 821 plateau : Obs - 822 Plateau value to be visualized in the figure. - 823 fit_res : Fit_result - 824 Fit_result object to be visualized. - 825 fit_key : str - 826 Key for the fit function in Fit_result.fit_function (for combined fits). - 827 ylabel : str - 828 Label for the y-axis. - 829 save : str - 830 path to file in which the figure should be saved. - 831 auto_gamma : bool - 832 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 833 hide_sigma : float - 834 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 835 references : list - 836 List of floating point values that are displayed as horizontal lines for reference. - 837 title : string - 838 Optional title of the figure. - 839 """ - 840 if self.N != 1: - 841 raise Exception("Correlator must be projected before plotting") - 842 - 843 if auto_gamma: - 844 self.gamma_method() - 845 - 846 if x_range is None: - 847 x_range = [0, self.T - 1] - 848 - 849 fig = plt.figure() - 850 ax1 = fig.add_subplot(111) - 851 - 852 x, y, y_err = self.plottable() - 853 if hide_sigma: - 854 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 855 else: - 856 hide_from = None - 857 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 858 if logscale: - 859 ax1.set_yscale('log') - 860 else: - 861 if y_range is None: - 862 try: - 863 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)]) - 864 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)]) - 865 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 866 except Exception: - 867 pass - 868 else: - 869 ax1.set_ylim(y_range) - 870 if comp: - 871 if isinstance(comp, (Corr, list)): - 872 for corr in comp if isinstance(comp, list) else [comp]: - 873 if auto_gamma: - 874 corr.gamma_method() - 875 x, y, y_err = corr.plottable() - 876 if hide_sigma: - 877 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 878 else: - 879 hide_from = None - 880 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 881 else: - 882 raise Exception("'comp' must be a correlator or a list of correlators.") - 883 - 884 if plateau: - 885 if isinstance(plateau, Obs): - 886 if auto_gamma: - 887 plateau.gamma_method() - 888 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 889 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 890 else: - 891 raise Exception("'plateau' must be an Obs") - 892 - 893 if references: - 894 if isinstance(references, list): - 895 for ref in references: - 896 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 897 else: - 898 raise Exception("'references' must be a list of floating pint values.") - 899 - 900 if self.prange: - 901 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0) - 902 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0) - 903 - 904 if fit_res: - 905 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 906 if isinstance(fit_res.fit_function, dict): - 907 if fit_key: - 908 ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) - 909 else: - 910 raise ValueError("Please provide a 'fit_key' for visualizing combined fits.") - 911 else: - 912 ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) - 913 - 914 ax1.set_xlabel(r'$x_0 / a$') - 915 if ylabel: - 916 ax1.set_ylabel(ylabel) - 917 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 918 - 919 handles, labels = ax1.get_legend_handles_labels() - 920 if labels: - 921 ax1.legend() - 922 - 923 if title: - 924 plt.title(title) + 809 def set_prange(self, prange): + 810 """Sets the attribute prange of the Corr object.""" + 811 if not len(prange) == 2: + 812 raise Exception("prange must be a list or array with two values") + 813 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 814 raise Exception("Start and end point must be integers") + 815 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 816 raise Exception("Start and end point must define a range in the interval 0,T") + 817 + 818 self.prange = prange + 819 return + 820 + 821 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): + 822 """Plots the correlator using the tag of the correlator as label if available. + 823 + 824 Parameters + 825 ---------- + 826 x_range : list + 827 list of two values, determining the range of the x-axis e.g. [4, 8]. + 828 comp : Corr or list of Corr + 829 Correlator or list of correlators which are plotted for comparison. + 830 The tags of these correlators are used as labels if available. + 831 logscale : bool + 832 Sets y-axis to logscale. + 833 plateau : Obs + 834 Plateau value to be visualized in the figure. + 835 fit_res : Fit_result + 836 Fit_result object to be visualized. + 837 fit_key : str + 838 Key for the fit function in Fit_result.fit_function (for combined fits). + 839 ylabel : str + 840 Label for the y-axis. + 841 save : str + 842 path to file in which the figure should be saved. + 843 auto_gamma : bool + 844 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 845 hide_sigma : float + 846 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 847 references : list + 848 List of floating point values that are displayed as horizontal lines for reference. + 849 title : string + 850 Optional title of the figure. + 851 """ + 852 if self.N != 1: + 853 raise Exception("Correlator must be projected before plotting") + 854 + 855 if auto_gamma: + 856 self.gamma_method() + 857 + 858 if x_range is None: + 859 x_range = [0, self.T - 1] + 860 + 861 fig = plt.figure() + 862 ax1 = fig.add_subplot(111) + 863 + 864 x, y, y_err = self.plottable() + 865 if hide_sigma: + 866 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 867 else: + 868 hide_from = None + 869 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 870 if logscale: + 871 ax1.set_yscale('log') + 872 else: + 873 if y_range is None: + 874 try: + 875 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 876 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 877 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 878 except Exception: + 879 pass + 880 else: + 881 ax1.set_ylim(y_range) + 882 if comp: + 883 if isinstance(comp, (Corr, list)): + 884 for corr in comp if isinstance(comp, list) else [comp]: + 885 if auto_gamma: + 886 corr.gamma_method() + 887 x, y, y_err = corr.plottable() + 888 if hide_sigma: + 889 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 890 else: + 891 hide_from = None + 892 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 893 else: + 894 raise Exception("'comp' must be a correlator or a list of correlators.") + 895 + 896 if plateau: + 897 if isinstance(plateau, Obs): + 898 if auto_gamma: + 899 plateau.gamma_method() + 900 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 901 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 902 else: + 903 raise Exception("'plateau' must be an Obs") + 904 + 905 if references: + 906 if isinstance(references, list): + 907 for ref in references: + 908 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 909 else: + 910 raise Exception("'references' must be a list of floating pint values.") + 911 + 912 if self.prange: + 913 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0) + 914 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0) + 915 + 916 if fit_res: + 917 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 918 if isinstance(fit_res.fit_function, dict): + 919 if fit_key: + 920 ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) + 921 else: + 922 raise ValueError("Please provide a 'fit_key' for visualizing combined fits.") + 923 else: + 924 ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) 925 - 926 plt.draw() - 927 - 928 if save: - 929 if isinstance(save, str): - 930 fig.savefig(save, bbox_inches='tight') - 931 else: - 932 raise Exception("'save' has to be a string.") - 933 - 934 def spaghetti_plot(self, logscale=True): - 935 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 936 - 937 Parameters - 938 ---------- - 939 logscale : bool - 940 Determines whether the scale of the y-axis is logarithmic or standard. - 941 """ - 942 if self.N != 1: - 943 raise Exception("Correlator needs to be projected first.") - 944 - 945 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) - 946 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 947 - 948 for name in mc_names: - 949 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T - 950 - 951 fig = plt.figure() - 952 ax = fig.add_subplot(111) - 953 for dat in data: - 954 ax.plot(x0_vals, dat, ls='-', marker='') - 955 - 956 if logscale is True: - 957 ax.set_yscale('log') - 958 - 959 ax.set_xlabel(r'$x_0 / a$') - 960 plt.title(name) - 961 plt.draw() + 926 ax1.set_xlabel(r'$x_0 / a$') + 927 if ylabel: + 928 ax1.set_ylabel(ylabel) + 929 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 930 + 931 handles, labels = ax1.get_legend_handles_labels() + 932 if labels: + 933 ax1.legend() + 934 + 935 if title: + 936 plt.title(title) + 937 + 938 plt.draw() + 939 + 940 if save: + 941 if isinstance(save, str): + 942 fig.savefig(save, bbox_inches='tight') + 943 else: + 944 raise Exception("'save' has to be a string.") + 945 + 946 def spaghetti_plot(self, logscale=True): + 947 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 948 + 949 Parameters + 950 ---------- + 951 logscale : bool + 952 Determines whether the scale of the y-axis is logarithmic or standard. + 953 """ + 954 if self.N != 1: + 955 raise Exception("Correlator needs to be projected first.") + 956 + 957 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) + 958 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 959 + 960 for name in mc_names: + 961 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T 962 - 963 def dump(self, filename, datatype="json.gz", **kwargs): - 964 """Dumps the Corr into a file of chosen type - 965 Parameters - 966 ---------- - 967 filename : str - 968 Name of the file to be saved. - 969 datatype : str - 970 Format of the exported file. Supported formats include - 971 "json.gz" and "pickle" - 972 path : str - 973 specifies a custom path for the file (default '.') - 974 """ - 975 if datatype == "json.gz": - 976 from .input.json import dump_to_json - 977 if 'path' in kwargs: - 978 file_name = kwargs.get('path') + '/' + filename - 979 else: - 980 file_name = filename - 981 dump_to_json(self, file_name) - 982 elif datatype == "pickle": - 983 dump_object(self, filename, **kwargs) - 984 else: - 985 raise Exception("Unknown datatype " + str(datatype)) - 986 - 987 def print(self, print_range=None): - 988 print(self.__repr__(print_range)) - 989 - 990 def __repr__(self, print_range=None): - 991 if print_range is None: - 992 print_range = [0, None] - 993 - 994 content_string = "" - 995 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 - 996 - 997 if self.tag is not None: - 998 content_string += "Description: " + self.tag + "\n" - 999 if self.N != 1: -1000 return content_string + 963 fig = plt.figure() + 964 ax = fig.add_subplot(111) + 965 for dat in data: + 966 ax.plot(x0_vals, dat, ls='-', marker='') + 967 + 968 if logscale is True: + 969 ax.set_yscale('log') + 970 + 971 ax.set_xlabel(r'$x_0 / a$') + 972 plt.title(name) + 973 plt.draw() + 974 + 975 def dump(self, filename, datatype="json.gz", **kwargs): + 976 """Dumps the Corr into a file of chosen type + 977 Parameters + 978 ---------- + 979 filename : str + 980 Name of the file to be saved. + 981 datatype : str + 982 Format of the exported file. Supported formats include + 983 "json.gz" and "pickle" + 984 path : str + 985 specifies a custom path for the file (default '.') + 986 """ + 987 if datatype == "json.gz": + 988 from .input.json import dump_to_json + 989 if 'path' in kwargs: + 990 file_name = kwargs.get('path') + '/' + filename + 991 else: + 992 file_name = filename + 993 dump_to_json(self, file_name) + 994 elif datatype == "pickle": + 995 dump_object(self, filename, **kwargs) + 996 else: + 997 raise Exception("Unknown datatype " + str(datatype)) + 998 + 999 def print(self, print_range=None): +1000 print(self.__repr__(print_range)) 1001 -1002 if print_range[1]: -1003 print_range[1] += 1 -1004 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' -1005 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): -1006 if sub_corr is None: -1007 content_string += str(i + print_range[0]) + '\n' -1008 else: -1009 content_string += str(i + print_range[0]) -1010 for element in sub_corr: -1011 content_string += f"\t{element:+2}" -1012 content_string += '\n' -1013 return content_string -1014 -1015 def __str__(self): -1016 return self.__repr__() -1017 -1018 # We define the basic operations, that can be performed with correlators. -1019 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. -1020 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. -1021 # One could try and tell Obs to check if the y in __mul__ is a Corr and -1022 -1023 def __add__(self, y): -1024 if isinstance(y, Corr): -1025 if ((self.N != y.N) or (self.T != y.T)): -1026 raise Exception("Addition of Corrs with different shape") -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 return Corr(newcontent) +1002 def __repr__(self, print_range=None): +1003 if print_range is None: +1004 print_range = [0, None] +1005 +1006 content_string = "" +1007 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here +1008 +1009 if self.tag is not None: +1010 content_string += "Description: " + self.tag + "\n" +1011 if self.N != 1: +1012 return content_string +1013 +1014 if print_range[1]: +1015 print_range[1] += 1 +1016 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' +1017 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): +1018 if sub_corr is None: +1019 content_string += str(i + print_range[0]) + '\n' +1020 else: +1021 content_string += str(i + print_range[0]) +1022 for element in sub_corr: +1023 content_string += f"\t{element:+2}" +1024 content_string += '\n' +1025 return content_string +1026 +1027 def __str__(self): +1028 return self.__repr__() +1029 +1030 # We define the basic operations, that can be performed with correlators. +1031 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. +1032 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. +1033 # One could try and tell Obs to check if the y in __mul__ is a Corr and 1034 -1035 elif isinstance(y, (Obs, int, float, CObs)): -1036 newcontent = [] -1037 for t in range(self.T): -1038 if _check_for_none(self, self.content[t]): -1039 newcontent.append(None) -1040 else: -1041 newcontent.append(self.content[t] + y) -1042 return Corr(newcontent, prange=self.prange) -1043 elif isinstance(y, np.ndarray): -1044 if y.shape == (self.T,): -1045 return Corr(list((np.array(self.content).T + y).T)) -1046 else: -1047 raise ValueError("operands could not be broadcast together") -1048 else: -1049 raise TypeError("Corr + wrong type") -1050 -1051 def __mul__(self, y): -1052 if isinstance(y, Corr): -1053 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1054 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1055 newcontent = [] -1056 for t in range(self.T): -1057 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1058 newcontent.append(None) -1059 else: -1060 newcontent.append(self.content[t] * y.content[t]) -1061 return Corr(newcontent) -1062 -1063 elif isinstance(y, (Obs, int, float, CObs)): -1064 newcontent = [] -1065 for t in range(self.T): -1066 if _check_for_none(self, self.content[t]): -1067 newcontent.append(None) -1068 else: -1069 newcontent.append(self.content[t] * y) -1070 return Corr(newcontent, prange=self.prange) -1071 elif isinstance(y, np.ndarray): -1072 if y.shape == (self.T,): -1073 return Corr(list((np.array(self.content).T * y).T)) -1074 else: -1075 raise ValueError("operands could not be broadcast together") -1076 else: -1077 raise TypeError("Corr * wrong type") -1078 -1079 def __truediv__(self, y): -1080 if isinstance(y, Corr): -1081 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1082 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1083 newcontent = [] -1084 for t in range(self.T): -1085 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1086 newcontent.append(None) -1087 else: -1088 newcontent.append(self.content[t] / y.content[t]) -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 -1095 if all([item is None for item in newcontent]): -1096 raise Exception("Division returns completely undefined correlator") -1097 return Corr(newcontent) -1098 -1099 elif isinstance(y, (Obs, CObs)): -1100 if isinstance(y, Obs): -1101 if y.value == 0: -1102 raise Exception('Division by zero will return undefined correlator') -1103 if isinstance(y, CObs): -1104 if y.is_zero(): -1105 raise Exception('Division by zero will return undefined correlator') -1106 -1107 newcontent = [] -1108 for t in range(self.T): -1109 if _check_for_none(self, self.content[t]): -1110 newcontent.append(None) -1111 else: -1112 newcontent.append(self.content[t] / y) -1113 return Corr(newcontent, prange=self.prange) -1114 -1115 elif isinstance(y, (int, float)): -1116 if y == 0: -1117 raise Exception('Division by zero will return undefined correlator') -1118 newcontent = [] -1119 for t in range(self.T): -1120 if _check_for_none(self, self.content[t]): -1121 newcontent.append(None) -1122 else: -1123 newcontent.append(self.content[t] / y) -1124 return Corr(newcontent, prange=self.prange) -1125 elif isinstance(y, np.ndarray): -1126 if y.shape == (self.T,): -1127 return Corr(list((np.array(self.content).T / y).T)) -1128 else: -1129 raise ValueError("operands could not be broadcast together") -1130 else: -1131 raise TypeError('Corr / wrong type') -1132 -1133 def __neg__(self): -1134 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1135 return Corr(newcontent, prange=self.prange) -1136 -1137 def __sub__(self, y): -1138 return self + (-y) -1139 -1140 def __pow__(self, y): -1141 if isinstance(y, (Obs, int, float, CObs)): -1142 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1143 return Corr(newcontent, prange=self.prange) -1144 else: -1145 raise TypeError('Type of exponent not supported') -1146 -1147 def __abs__(self): -1148 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1149 return Corr(newcontent, prange=self.prange) -1150 -1151 # The numpy functions: -1152 def sqrt(self): -1153 return self ** 0.5 -1154 -1155 def log(self): -1156 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1157 return Corr(newcontent, prange=self.prange) -1158 -1159 def exp(self): -1160 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1161 return Corr(newcontent, prange=self.prange) -1162 -1163 def _apply_func_to_corr(self, func): -1164 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1165 for t in range(self.T): -1166 if _check_for_none(self, newcontent[t]): -1167 continue -1168 tmp_sum = np.sum(newcontent[t]) -1169 if hasattr(tmp_sum, "value"): -1170 if np.isnan(tmp_sum.value): -1171 newcontent[t] = None -1172 if all([item is None for item in newcontent]): -1173 raise Exception('Operation returns undefined correlator') -1174 return Corr(newcontent) -1175 -1176 def sin(self): -1177 return self._apply_func_to_corr(np.sin) -1178 -1179 def cos(self): -1180 return self._apply_func_to_corr(np.cos) -1181 -1182 def tan(self): -1183 return self._apply_func_to_corr(np.tan) -1184 -1185 def sinh(self): -1186 return self._apply_func_to_corr(np.sinh) -1187 -1188 def cosh(self): -1189 return self._apply_func_to_corr(np.cosh) -1190 -1191 def tanh(self): -1192 return self._apply_func_to_corr(np.tanh) +1035 __array_priority__ = 10000 +1036 +1037 def __add__(self, y): +1038 if isinstance(y, Corr): +1039 if ((self.N != y.N) or (self.T != y.T)): +1040 raise Exception("Addition of Corrs with different shape") +1041 newcontent = [] +1042 for t in range(self.T): +1043 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1044 newcontent.append(None) +1045 else: +1046 newcontent.append(self.content[t] + y.content[t]) +1047 return Corr(newcontent) +1048 +1049 elif isinstance(y, (Obs, int, float, CObs)): +1050 newcontent = [] +1051 for t in range(self.T): +1052 if _check_for_none(self, self.content[t]): +1053 newcontent.append(None) +1054 else: +1055 newcontent.append(self.content[t] + y) +1056 return Corr(newcontent, prange=self.prange) +1057 elif isinstance(y, np.ndarray): +1058 if y.shape == (self.T,): +1059 return Corr(list((np.array(self.content).T + y).T)) +1060 else: +1061 raise ValueError("operands could not be broadcast together") +1062 else: +1063 raise TypeError("Corr + wrong type") +1064 +1065 def __mul__(self, y): +1066 if isinstance(y, Corr): +1067 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1068 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1069 newcontent = [] +1070 for t in range(self.T): +1071 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1072 newcontent.append(None) +1073 else: +1074 newcontent.append(self.content[t] * y.content[t]) +1075 return Corr(newcontent) +1076 +1077 elif isinstance(y, (Obs, int, float, CObs)): +1078 newcontent = [] +1079 for t in range(self.T): +1080 if _check_for_none(self, self.content[t]): +1081 newcontent.append(None) +1082 else: +1083 newcontent.append(self.content[t] * y) +1084 return Corr(newcontent, prange=self.prange) +1085 elif isinstance(y, np.ndarray): +1086 if y.shape == (self.T,): +1087 return Corr(list((np.array(self.content).T * y).T)) +1088 else: +1089 raise ValueError("operands could not be broadcast together") +1090 else: +1091 raise TypeError("Corr * wrong type") +1092 +1093 def __matmul__(self, y): +1094 if isinstance(y, np.ndarray): +1095 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1096 raise ValueError("Can only multiply correlators by square matrices.") +1097 if not self.N == y.shape[0]: +1098 raise ValueError("matmul: mismatch of matrix dimensions") +1099 newcontent = [] +1100 for t in range(self.T): +1101 if _check_for_none(self, self.content[t]): +1102 newcontent.append(None) +1103 else: +1104 newcontent.append(self.content[t] @ y) +1105 return Corr(newcontent) +1106 elif isinstance(y, Corr): +1107 if not self.N == y.N: +1108 raise ValueError("matmul: mismatch of matrix dimensions") +1109 newcontent = [] +1110 for t in range(self.T): +1111 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1112 newcontent.append(None) +1113 else: +1114 newcontent.append(self.content[t] @ y.content[t]) +1115 return Corr(newcontent) +1116 +1117 else: +1118 return NotImplemented +1119 +1120 def __rmatmul__(self, y): +1121 if isinstance(y, np.ndarray): +1122 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1123 raise ValueError("Can only multiply correlators by square matrices.") +1124 if not self.N == y.shape[0]: +1125 raise ValueError("matmul: mismatch of matrix dimensions") +1126 newcontent = [] +1127 for t in range(self.T): +1128 if _check_for_none(self, self.content[t]): +1129 newcontent.append(None) +1130 else: +1131 newcontent.append(y @ self.content[t]) +1132 return Corr(newcontent) +1133 else: +1134 return NotImplemented +1135 +1136 def __truediv__(self, y): +1137 if isinstance(y, Corr): +1138 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1139 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1140 newcontent = [] +1141 for t in range(self.T): +1142 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1143 newcontent.append(None) +1144 else: +1145 newcontent.append(self.content[t] / y.content[t]) +1146 for t in range(self.T): +1147 if _check_for_none(self, newcontent[t]): +1148 continue +1149 if np.isnan(np.sum(newcontent[t]).value): +1150 newcontent[t] = None +1151 +1152 if all([item is None for item in newcontent]): +1153 raise Exception("Division returns completely undefined correlator") +1154 return Corr(newcontent) +1155 +1156 elif isinstance(y, (Obs, CObs)): +1157 if isinstance(y, Obs): +1158 if y.value == 0: +1159 raise Exception('Division by zero will return undefined correlator') +1160 if isinstance(y, CObs): +1161 if y.is_zero(): +1162 raise Exception('Division by zero will return undefined correlator') +1163 +1164 newcontent = [] +1165 for t in range(self.T): +1166 if _check_for_none(self, self.content[t]): +1167 newcontent.append(None) +1168 else: +1169 newcontent.append(self.content[t] / y) +1170 return Corr(newcontent, prange=self.prange) +1171 +1172 elif isinstance(y, (int, float)): +1173 if y == 0: +1174 raise Exception('Division by zero will return undefined correlator') +1175 newcontent = [] +1176 for t in range(self.T): +1177 if _check_for_none(self, self.content[t]): +1178 newcontent.append(None) +1179 else: +1180 newcontent.append(self.content[t] / y) +1181 return Corr(newcontent, prange=self.prange) +1182 elif isinstance(y, np.ndarray): +1183 if y.shape == (self.T,): +1184 return Corr(list((np.array(self.content).T / y).T)) +1185 else: +1186 raise ValueError("operands could not be broadcast together") +1187 else: +1188 raise TypeError('Corr / wrong type') +1189 +1190 def __neg__(self): +1191 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1192 return Corr(newcontent, prange=self.prange) 1193 -1194 def arcsin(self): -1195 return self._apply_func_to_corr(np.arcsin) +1194 def __sub__(self, y): +1195 return self + (-y) 1196 -1197 def arccos(self): -1198 return self._apply_func_to_corr(np.arccos) -1199 -1200 def arctan(self): -1201 return self._apply_func_to_corr(np.arctan) -1202 -1203 def arcsinh(self): -1204 return self._apply_func_to_corr(np.arcsinh) -1205 -1206 def arccosh(self): -1207 return self._apply_func_to_corr(np.arccosh) -1208 -1209 def arctanh(self): -1210 return self._apply_func_to_corr(np.arctanh) +1197 def __pow__(self, y): +1198 if isinstance(y, (Obs, int, float, CObs)): +1199 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1200 return Corr(newcontent, prange=self.prange) +1201 else: +1202 raise TypeError('Type of exponent not supported') +1203 +1204 def __abs__(self): +1205 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1206 return Corr(newcontent, prange=self.prange) +1207 +1208 # The numpy functions: +1209 def sqrt(self): +1210 return self ** 0.5 1211 -1212 # Right hand side operations (require tweak in main module to work) -1213 def __radd__(self, y): -1214 return self + y +1212 def log(self): +1213 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1214 return Corr(newcontent, prange=self.prange) 1215 -1216 def __rsub__(self, y): -1217 return -self + y -1218 -1219 def __rmul__(self, y): -1220 return self * y -1221 -1222 def __rtruediv__(self, y): -1223 return (self / y) ** (-1) -1224 -1225 @property -1226 def real(self): -1227 def return_real(obs_OR_cobs): -1228 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1229 return np.vectorize(lambda x: x.real)(obs_OR_cobs) -1230 else: -1231 return obs_OR_cobs +1216 def exp(self): +1217 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1218 return Corr(newcontent, prange=self.prange) +1219 +1220 def _apply_func_to_corr(self, func): +1221 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1222 for t in range(self.T): +1223 if _check_for_none(self, newcontent[t]): +1224 continue +1225 tmp_sum = np.sum(newcontent[t]) +1226 if hasattr(tmp_sum, "value"): +1227 if np.isnan(tmp_sum.value): +1228 newcontent[t] = None +1229 if all([item is None for item in newcontent]): +1230 raise Exception('Operation returns undefined correlator') +1231 return Corr(newcontent) 1232 -1233 return self._apply_func_to_corr(return_real) -1234 -1235 @property -1236 def imag(self): -1237 def return_imag(obs_OR_cobs): -1238 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1239 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) -1240 else: -1241 return obs_OR_cobs * 0 # So it stays the right type -1242 -1243 return self._apply_func_to_corr(return_imag) +1233 def sin(self): +1234 return self._apply_func_to_corr(np.sin) +1235 +1236 def cos(self): +1237 return self._apply_func_to_corr(np.cos) +1238 +1239 def tan(self): +1240 return self._apply_func_to_corr(np.tan) +1241 +1242 def sinh(self): +1243 return self._apply_func_to_corr(np.sinh) 1244 -1245 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1246 r''' Project large correlation matrix to lowest states +1245 def cosh(self): +1246 return self._apply_func_to_corr(np.cosh) 1247 -1248 This method can be used to reduce the size of an (N x N) correlation matrix -1249 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1250 is still small. -1251 -1252 Parameters -1253 ---------- -1254 Ntrunc: int -1255 Rank of the target matrix. -1256 tproj: int -1257 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1258 The default value is 3. -1259 t0proj: int -1260 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1261 discouraged for O(a) improved theories, since the correctness of the procedure -1262 cannot be granted in this case. The default value is 2. -1263 basematrix : Corr -1264 Correlation matrix that is used to determine the eigenvectors of the -1265 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1266 is is not specified. -1267 -1268 Notes -1269 ----- -1270 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1271 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1272 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1273 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1274 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1275 correlation matrix and to remove some noise that is added by irrelevant operators. -1276 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1277 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1278 ''' -1279 -1280 if self.N == 1: -1281 raise Exception('Method cannot be applied to one-dimensional correlators.') -1282 if basematrix is None: -1283 basematrix = self -1284 if Ntrunc >= basematrix.N: -1285 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1286 if basematrix.N != self.N: -1287 raise Exception('basematrix and targetmatrix have to be of the same size.') -1288 -1289 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1290 -1291 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1292 rmat = [] -1293 for t in range(basematrix.T): -1294 for i in range(Ntrunc): -1295 for j in range(Ntrunc): -1296 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1297 rmat.append(np.copy(tmpmat)) -1298 -1299 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1300 return Corr(newcontent) +1248 def tanh(self): +1249 return self._apply_func_to_corr(np.tanh) +1250 +1251 def arcsin(self): +1252 return self._apply_func_to_corr(np.arcsin) +1253 +1254 def arccos(self): +1255 return self._apply_func_to_corr(np.arccos) +1256 +1257 def arctan(self): +1258 return self._apply_func_to_corr(np.arctan) +1259 +1260 def arcsinh(self): +1261 return self._apply_func_to_corr(np.arcsinh) +1262 +1263 def arccosh(self): +1264 return self._apply_func_to_corr(np.arccosh) +1265 +1266 def arctanh(self): +1267 return self._apply_func_to_corr(np.arctanh) +1268 +1269 # Right hand side operations (require tweak in main module to work) +1270 def __radd__(self, y): +1271 return self + y +1272 +1273 def __rsub__(self, y): +1274 return -self + y +1275 +1276 def __rmul__(self, y): +1277 return self * y +1278 +1279 def __rtruediv__(self, y): +1280 return (self / y) ** (-1) +1281 +1282 @property +1283 def real(self): +1284 def return_real(obs_OR_cobs): +1285 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1286 return np.vectorize(lambda x: x.real)(obs_OR_cobs) +1287 else: +1288 return obs_OR_cobs +1289 +1290 return self._apply_func_to_corr(return_real) +1291 +1292 @property +1293 def imag(self): +1294 def return_imag(obs_OR_cobs): +1295 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1296 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) +1297 else: +1298 return obs_OR_cobs * 0 # So it stays the right type +1299 +1300 return self._apply_func_to_corr(return_imag) 1301 -1302 -1303def _sort_vectors(vec_set, ts): -1304 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" -1305 reference_sorting = np.array(vec_set[ts]) -1306 N = reference_sorting.shape[0] -1307 sorted_vec_set = [] -1308 for t in range(len(vec_set)): -1309 if vec_set[t] is None: -1310 sorted_vec_set.append(None) -1311 elif not t == ts: -1312 perms = [list(o) for o in permutations([i for i in range(N)], N)] -1313 best_score = 0 -1314 for perm in perms: -1315 current_score = 1 -1316 for k in range(N): -1317 new_sorting = reference_sorting.copy() -1318 new_sorting[perm[k], :] = vec_set[t][k] -1319 current_score *= abs(np.linalg.det(new_sorting)) -1320 if current_score > best_score: -1321 best_score = current_score -1322 best_perm = perm -1323 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) -1324 else: -1325 sorted_vec_set.append(vec_set[t]) -1326 -1327 return sorted_vec_set -1328 -1329 -1330def _check_for_none(corr, entry): -1331 """Checks if entry for correlator corr is None""" -1332 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 -1333 -1334 -1335def _GEVP_solver(Gt, G0): -1336 """Helper function for solving the GEVP and sorting the eigenvectors. -1337 -1338 The helper function assumes that both provided matrices are symmetric and -1339 only processes the lower triangular part of both matrices. In case the matrices -1340 are not symmetric the upper triangular parts are effectively discarded.""" -1341 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] +1302 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1303 r''' Project large correlation matrix to lowest states +1304 +1305 This method can be used to reduce the size of an (N x N) correlation matrix +1306 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1307 is still small. +1308 +1309 Parameters +1310 ---------- +1311 Ntrunc: int +1312 Rank of the target matrix. +1313 tproj: int +1314 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1315 The default value is 3. +1316 t0proj: int +1317 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1318 discouraged for O(a) improved theories, since the correctness of the procedure +1319 cannot be granted in this case. The default value is 2. +1320 basematrix : Corr +1321 Correlation matrix that is used to determine the eigenvectors of the +1322 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1323 is is not specified. +1324 +1325 Notes +1326 ----- +1327 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1328 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1329 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1330 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1331 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1332 correlation matrix and to remove some noise that is added by irrelevant operators. +1333 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1334 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1335 ''' +1336 +1337 if self.N == 1: +1338 raise Exception('Method cannot be applied to one-dimensional correlators.') +1339 if basematrix is None: +1340 basematrix = self +1341 if Ntrunc >= basematrix.N: +1342 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1343 if basematrix.N != self.N: +1344 raise Exception('basematrix and targetmatrix have to be of the same size.') +1345 +1346 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1347 +1348 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1349 rmat = [] +1350 for t in range(basematrix.T): +1351 for i in range(Ntrunc): +1352 for j in range(Ntrunc): +1353 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1354 rmat.append(np.copy(tmpmat)) +1355 +1356 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1357 return Corr(newcontent) +1358 +1359 +1360def _sort_vectors(vec_set, ts): +1361 """Helper function used to find a set of Eigenvectors consistent over all timeslices""" +1362 reference_sorting = np.array(vec_set[ts]) +1363 N = reference_sorting.shape[0] +1364 sorted_vec_set = [] +1365 for t in range(len(vec_set)): +1366 if vec_set[t] is None: +1367 sorted_vec_set.append(None) +1368 elif not t == ts: +1369 perms = [list(o) for o in permutations([i for i in range(N)], N)] +1370 best_score = 0 +1371 for perm in perms: +1372 current_score = 1 +1373 for k in range(N): +1374 new_sorting = reference_sorting.copy() +1375 new_sorting[perm[k], :] = vec_set[t][k] +1376 current_score *= abs(np.linalg.det(new_sorting)) +1377 if current_score > best_score: +1378 best_score = current_score +1379 best_perm = perm +1380 sorted_vec_set.append([vec_set[t][k] for k in best_perm]) +1381 else: +1382 sorted_vec_set.append(vec_set[t]) +1383 +1384 return sorted_vec_set +1385 +1386 +1387def _check_for_none(corr, entry): +1388 """Checks if entry for correlator corr is None""" +1389 return len(list(filter(None, np.asarray(entry).flatten()))) < corr.N ** 2 +1390 +1391 +1392def _GEVP_solver(Gt, G0): +1393 """Helper function for solving the GEVP and sorting the eigenvectors. +1394 +1395 The helper function assumes that both provided matrices are symmetric and +1396 only processes the lower triangular part of both matrices. In case the matrices +1397 are not symmetric the upper triangular parts are effectively discarded.""" +1398 return scipy.linalg.eigh(Gt, G0, lower=True)[1].T[::-1] @@ -1804,7 +1864,7 @@ 221 def anti_symmetric(self): 222 """Anti-symmetrize the correlator around x0=0.""" 223 if self.N != 1: - 224 raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.') + 224 raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.') 225 if self.T % 2 != 0: 226 raise Exception("Can not symmetrize odd T") 227 @@ -1826,7 +1886,7 @@ 243 def is_matrix_symmetric(self): 244 """Checks whether a correlator matrices is symmetric on every timeslice.""" 245 if self.N == 1: - 246 raise Exception("Only works for correlator matrices.") + 246 raise TypeError("Only works for correlator matrices.") 247 for t in range(self.T): 248 if self[t] is None: 249 continue @@ -1838,1050 +1898,1107 @@ 255 return False 256 return True 257 - 258 def matrix_symmetric(self): - 259 """Symmetrizes the correlator matrices on every timeslice.""" + 258 def trace(self): + 259 """Calculates the per-timeslice trace of a correlator matrix.""" 260 if self.N == 1: - 261 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") - 262 if self.is_matrix_symmetric(): - 263 return 1.0 * self - 264 else: - 265 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] - 266 return 0.5 * (Corr(transposed) + self) - 267 - 268 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): - 269 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. - 270 - 271 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the - 272 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing - 273 ```python - 274 C.GEVP(t0=2)[0] # Ground state vector(s) - 275 C.GEVP(t0=2)[:3] # Vectors for the lowest three states - 276 ``` - 277 - 278 Parameters - 279 ---------- - 280 t0 : int - 281 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ - 282 ts : int - 283 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. - 284 If sort="Eigenvector" it gives a reference point for the sorting method. - 285 sort : string - 286 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. - 287 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. - 288 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. - 289 The reference state is identified by its eigenvalue at $t=t_s$. - 290 - 291 Other Parameters - 292 ---------------- - 293 state : int - 294 Returns only the vector(s) for a specified state. The lowest state is zero. - 295 ''' - 296 - 297 if self.N == 1: - 298 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") - 299 if ts is not None: - 300 if (ts <= t0): - 301 raise Exception("ts has to be larger than t0.") + 261 raise ValueError("Only works for correlator matrices.") + 262 newcontent = [] + 263 for t in range(self.T): + 264 if _check_for_none(self, self.content[t]): + 265 newcontent.append(None) + 266 else: + 267 newcontent.append(np.trace(self.content[t])) + 268 return Corr(newcontent) + 269 + 270 def matrix_symmetric(self): + 271 """Symmetrizes the correlator matrices on every timeslice.""" + 272 if self.N == 1: + 273 raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.") + 274 if self.is_matrix_symmetric(): + 275 return 1.0 * self + 276 else: + 277 transposed = [None if _check_for_none(self, G) else G.T for G in self.content] + 278 return 0.5 * (Corr(transposed) + self) + 279 + 280 def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs): + 281 r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors. + 282 + 283 The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the + 284 largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing + 285 ```python + 286 C.GEVP(t0=2)[0] # Ground state vector(s) + 287 C.GEVP(t0=2)[:3] # Vectors for the lowest three states + 288 ``` + 289 + 290 Parameters + 291 ---------- + 292 t0 : int + 293 The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$ + 294 ts : int + 295 fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None. + 296 If sort="Eigenvector" it gives a reference point for the sorting method. + 297 sort : string + 298 If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned. + 299 - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. + 300 - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state. + 301 The reference state is identified by its eigenvalue at $t=t_s$. 302 - 303 if "sorted_list" in kwargs: - 304 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) - 305 sort = kwargs.get("sorted_list") - 306 - 307 if self.is_matrix_symmetric(): - 308 symmetric_corr = self - 309 else: - 310 symmetric_corr = self.matrix_symmetric() - 311 - 312 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) - 313 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. + 303 Other Parameters + 304 ---------------- + 305 state : int + 306 Returns only the vector(s) for a specified state. The lowest state is zero. + 307 ''' + 308 + 309 if self.N == 1: + 310 raise Exception("GEVP methods only works on correlator matrices and not single correlators.") + 311 if ts is not None: + 312 if (ts <= t0): + 313 raise Exception("ts has to be larger than t0.") 314 - 315 if sort is None: - 316 if (ts is None): - 317 raise Exception("ts is required if sort=None.") - 318 if (self.content[t0] is None) or (self.content[ts] is None): - 319 raise Exception("Corr not defined at t0/ts.") - 320 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) - 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 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) - 330 all_vecs.append(_GEVP_solver(Gt, G0)) - 331 except Exception: - 332 all_vecs.append(None) - 333 if sort == "Eigenvector": - 334 if ts is None: - 335 raise Exception("ts is required for the Eigenvector sorting method.") - 336 all_vecs = _sort_vectors(all_vecs, ts) - 337 - 338 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] - 339 else: - 340 raise Exception("Unkown value for 'sort'.") - 341 - 342 if "state" in kwargs: - 343 return reordered_vecs[kwargs.get("state")] - 344 else: - 345 return reordered_vecs - 346 - 347 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): - 348 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 315 if "sorted_list" in kwargs: + 316 warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning) + 317 sort = kwargs.get("sorted_list") + 318 + 319 if self.is_matrix_symmetric(): + 320 symmetric_corr = self + 321 else: + 322 symmetric_corr = self.matrix_symmetric() + 323 + 324 G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0]) + 325 np.linalg.cholesky(G0) # Check if matrix G0 is positive-semidefinite. + 326 + 327 if sort is None: + 328 if (ts is None): + 329 raise Exception("ts is required if sort=None.") + 330 if (self.content[t0] is None) or (self.content[ts] is None): + 331 raise Exception("Corr not defined at t0/ts.") + 332 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts]) + 333 reordered_vecs = _GEVP_solver(Gt, G0) + 334 + 335 elif sort in ["Eigenvalue", "Eigenvector"]: + 336 if sort == "Eigenvalue" and ts is not None: + 337 warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning) + 338 all_vecs = [None] * (t0 + 1) + 339 for t in range(t0 + 1, self.T): + 340 try: + 341 Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t]) + 342 all_vecs.append(_GEVP_solver(Gt, G0)) + 343 except Exception: + 344 all_vecs.append(None) + 345 if sort == "Eigenvector": + 346 if ts is None: + 347 raise Exception("ts is required for the Eigenvector sorting method.") + 348 all_vecs = _sort_vectors(all_vecs, ts) 349 - 350 Parameters - 351 ---------- - 352 state : int - 353 The state one is interested in ordered by energy. The lowest state is zero. - 354 - 355 All other parameters are identical to the ones of Corr.GEVP. - 356 """ - 357 vec = self.GEVP(t0, ts=ts, sort=sort)[state] - 358 return self.projected(vec) - 359 - 360 def Hankel(self, N, periodic=False): - 361 """Constructs an NxN Hankel matrix - 362 - 363 C(t) c(t+1) ... c(t+n-1) - 364 C(t+1) c(t+2) ... c(t+n) - 365 ................. - 366 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) - 367 - 368 Parameters - 369 ---------- - 370 N : int - 371 Dimension of the Hankel matrix - 372 periodic : bool, optional - 373 determines whether the matrix is extended periodically - 374 """ - 375 - 376 if self.N != 1: - 377 raise Exception("Multi-operator Prony not implemented!") - 378 - 379 array = np.empty([N, N], dtype="object") - 380 new_content = [] - 381 for t in range(self.T): - 382 new_content.append(array.copy()) - 383 - 384 def wrap(i): - 385 while i >= self.T: - 386 i -= self.T - 387 return i - 388 - 389 for t in range(self.T): - 390 for i in range(N): - 391 for j in range(N): - 392 if periodic: - 393 new_content[t][i, j] = self.content[wrap(t + i + j)][0] - 394 elif (t + i + j) >= self.T: - 395 new_content[t] = None - 396 else: - 397 new_content[t][i, j] = self.content[t + i + j][0] - 398 - 399 return Corr(new_content) + 350 reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)] + 351 else: + 352 raise Exception("Unkown value for 'sort'.") + 353 + 354 if "state" in kwargs: + 355 return reordered_vecs[kwargs.get("state")] + 356 else: + 357 return reordered_vecs + 358 + 359 def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"): + 360 """Determines the eigenvalue of the GEVP by solving and projecting the correlator + 361 + 362 Parameters + 363 ---------- + 364 state : int + 365 The state one is interested in ordered by energy. The lowest state is zero. + 366 + 367 All other parameters are identical to the ones of Corr.GEVP. + 368 """ + 369 vec = self.GEVP(t0, ts=ts, sort=sort)[state] + 370 return self.projected(vec) + 371 + 372 def Hankel(self, N, periodic=False): + 373 """Constructs an NxN Hankel matrix + 374 + 375 C(t) c(t+1) ... c(t+n-1) + 376 C(t+1) c(t+2) ... c(t+n) + 377 ................. + 378 C(t+(n-1)) c(t+n) ... c(t+2(n-1)) + 379 + 380 Parameters + 381 ---------- + 382 N : int + 383 Dimension of the Hankel matrix + 384 periodic : bool, optional + 385 determines whether the matrix is extended periodically + 386 """ + 387 + 388 if self.N != 1: + 389 raise Exception("Multi-operator Prony not implemented!") + 390 + 391 array = np.empty([N, N], dtype="object") + 392 new_content = [] + 393 for t in range(self.T): + 394 new_content.append(array.copy()) + 395 + 396 def wrap(i): + 397 while i >= self.T: + 398 i -= self.T + 399 return i 400 - 401 def roll(self, dt): - 402 """Periodically shift the correlator by dt timeslices - 403 - 404 Parameters - 405 ---------- - 406 dt : int - 407 number of timeslices - 408 """ - 409 return Corr(list(np.roll(np.array(self.content, dtype=object), dt))) + 401 for t in range(self.T): + 402 for i in range(N): + 403 for j in range(N): + 404 if periodic: + 405 new_content[t][i, j] = self.content[wrap(t + i + j)][0] + 406 elif (t + i + j) >= self.T: + 407 new_content[t] = None + 408 else: + 409 new_content[t][i, j] = self.content[t + i + j][0] 410 - 411 def reverse(self): - 412 """Reverse the time ordering of the Corr""" - 413 return Corr(self.content[:: -1]) - 414 - 415 def thin(self, spacing=2, offset=0): - 416 """Thin out a correlator to suppress correlations - 417 - 418 Parameters - 419 ---------- - 420 spacing : int - 421 Keep only every 'spacing'th entry of the correlator - 422 offset : int - 423 Offset the equal spacing - 424 """ - 425 new_content = [] - 426 for t in range(self.T): - 427 if (offset + t) % spacing != 0: - 428 new_content.append(None) - 429 else: - 430 new_content.append(self.content[t]) - 431 return Corr(new_content) - 432 - 433 def correlate(self, partner): - 434 """Correlate the correlator with another correlator or Obs - 435 - 436 Parameters - 437 ---------- - 438 partner : Obs or Corr - 439 partner to correlate the correlator with. - 440 Can either be an Obs which is correlated with all entries of the - 441 correlator or a Corr of same length. - 442 """ - 443 if self.N != 1: - 444 raise Exception("Only one-dimensional correlators can be safely correlated.") - 445 new_content = [] - 446 for x0, t_slice in enumerate(self.content): - 447 if _check_for_none(self, t_slice): - 448 new_content.append(None) - 449 else: - 450 if isinstance(partner, Corr): - 451 if _check_for_none(partner, partner.content[x0]): - 452 new_content.append(None) - 453 else: - 454 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) - 455 elif isinstance(partner, Obs): # Should this include CObs? - 456 new_content.append(np.array([correlate(o, partner) for o in t_slice])) - 457 else: - 458 raise Exception("Can only correlate with an Obs or a Corr.") - 459 - 460 return Corr(new_content) - 461 - 462 def reweight(self, weight, **kwargs): - 463 """Reweight the correlator. - 464 - 465 Parameters - 466 ---------- - 467 weight : Obs - 468 Reweighting factor. An Observable that has to be defined on a superset of the - 469 configurations in obs[i].idl for all i. - 470 all_configs : bool - 471 if True, the reweighted observables are normalized by the average of - 472 the reweighting factor on all configurations in weight.idl and not - 473 on the configurations in obs[i].idl. - 474 """ - 475 if self.N != 1: - 476 raise Exception("Reweighting only implemented for one-dimensional correlators.") - 477 new_content = [] - 478 for t_slice in self.content: - 479 if _check_for_none(self, t_slice): - 480 new_content.append(None) - 481 else: - 482 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) - 483 return Corr(new_content) - 484 - 485 def T_symmetry(self, partner, parity=+1): - 486 """Return the time symmetry average of the correlator and its partner - 487 - 488 Parameters - 489 ---------- - 490 partner : Corr - 491 Time symmetry partner of the Corr - 492 partity : int - 493 Parity quantum number of the correlator, can be +1 or -1 - 494 """ - 495 if self.N != 1: - 496 raise Exception("T_symmetry only implemented for one-dimensional correlators.") - 497 if not isinstance(partner, Corr): - 498 raise Exception("T partner has to be a Corr object.") - 499 if parity not in [+1, -1]: - 500 raise Exception("Parity has to be +1 or -1.") - 501 T_partner = parity * partner.reverse() - 502 - 503 t_slices = [] - 504 test = (self - T_partner) - 505 test.gamma_method() - 506 for x0, t_slice in enumerate(test.content): - 507 if t_slice is not None: - 508 if not t_slice[0].is_zero_within_error(5): - 509 t_slices.append(x0) - 510 if t_slices: - 511 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) - 512 - 513 return (self + T_partner) / 2 + 411 return Corr(new_content) + 412 + 413 def roll(self, dt): + 414 """Periodically shift the correlator by dt timeslices + 415 + 416 Parameters + 417 ---------- + 418 dt : int + 419 number of timeslices + 420 """ + 421 return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0))) + 422 + 423 def reverse(self): + 424 """Reverse the time ordering of the Corr""" + 425 return Corr(self.content[:: -1]) + 426 + 427 def thin(self, spacing=2, offset=0): + 428 """Thin out a correlator to suppress correlations + 429 + 430 Parameters + 431 ---------- + 432 spacing : int + 433 Keep only every 'spacing'th entry of the correlator + 434 offset : int + 435 Offset the equal spacing + 436 """ + 437 new_content = [] + 438 for t in range(self.T): + 439 if (offset + t) % spacing != 0: + 440 new_content.append(None) + 441 else: + 442 new_content.append(self.content[t]) + 443 return Corr(new_content) + 444 + 445 def correlate(self, partner): + 446 """Correlate the correlator with another correlator or Obs + 447 + 448 Parameters + 449 ---------- + 450 partner : Obs or Corr + 451 partner to correlate the correlator with. + 452 Can either be an Obs which is correlated with all entries of the + 453 correlator or a Corr of same length. + 454 """ + 455 if self.N != 1: + 456 raise Exception("Only one-dimensional correlators can be safely correlated.") + 457 new_content = [] + 458 for x0, t_slice in enumerate(self.content): + 459 if _check_for_none(self, t_slice): + 460 new_content.append(None) + 461 else: + 462 if isinstance(partner, Corr): + 463 if _check_for_none(partner, partner.content[x0]): + 464 new_content.append(None) + 465 else: + 466 new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice])) + 467 elif isinstance(partner, Obs): # Should this include CObs? + 468 new_content.append(np.array([correlate(o, partner) for o in t_slice])) + 469 else: + 470 raise Exception("Can only correlate with an Obs or a Corr.") + 471 + 472 return Corr(new_content) + 473 + 474 def reweight(self, weight, **kwargs): + 475 """Reweight the correlator. + 476 + 477 Parameters + 478 ---------- + 479 weight : Obs + 480 Reweighting factor. An Observable that has to be defined on a superset of the + 481 configurations in obs[i].idl for all i. + 482 all_configs : bool + 483 if True, the reweighted observables are normalized by the average of + 484 the reweighting factor on all configurations in weight.idl and not + 485 on the configurations in obs[i].idl. + 486 """ + 487 if self.N != 1: + 488 raise Exception("Reweighting only implemented for one-dimensional correlators.") + 489 new_content = [] + 490 for t_slice in self.content: + 491 if _check_for_none(self, t_slice): + 492 new_content.append(None) + 493 else: + 494 new_content.append(np.array(reweight(weight, t_slice, **kwargs))) + 495 return Corr(new_content) + 496 + 497 def T_symmetry(self, partner, parity=+1): + 498 """Return the time symmetry average of the correlator and its partner + 499 + 500 Parameters + 501 ---------- + 502 partner : Corr + 503 Time symmetry partner of the Corr + 504 partity : int + 505 Parity quantum number of the correlator, can be +1 or -1 + 506 """ + 507 if self.N != 1: + 508 raise Exception("T_symmetry only implemented for one-dimensional correlators.") + 509 if not isinstance(partner, Corr): + 510 raise Exception("T partner has to be a Corr object.") + 511 if parity not in [+1, -1]: + 512 raise Exception("Parity has to be +1 or -1.") + 513 T_partner = parity * partner.reverse() 514 - 515 def deriv(self, variant="symmetric"): - 516 """Return the first derivative of the correlator with respect to x0. - 517 - 518 Parameters - 519 ---------- - 520 variant : str - 521 decides which definition of the finite differences derivative is used. - 522 Available choice: symmetric, forward, backward, improved, log, default: symmetric - 523 """ - 524 if self.N != 1: - 525 raise Exception("deriv only implemented for one-dimensional correlators.") - 526 if variant == "symmetric": - 527 newcontent = [] - 528 for t in range(1, self.T - 1): - 529 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 530 newcontent.append(None) - 531 else: - 532 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) - 533 if (all([x is None for x in newcontent])): - 534 raise Exception('Derivative is undefined at all timeslices') - 535 return Corr(newcontent, padding=[1, 1]) - 536 elif variant == "forward": - 537 newcontent = [] - 538 for t in range(self.T - 1): - 539 if (self.content[t] is None) or (self.content[t + 1] is None): - 540 newcontent.append(None) - 541 else: - 542 newcontent.append(self.content[t + 1] - self.content[t]) - 543 if (all([x is None for x in newcontent])): - 544 raise Exception("Derivative is undefined at all timeslices") - 545 return Corr(newcontent, padding=[0, 1]) - 546 elif variant == "backward": - 547 newcontent = [] - 548 for t in range(1, self.T): - 549 if (self.content[t - 1] is None) or (self.content[t] is None): - 550 newcontent.append(None) - 551 else: - 552 newcontent.append(self.content[t] - self.content[t - 1]) - 553 if (all([x is None for x in newcontent])): - 554 raise Exception("Derivative is undefined at all timeslices") - 555 return Corr(newcontent, padding=[1, 0]) - 556 elif variant == "improved": - 557 newcontent = [] - 558 for t in range(2, self.T - 2): - 559 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): - 560 newcontent.append(None) - 561 else: - 562 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) - 563 if (all([x is None for x in newcontent])): - 564 raise Exception('Derivative is undefined at all timeslices') - 565 return Corr(newcontent, padding=[2, 2]) - 566 elif variant == 'log': - 567 newcontent = [] - 568 for t in range(self.T): - 569 if (self.content[t] is None) or (self.content[t] <= 0): - 570 newcontent.append(None) - 571 else: - 572 newcontent.append(np.log(self.content[t])) - 573 if (all([x is None for x in newcontent])): - 574 raise Exception("Log is undefined at all timeslices") - 575 logcorr = Corr(newcontent) - 576 return self * logcorr.deriv('symmetric') - 577 else: - 578 raise Exception("Unknown variant.") - 579 - 580 def second_deriv(self, variant="symmetric"): - 581 r"""Return the second derivative of the correlator with respect to x0. - 582 - 583 Parameters - 584 ---------- - 585 variant : str - 586 decides which definition of the finite differences derivative is used. - 587 Available choice: - 588 - symmetric (default) - 589 $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$ - 590 - big_symmetric - 591 $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$ - 592 - improved - 593 $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$ - 594 - log - 595 $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$ - 596 """ - 597 if self.N != 1: - 598 raise Exception("second_deriv only implemented for one-dimensional correlators.") - 599 if variant == "symmetric": - 600 newcontent = [] - 601 for t in range(1, self.T - 1): - 602 if (self.content[t - 1] is None) or (self.content[t + 1] is None): - 603 newcontent.append(None) - 604 else: - 605 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) - 606 if (all([x is None for x in newcontent])): - 607 raise Exception("Derivative is undefined at all timeslices") - 608 return Corr(newcontent, padding=[1, 1]) - 609 elif variant == "big_symmetric": - 610 newcontent = [] - 611 for t in range(2, self.T - 2): - 612 if (self.content[t - 2] is None) or (self.content[t + 2] is None): - 613 newcontent.append(None) - 614 else: - 615 newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4) - 616 if (all([x is None for x in newcontent])): - 617 raise Exception("Derivative is undefined at all timeslices") - 618 return Corr(newcontent, padding=[2, 2]) - 619 elif variant == "improved": - 620 newcontent = [] - 621 for t in range(2, self.T - 2): - 622 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): - 623 newcontent.append(None) - 624 else: - 625 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])) - 626 if (all([x is None for x in newcontent])): - 627 raise Exception("Derivative is undefined at all timeslices") - 628 return Corr(newcontent, padding=[2, 2]) - 629 elif variant == 'log': - 630 newcontent = [] - 631 for t in range(self.T): - 632 if (self.content[t] is None) or (self.content[t] <= 0): - 633 newcontent.append(None) - 634 else: - 635 newcontent.append(np.log(self.content[t])) - 636 if (all([x is None for x in newcontent])): - 637 raise Exception("Log is undefined at all timeslices") - 638 logcorr = Corr(newcontent) - 639 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) - 640 else: - 641 raise Exception("Unknown variant.") - 642 - 643 def m_eff(self, variant='log', guess=1.0): - 644 """Returns the effective mass of the correlator as correlator object - 645 - 646 Parameters - 647 ---------- - 648 variant : str - 649 log : uses the standard effective mass log(C(t) / C(t+1)) - 650 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. - 651 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. - 652 See, e.g., arXiv:1205.5380 - 653 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) - 654 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 - 655 guess : float - 656 guess for the root finder, only relevant for the root variant - 657 """ - 658 if self.N != 1: - 659 raise Exception('Correlator must be projected before getting m_eff') - 660 if variant == 'log': - 661 newcontent = [] - 662 for t in range(self.T - 1): - 663 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): - 664 newcontent.append(None) - 665 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 666 newcontent.append(None) - 667 else: - 668 newcontent.append(self.content[t] / self.content[t + 1]) - 669 if (all([x is None for x in newcontent])): - 670 raise Exception('m_eff is undefined at all timeslices') - 671 - 672 return np.log(Corr(newcontent, padding=[0, 1])) - 673 - 674 elif variant == 'logsym': - 675 newcontent = [] - 676 for t in range(1, self.T - 1): - 677 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 515 t_slices = [] + 516 test = (self - T_partner) + 517 test.gamma_method() + 518 for x0, t_slice in enumerate(test.content): + 519 if t_slice is not None: + 520 if not t_slice[0].is_zero_within_error(5): + 521 t_slices.append(x0) + 522 if t_slices: + 523 warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning) + 524 + 525 return (self + T_partner) / 2 + 526 + 527 def deriv(self, variant="symmetric"): + 528 """Return the first derivative of the correlator with respect to x0. + 529 + 530 Parameters + 531 ---------- + 532 variant : str + 533 decides which definition of the finite differences derivative is used. + 534 Available choice: symmetric, forward, backward, improved, log, default: symmetric + 535 """ + 536 if self.N != 1: + 537 raise Exception("deriv only implemented for one-dimensional correlators.") + 538 if variant == "symmetric": + 539 newcontent = [] + 540 for t in range(1, self.T - 1): + 541 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 542 newcontent.append(None) + 543 else: + 544 newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1])) + 545 if (all([x is None for x in newcontent])): + 546 raise Exception('Derivative is undefined at all timeslices') + 547 return Corr(newcontent, padding=[1, 1]) + 548 elif variant == "forward": + 549 newcontent = [] + 550 for t in range(self.T - 1): + 551 if (self.content[t] is None) or (self.content[t + 1] is None): + 552 newcontent.append(None) + 553 else: + 554 newcontent.append(self.content[t + 1] - self.content[t]) + 555 if (all([x is None for x in newcontent])): + 556 raise Exception("Derivative is undefined at all timeslices") + 557 return Corr(newcontent, padding=[0, 1]) + 558 elif variant == "backward": + 559 newcontent = [] + 560 for t in range(1, self.T): + 561 if (self.content[t - 1] is None) or (self.content[t] is None): + 562 newcontent.append(None) + 563 else: + 564 newcontent.append(self.content[t] - self.content[t - 1]) + 565 if (all([x is None for x in newcontent])): + 566 raise Exception("Derivative is undefined at all timeslices") + 567 return Corr(newcontent, padding=[1, 0]) + 568 elif variant == "improved": + 569 newcontent = [] + 570 for t in range(2, self.T - 2): + 571 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 572 newcontent.append(None) + 573 else: + 574 newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2])) + 575 if (all([x is None for x in newcontent])): + 576 raise Exception('Derivative is undefined at all timeslices') + 577 return Corr(newcontent, padding=[2, 2]) + 578 elif variant == 'log': + 579 newcontent = [] + 580 for t in range(self.T): + 581 if (self.content[t] is None) or (self.content[t] <= 0): + 582 newcontent.append(None) + 583 else: + 584 newcontent.append(np.log(self.content[t])) + 585 if (all([x is None for x in newcontent])): + 586 raise Exception("Log is undefined at all timeslices") + 587 logcorr = Corr(newcontent) + 588 return self * logcorr.deriv('symmetric') + 589 else: + 590 raise Exception("Unknown variant.") + 591 + 592 def second_deriv(self, variant="symmetric"): + 593 r"""Return the second derivative of the correlator with respect to x0. + 594 + 595 Parameters + 596 ---------- + 597 variant : str + 598 decides which definition of the finite differences derivative is used. + 599 Available choice: + 600 - symmetric (default) + 601 $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$ + 602 - big_symmetric + 603 $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$ + 604 - improved + 605 $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$ + 606 - log + 607 $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$ + 608 """ + 609 if self.N != 1: + 610 raise Exception("second_deriv only implemented for one-dimensional correlators.") + 611 if variant == "symmetric": + 612 newcontent = [] + 613 for t in range(1, self.T - 1): + 614 if (self.content[t - 1] is None) or (self.content[t + 1] is None): + 615 newcontent.append(None) + 616 else: + 617 newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1])) + 618 if (all([x is None for x in newcontent])): + 619 raise Exception("Derivative is undefined at all timeslices") + 620 return Corr(newcontent, padding=[1, 1]) + 621 elif variant == "big_symmetric": + 622 newcontent = [] + 623 for t in range(2, self.T - 2): + 624 if (self.content[t - 2] is None) or (self.content[t + 2] is None): + 625 newcontent.append(None) + 626 else: + 627 newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4) + 628 if (all([x is None for x in newcontent])): + 629 raise Exception("Derivative is undefined at all timeslices") + 630 return Corr(newcontent, padding=[2, 2]) + 631 elif variant == "improved": + 632 newcontent = [] + 633 for t in range(2, self.T - 2): + 634 if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None): + 635 newcontent.append(None) + 636 else: + 637 newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2])) + 638 if (all([x is None for x in newcontent])): + 639 raise Exception("Derivative is undefined at all timeslices") + 640 return Corr(newcontent, padding=[2, 2]) + 641 elif variant == 'log': + 642 newcontent = [] + 643 for t in range(self.T): + 644 if (self.content[t] is None) or (self.content[t] <= 0): + 645 newcontent.append(None) + 646 else: + 647 newcontent.append(np.log(self.content[t])) + 648 if (all([x is None for x in newcontent])): + 649 raise Exception("Log is undefined at all timeslices") + 650 logcorr = Corr(newcontent) + 651 return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2) + 652 else: + 653 raise Exception("Unknown variant.") + 654 + 655 def m_eff(self, variant='log', guess=1.0): + 656 """Returns the effective mass of the correlator as correlator object + 657 + 658 Parameters + 659 ---------- + 660 variant : str + 661 log : uses the standard effective mass log(C(t) / C(t+1)) + 662 cosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m. + 663 sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m. + 664 See, e.g., arXiv:1205.5380 + 665 arccosh : Uses the explicit form of the symmetrized correlator (not recommended) + 666 logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2 + 667 guess : float + 668 guess for the root finder, only relevant for the root variant + 669 """ + 670 if self.N != 1: + 671 raise Exception('Correlator must be projected before getting m_eff') + 672 if variant == 'log': + 673 newcontent = [] + 674 for t in range(self.T - 1): + 675 if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 676 newcontent.append(None) + 677 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 678 newcontent.append(None) - 679 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: - 680 newcontent.append(None) - 681 else: - 682 newcontent.append(self.content[t - 1] / self.content[t + 1]) - 683 if (all([x is None for x in newcontent])): - 684 raise Exception('m_eff is undefined at all timeslices') + 679 else: + 680 newcontent.append(self.content[t] / self.content[t + 1]) + 681 if (all([x is None for x in newcontent])): + 682 raise Exception('m_eff is undefined at all timeslices') + 683 + 684 return np.log(Corr(newcontent, padding=[0, 1])) 685 - 686 return np.log(Corr(newcontent, padding=[1, 1])) / 2 - 687 - 688 elif variant in ['periodic', 'cosh', 'sinh']: - 689 if variant in ['periodic', 'cosh']: - 690 func = anp.cosh - 691 else: - 692 func = anp.sinh - 693 - 694 def root_function(x, d): - 695 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d - 696 - 697 newcontent = [] - 698 for t in range(self.T - 1): - 699 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): - 700 newcontent.append(None) - 701 # Fill the two timeslices in the middle of the lattice with their predecessors - 702 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: - 703 newcontent.append(newcontent[-1]) - 704 elif self.content[t][0].value / self.content[t + 1][0].value < 0: - 705 newcontent.append(None) - 706 else: - 707 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) - 708 if (all([x is None for x in newcontent])): - 709 raise Exception('m_eff is undefined at all timeslices') - 710 - 711 return Corr(newcontent, padding=[0, 1]) - 712 - 713 elif variant == 'arccosh': - 714 newcontent = [] - 715 for t in range(1, self.T - 1): - 716 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): + 686 elif variant == 'logsym': + 687 newcontent = [] + 688 for t in range(1, self.T - 1): + 689 if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0): + 690 newcontent.append(None) + 691 elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0: + 692 newcontent.append(None) + 693 else: + 694 newcontent.append(self.content[t - 1] / self.content[t + 1]) + 695 if (all([x is None for x in newcontent])): + 696 raise Exception('m_eff is undefined at all timeslices') + 697 + 698 return np.log(Corr(newcontent, padding=[1, 1])) / 2 + 699 + 700 elif variant in ['periodic', 'cosh', 'sinh']: + 701 if variant in ['periodic', 'cosh']: + 702 func = anp.cosh + 703 else: + 704 func = anp.sinh + 705 + 706 def root_function(x, d): + 707 return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d + 708 + 709 newcontent = [] + 710 for t in range(self.T - 1): + 711 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0): + 712 newcontent.append(None) + 713 # Fill the two timeslices in the middle of the lattice with their predecessors + 714 elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]: + 715 newcontent.append(newcontent[-1]) + 716 elif self.content[t][0].value / self.content[t + 1][0].value < 0: 717 newcontent.append(None) 718 else: - 719 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 719 newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess))) 720 if (all([x is None for x in newcontent])): - 721 raise Exception("m_eff is undefined at all timeslices") - 722 return np.arccosh(Corr(newcontent, padding=[1, 1])) - 723 - 724 else: - 725 raise Exception('Unknown variant.') - 726 - 727 def fit(self, function, fitrange=None, silent=False, **kwargs): - 728 r'''Fits function to the data - 729 - 730 Parameters - 731 ---------- - 732 function : obj - 733 function to fit to the data. See fits.least_squares for details. - 734 fitrange : list - 735 Two element list containing the timeslices on which the fit is supposed to start and stop. - 736 Caution: This range is inclusive as opposed to standard python indexing. - 737 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. - 738 If not specified, self.prange or all timeslices are used. - 739 silent : bool - 740 Decides whether output is printed to the standard output. - 741 ''' - 742 if self.N != 1: - 743 raise Exception("Correlator must be projected before fitting") - 744 - 745 if fitrange is None: - 746 if self.prange: - 747 fitrange = self.prange - 748 else: - 749 fitrange = [0, self.T - 1] - 750 else: - 751 if not isinstance(fitrange, list): - 752 raise Exception("fitrange has to be a list with two elements") - 753 if len(fitrange) != 2: - 754 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") - 755 - 756 xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 757 ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) - 758 result = least_squares(xs, ys, function, silent=silent, **kwargs) - 759 return result - 760 - 761 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): - 762 """ Extract a plateau value from a Corr object - 763 - 764 Parameters - 765 ---------- - 766 plateau_range : list - 767 list with two entries, indicating the first and the last timeslice - 768 of the plateau region. - 769 method : str - 770 method to extract the plateau. - 771 'fit' fits a constant to the plateau region - 772 'avg', 'average' or 'mean' just average over the given timeslices. - 773 auto_gamma : bool - 774 apply gamma_method with default parameters to the Corr. Defaults to None - 775 """ - 776 if not plateau_range: - 777 if self.prange: - 778 plateau_range = self.prange - 779 else: - 780 raise Exception("no plateau range provided") - 781 if self.N != 1: - 782 raise Exception("Correlator must be projected before getting a plateau.") - 783 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): - 784 raise Exception("plateau is undefined at all timeslices in plateaurange.") - 785 if auto_gamma: - 786 self.gamma_method() - 787 if method == "fit": - 788 def const_func(a, t): - 789 return a[0] - 790 return self.fit(const_func, plateau_range)[0] - 791 elif method in ["avg", "average", "mean"]: - 792 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) - 793 return returnvalue - 794 - 795 else: - 796 raise Exception("Unsupported plateau method: " + method) - 797 - 798 def set_prange(self, prange): - 799 """Sets the attribute prange of the Corr object.""" - 800 if not len(prange) == 2: - 801 raise Exception("prange must be a list or array with two values") - 802 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): - 803 raise Exception("Start and end point must be integers") - 804 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): - 805 raise Exception("Start and end point must define a range in the interval 0,T") + 721 raise Exception('m_eff is undefined at all timeslices') + 722 + 723 return Corr(newcontent, padding=[0, 1]) + 724 + 725 elif variant == 'arccosh': + 726 newcontent = [] + 727 for t in range(1, self.T - 1): + 728 if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0): + 729 newcontent.append(None) + 730 else: + 731 newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t])) + 732 if (all([x is None for x in newcontent])): + 733 raise Exception("m_eff is undefined at all timeslices") + 734 return np.arccosh(Corr(newcontent, padding=[1, 1])) + 735 + 736 else: + 737 raise Exception('Unknown variant.') + 738 + 739 def fit(self, function, fitrange=None, silent=False, **kwargs): + 740 r'''Fits function to the data + 741 + 742 Parameters + 743 ---------- + 744 function : obj + 745 function to fit to the data. See fits.least_squares for details. + 746 fitrange : list + 747 Two element list containing the timeslices on which the fit is supposed to start and stop. + 748 Caution: This range is inclusive as opposed to standard python indexing. + 749 `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6. + 750 If not specified, self.prange or all timeslices are used. + 751 silent : bool + 752 Decides whether output is printed to the standard output. + 753 ''' + 754 if self.N != 1: + 755 raise Exception("Correlator must be projected before fitting") + 756 + 757 if fitrange is None: + 758 if self.prange: + 759 fitrange = self.prange + 760 else: + 761 fitrange = [0, self.T - 1] + 762 else: + 763 if not isinstance(fitrange, list): + 764 raise Exception("fitrange has to be a list with two elements") + 765 if len(fitrange) != 2: + 766 raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]") + 767 + 768 xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) + 769 ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None]) + 770 result = least_squares(xs, ys, function, silent=silent, **kwargs) + 771 return result + 772 + 773 def plateau(self, plateau_range=None, method="fit", auto_gamma=False): + 774 """ Extract a plateau value from a Corr object + 775 + 776 Parameters + 777 ---------- + 778 plateau_range : list + 779 list with two entries, indicating the first and the last timeslice + 780 of the plateau region. + 781 method : str + 782 method to extract the plateau. + 783 'fit' fits a constant to the plateau region + 784 'avg', 'average' or 'mean' just average over the given timeslices. + 785 auto_gamma : bool + 786 apply gamma_method with default parameters to the Corr. Defaults to None + 787 """ + 788 if not plateau_range: + 789 if self.prange: + 790 plateau_range = self.prange + 791 else: + 792 raise Exception("no plateau range provided") + 793 if self.N != 1: + 794 raise Exception("Correlator must be projected before getting a plateau.") + 795 if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])): + 796 raise Exception("plateau is undefined at all timeslices in plateaurange.") + 797 if auto_gamma: + 798 self.gamma_method() + 799 if method == "fit": + 800 def const_func(a, t): + 801 return a[0] + 802 return self.fit(const_func, plateau_range)[0] + 803 elif method in ["avg", "average", "mean"]: + 804 returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None]) + 805 return returnvalue 806 - 807 self.prange = prange - 808 return + 807 else: + 808 raise Exception("Unsupported plateau method: " + method) 809 - 810 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): - 811 """Plots the correlator using the tag of the correlator as label if available. - 812 - 813 Parameters - 814 ---------- - 815 x_range : list - 816 list of two values, determining the range of the x-axis e.g. [4, 8]. - 817 comp : Corr or list of Corr - 818 Correlator or list of correlators which are plotted for comparison. - 819 The tags of these correlators are used as labels if available. - 820 logscale : bool - 821 Sets y-axis to logscale. - 822 plateau : Obs - 823 Plateau value to be visualized in the figure. - 824 fit_res : Fit_result - 825 Fit_result object to be visualized. - 826 fit_key : str - 827 Key for the fit function in Fit_result.fit_function (for combined fits). - 828 ylabel : str - 829 Label for the y-axis. - 830 save : str - 831 path to file in which the figure should be saved. - 832 auto_gamma : bool - 833 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. - 834 hide_sigma : float - 835 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. - 836 references : list - 837 List of floating point values that are displayed as horizontal lines for reference. - 838 title : string - 839 Optional title of the figure. - 840 """ - 841 if self.N != 1: - 842 raise Exception("Correlator must be projected before plotting") - 843 - 844 if auto_gamma: - 845 self.gamma_method() - 846 - 847 if x_range is None: - 848 x_range = [0, self.T - 1] - 849 - 850 fig = plt.figure() - 851 ax1 = fig.add_subplot(111) - 852 - 853 x, y, y_err = self.plottable() - 854 if hide_sigma: - 855 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 856 else: - 857 hide_from = None - 858 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) - 859 if logscale: - 860 ax1.set_yscale('log') - 861 else: - 862 if y_range is None: - 863 try: - 864 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)]) - 865 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)]) - 866 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) - 867 except Exception: - 868 pass - 869 else: - 870 ax1.set_ylim(y_range) - 871 if comp: - 872 if isinstance(comp, (Corr, list)): - 873 for corr in comp if isinstance(comp, list) else [comp]: - 874 if auto_gamma: - 875 corr.gamma_method() - 876 x, y, y_err = corr.plottable() - 877 if hide_sigma: - 878 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 - 879 else: - 880 hide_from = None - 881 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) - 882 else: - 883 raise Exception("'comp' must be a correlator or a list of correlators.") - 884 - 885 if plateau: - 886 if isinstance(plateau, Obs): - 887 if auto_gamma: - 888 plateau.gamma_method() - 889 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) - 890 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') - 891 else: - 892 raise Exception("'plateau' must be an Obs") - 893 - 894 if references: - 895 if isinstance(references, list): - 896 for ref in references: - 897 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') - 898 else: - 899 raise Exception("'references' must be a list of floating pint values.") - 900 - 901 if self.prange: - 902 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0) - 903 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0) - 904 - 905 if fit_res: - 906 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) - 907 if isinstance(fit_res.fit_function, dict): - 908 if fit_key: - 909 ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) - 910 else: - 911 raise ValueError("Please provide a 'fit_key' for visualizing combined fits.") - 912 else: - 913 ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) - 914 - 915 ax1.set_xlabel(r'$x_0 / a$') - 916 if ylabel: - 917 ax1.set_ylabel(ylabel) - 918 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) - 919 - 920 handles, labels = ax1.get_legend_handles_labels() - 921 if labels: - 922 ax1.legend() - 923 - 924 if title: - 925 plt.title(title) + 810 def set_prange(self, prange): + 811 """Sets the attribute prange of the Corr object.""" + 812 if not len(prange) == 2: + 813 raise Exception("prange must be a list or array with two values") + 814 if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))): + 815 raise Exception("Start and end point must be integers") + 816 if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]): + 817 raise Exception("Start and end point must define a range in the interval 0,T") + 818 + 819 self.prange = prange + 820 return + 821 + 822 def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None): + 823 """Plots the correlator using the tag of the correlator as label if available. + 824 + 825 Parameters + 826 ---------- + 827 x_range : list + 828 list of two values, determining the range of the x-axis e.g. [4, 8]. + 829 comp : Corr or list of Corr + 830 Correlator or list of correlators which are plotted for comparison. + 831 The tags of these correlators are used as labels if available. + 832 logscale : bool + 833 Sets y-axis to logscale. + 834 plateau : Obs + 835 Plateau value to be visualized in the figure. + 836 fit_res : Fit_result + 837 Fit_result object to be visualized. + 838 fit_key : str + 839 Key for the fit function in Fit_result.fit_function (for combined fits). + 840 ylabel : str + 841 Label for the y-axis. + 842 save : str + 843 path to file in which the figure should be saved. + 844 auto_gamma : bool + 845 Apply the gamma method with standard parameters to all correlators and plateau values before plotting. + 846 hide_sigma : float + 847 Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors. + 848 references : list + 849 List of floating point values that are displayed as horizontal lines for reference. + 850 title : string + 851 Optional title of the figure. + 852 """ + 853 if self.N != 1: + 854 raise Exception("Correlator must be projected before plotting") + 855 + 856 if auto_gamma: + 857 self.gamma_method() + 858 + 859 if x_range is None: + 860 x_range = [0, self.T - 1] + 861 + 862 fig = plt.figure() + 863 ax1 = fig.add_subplot(111) + 864 + 865 x, y, y_err = self.plottable() + 866 if hide_sigma: + 867 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 868 else: + 869 hide_from = None + 870 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag) + 871 if logscale: + 872 ax1.set_yscale('log') + 873 else: + 874 if y_range is None: + 875 try: + 876 y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 877 y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)]) + 878 ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)]) + 879 except Exception: + 880 pass + 881 else: + 882 ax1.set_ylim(y_range) + 883 if comp: + 884 if isinstance(comp, (Corr, list)): + 885 for corr in comp if isinstance(comp, list) else [comp]: + 886 if auto_gamma: + 887 corr.gamma_method() + 888 x, y, y_err = corr.plottable() + 889 if hide_sigma: + 890 hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1 + 891 else: + 892 hide_from = None + 893 ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor']) + 894 else: + 895 raise Exception("'comp' must be a correlator or a list of correlators.") + 896 + 897 if plateau: + 898 if isinstance(plateau, Obs): + 899 if auto_gamma: + 900 plateau.gamma_method() + 901 ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau)) + 902 ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-') + 903 else: + 904 raise Exception("'plateau' must be an Obs") + 905 + 906 if references: + 907 if isinstance(references, list): + 908 for ref in references: + 909 ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--') + 910 else: + 911 raise Exception("'references' must be a list of floating pint values.") + 912 + 913 if self.prange: + 914 ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0) + 915 ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0) + 916 + 917 if fit_res: + 918 x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05) + 919 if isinstance(fit_res.fit_function, dict): + 920 if fit_key: + 921 ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) + 922 else: + 923 raise ValueError("Please provide a 'fit_key' for visualizing combined fits.") + 924 else: + 925 ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2) 926 - 927 plt.draw() - 928 - 929 if save: - 930 if isinstance(save, str): - 931 fig.savefig(save, bbox_inches='tight') - 932 else: - 933 raise Exception("'save' has to be a string.") - 934 - 935 def spaghetti_plot(self, logscale=True): - 936 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. - 937 - 938 Parameters - 939 ---------- - 940 logscale : bool - 941 Determines whether the scale of the y-axis is logarithmic or standard. - 942 """ - 943 if self.N != 1: - 944 raise Exception("Correlator needs to be projected first.") - 945 - 946 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) - 947 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] - 948 - 949 for name in mc_names: - 950 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T - 951 - 952 fig = plt.figure() - 953 ax = fig.add_subplot(111) - 954 for dat in data: - 955 ax.plot(x0_vals, dat, ls='-', marker='') - 956 - 957 if logscale is True: - 958 ax.set_yscale('log') - 959 - 960 ax.set_xlabel(r'$x_0 / a$') - 961 plt.title(name) - 962 plt.draw() + 927 ax1.set_xlabel(r'$x_0 / a$') + 928 if ylabel: + 929 ax1.set_ylabel(ylabel) + 930 ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5]) + 931 + 932 handles, labels = ax1.get_legend_handles_labels() + 933 if labels: + 934 ax1.legend() + 935 + 936 if title: + 937 plt.title(title) + 938 + 939 plt.draw() + 940 + 941 if save: + 942 if isinstance(save, str): + 943 fig.savefig(save, bbox_inches='tight') + 944 else: + 945 raise Exception("'save' has to be a string.") + 946 + 947 def spaghetti_plot(self, logscale=True): + 948 """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations. + 949 + 950 Parameters + 951 ---------- + 952 logscale : bool + 953 Determines whether the scale of the y-axis is logarithmic or standard. + 954 """ + 955 if self.N != 1: + 956 raise Exception("Correlator needs to be projected first.") + 957 + 958 mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist])) + 959 x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None] + 960 + 961 for name in mc_names: + 962 data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T 963 - 964 def dump(self, filename, datatype="json.gz", **kwargs): - 965 """Dumps the Corr into a file of chosen type - 966 Parameters - 967 ---------- - 968 filename : str - 969 Name of the file to be saved. - 970 datatype : str - 971 Format of the exported file. Supported formats include - 972 "json.gz" and "pickle" - 973 path : str - 974 specifies a custom path for the file (default '.') - 975 """ - 976 if datatype == "json.gz": - 977 from .input.json import dump_to_json - 978 if 'path' in kwargs: - 979 file_name = kwargs.get('path') + '/' + filename - 980 else: - 981 file_name = filename - 982 dump_to_json(self, file_name) - 983 elif datatype == "pickle": - 984 dump_object(self, filename, **kwargs) - 985 else: - 986 raise Exception("Unknown datatype " + str(datatype)) - 987 - 988 def print(self, print_range=None): - 989 print(self.__repr__(print_range)) - 990 - 991 def __repr__(self, print_range=None): - 992 if print_range is None: - 993 print_range = [0, None] - 994 - 995 content_string = "" - 996 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 - 997 - 998 if self.tag is not None: - 999 content_string += "Description: " + self.tag + "\n" -1000 if self.N != 1: -1001 return content_string + 964 fig = plt.figure() + 965 ax = fig.add_subplot(111) + 966 for dat in data: + 967 ax.plot(x0_vals, dat, ls='-', marker='') + 968 + 969 if logscale is True: + 970 ax.set_yscale('log') + 971 + 972 ax.set_xlabel(r'$x_0 / a$') + 973 plt.title(name) + 974 plt.draw() + 975 + 976 def dump(self, filename, datatype="json.gz", **kwargs): + 977 """Dumps the Corr into a file of chosen type + 978 Parameters + 979 ---------- + 980 filename : str + 981 Name of the file to be saved. + 982 datatype : str + 983 Format of the exported file. Supported formats include + 984 "json.gz" and "pickle" + 985 path : str + 986 specifies a custom path for the file (default '.') + 987 """ + 988 if datatype == "json.gz": + 989 from .input.json import dump_to_json + 990 if 'path' in kwargs: + 991 file_name = kwargs.get('path') + '/' + filename + 992 else: + 993 file_name = filename + 994 dump_to_json(self, file_name) + 995 elif datatype == "pickle": + 996 dump_object(self, filename, **kwargs) + 997 else: + 998 raise Exception("Unknown datatype " + str(datatype)) + 999 +1000 def print(self, print_range=None): +1001 print(self.__repr__(print_range)) 1002 -1003 if print_range[1]: -1004 print_range[1] += 1 -1005 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' -1006 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): -1007 if sub_corr is None: -1008 content_string += str(i + print_range[0]) + '\n' -1009 else: -1010 content_string += str(i + print_range[0]) -1011 for element in sub_corr: -1012 content_string += f"\t{element:+2}" -1013 content_string += '\n' -1014 return content_string -1015 -1016 def __str__(self): -1017 return self.__repr__() -1018 -1019 # We define the basic operations, that can be performed with correlators. -1020 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. -1021 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. -1022 # One could try and tell Obs to check if the y in __mul__ is a Corr and -1023 -1024 def __add__(self, y): -1025 if isinstance(y, Corr): -1026 if ((self.N != y.N) or (self.T != y.T)): -1027 raise Exception("Addition of Corrs with different shape") -1028 newcontent = [] -1029 for t in range(self.T): -1030 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1031 newcontent.append(None) -1032 else: -1033 newcontent.append(self.content[t] + y.content[t]) -1034 return Corr(newcontent) +1003 def __repr__(self, print_range=None): +1004 if print_range is None: +1005 print_range = [0, None] +1006 +1007 content_string = "" +1008 content_string += "Corr T=" + str(self.T) + " N=" + str(self.N) + "\n" # +" filled with"+ str(type(self.content[0][0])) there should be a good solution here +1009 +1010 if self.tag is not None: +1011 content_string += "Description: " + self.tag + "\n" +1012 if self.N != 1: +1013 return content_string +1014 +1015 if print_range[1]: +1016 print_range[1] += 1 +1017 content_string += 'x0/a\tCorr(x0/a)\n------------------\n' +1018 for i, sub_corr in enumerate(self.content[print_range[0]:print_range[1]]): +1019 if sub_corr is None: +1020 content_string += str(i + print_range[0]) + '\n' +1021 else: +1022 content_string += str(i + print_range[0]) +1023 for element in sub_corr: +1024 content_string += f"\t{element:+2}" +1025 content_string += '\n' +1026 return content_string +1027 +1028 def __str__(self): +1029 return self.__repr__() +1030 +1031 # We define the basic operations, that can be performed with correlators. +1032 # While */+- get defined here, they only work for Corr*Obs and not Obs*Corr. +1033 # This is because Obs*Corr checks Obs.__mul__ first and does not catch an exception. +1034 # One could try and tell Obs to check if the y in __mul__ is a Corr and 1035 -1036 elif isinstance(y, (Obs, int, float, CObs)): -1037 newcontent = [] -1038 for t in range(self.T): -1039 if _check_for_none(self, self.content[t]): -1040 newcontent.append(None) -1041 else: -1042 newcontent.append(self.content[t] + y) -1043 return Corr(newcontent, prange=self.prange) -1044 elif isinstance(y, np.ndarray): -1045 if y.shape == (self.T,): -1046 return Corr(list((np.array(self.content).T + y).T)) -1047 else: -1048 raise ValueError("operands could not be broadcast together") -1049 else: -1050 raise TypeError("Corr + wrong type") -1051 -1052 def __mul__(self, y): -1053 if isinstance(y, Corr): -1054 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1055 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1056 newcontent = [] -1057 for t in range(self.T): -1058 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1059 newcontent.append(None) -1060 else: -1061 newcontent.append(self.content[t] * y.content[t]) -1062 return Corr(newcontent) -1063 -1064 elif isinstance(y, (Obs, int, float, CObs)): -1065 newcontent = [] -1066 for t in range(self.T): -1067 if _check_for_none(self, self.content[t]): -1068 newcontent.append(None) -1069 else: -1070 newcontent.append(self.content[t] * y) -1071 return Corr(newcontent, prange=self.prange) -1072 elif isinstance(y, np.ndarray): -1073 if y.shape == (self.T,): -1074 return Corr(list((np.array(self.content).T * y).T)) -1075 else: -1076 raise ValueError("operands could not be broadcast together") -1077 else: -1078 raise TypeError("Corr * wrong type") -1079 -1080 def __truediv__(self, y): -1081 if isinstance(y, Corr): -1082 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): -1083 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") -1084 newcontent = [] -1085 for t in range(self.T): -1086 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): -1087 newcontent.append(None) -1088 else: -1089 newcontent.append(self.content[t] / y.content[t]) -1090 for t in range(self.T): -1091 if _check_for_none(self, newcontent[t]): -1092 continue -1093 if np.isnan(np.sum(newcontent[t]).value): -1094 newcontent[t] = None -1095 -1096 if all([item is None for item in newcontent]): -1097 raise Exception("Division returns completely undefined correlator") -1098 return Corr(newcontent) -1099 -1100 elif isinstance(y, (Obs, CObs)): -1101 if isinstance(y, Obs): -1102 if y.value == 0: -1103 raise Exception('Division by zero will return undefined correlator') -1104 if isinstance(y, CObs): -1105 if y.is_zero(): -1106 raise Exception('Division by zero will return undefined correlator') -1107 -1108 newcontent = [] -1109 for t in range(self.T): -1110 if _check_for_none(self, self.content[t]): -1111 newcontent.append(None) -1112 else: -1113 newcontent.append(self.content[t] / y) -1114 return Corr(newcontent, prange=self.prange) -1115 -1116 elif isinstance(y, (int, float)): -1117 if y == 0: -1118 raise Exception('Division by zero will return undefined correlator') -1119 newcontent = [] -1120 for t in range(self.T): -1121 if _check_for_none(self, self.content[t]): -1122 newcontent.append(None) -1123 else: -1124 newcontent.append(self.content[t] / y) -1125 return Corr(newcontent, prange=self.prange) -1126 elif isinstance(y, np.ndarray): -1127 if y.shape == (self.T,): -1128 return Corr(list((np.array(self.content).T / y).T)) -1129 else: -1130 raise ValueError("operands could not be broadcast together") -1131 else: -1132 raise TypeError('Corr / wrong type') -1133 -1134 def __neg__(self): -1135 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] -1136 return Corr(newcontent, prange=self.prange) -1137 -1138 def __sub__(self, y): -1139 return self + (-y) -1140 -1141 def __pow__(self, y): -1142 if isinstance(y, (Obs, int, float, CObs)): -1143 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] -1144 return Corr(newcontent, prange=self.prange) -1145 else: -1146 raise TypeError('Type of exponent not supported') -1147 -1148 def __abs__(self): -1149 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] -1150 return Corr(newcontent, prange=self.prange) -1151 -1152 # The numpy functions: -1153 def sqrt(self): -1154 return self ** 0.5 -1155 -1156 def log(self): -1157 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] -1158 return Corr(newcontent, prange=self.prange) -1159 -1160 def exp(self): -1161 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] -1162 return Corr(newcontent, prange=self.prange) -1163 -1164 def _apply_func_to_corr(self, func): -1165 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] -1166 for t in range(self.T): -1167 if _check_for_none(self, newcontent[t]): -1168 continue -1169 tmp_sum = np.sum(newcontent[t]) -1170 if hasattr(tmp_sum, "value"): -1171 if np.isnan(tmp_sum.value): -1172 newcontent[t] = None -1173 if all([item is None for item in newcontent]): -1174 raise Exception('Operation returns undefined correlator') -1175 return Corr(newcontent) -1176 -1177 def sin(self): -1178 return self._apply_func_to_corr(np.sin) -1179 -1180 def cos(self): -1181 return self._apply_func_to_corr(np.cos) -1182 -1183 def tan(self): -1184 return self._apply_func_to_corr(np.tan) -1185 -1186 def sinh(self): -1187 return self._apply_func_to_corr(np.sinh) -1188 -1189 def cosh(self): -1190 return self._apply_func_to_corr(np.cosh) -1191 -1192 def tanh(self): -1193 return self._apply_func_to_corr(np.tanh) +1036 __array_priority__ = 10000 +1037 +1038 def __add__(self, y): +1039 if isinstance(y, Corr): +1040 if ((self.N != y.N) or (self.T != y.T)): +1041 raise Exception("Addition of Corrs with different shape") +1042 newcontent = [] +1043 for t in range(self.T): +1044 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1045 newcontent.append(None) +1046 else: +1047 newcontent.append(self.content[t] + y.content[t]) +1048 return Corr(newcontent) +1049 +1050 elif isinstance(y, (Obs, int, float, CObs)): +1051 newcontent = [] +1052 for t in range(self.T): +1053 if _check_for_none(self, self.content[t]): +1054 newcontent.append(None) +1055 else: +1056 newcontent.append(self.content[t] + y) +1057 return Corr(newcontent, prange=self.prange) +1058 elif isinstance(y, np.ndarray): +1059 if y.shape == (self.T,): +1060 return Corr(list((np.array(self.content).T + y).T)) +1061 else: +1062 raise ValueError("operands could not be broadcast together") +1063 else: +1064 raise TypeError("Corr + wrong type") +1065 +1066 def __mul__(self, y): +1067 if isinstance(y, Corr): +1068 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1069 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1070 newcontent = [] +1071 for t in range(self.T): +1072 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1073 newcontent.append(None) +1074 else: +1075 newcontent.append(self.content[t] * y.content[t]) +1076 return Corr(newcontent) +1077 +1078 elif isinstance(y, (Obs, int, float, CObs)): +1079 newcontent = [] +1080 for t in range(self.T): +1081 if _check_for_none(self, self.content[t]): +1082 newcontent.append(None) +1083 else: +1084 newcontent.append(self.content[t] * y) +1085 return Corr(newcontent, prange=self.prange) +1086 elif isinstance(y, np.ndarray): +1087 if y.shape == (self.T,): +1088 return Corr(list((np.array(self.content).T * y).T)) +1089 else: +1090 raise ValueError("operands could not be broadcast together") +1091 else: +1092 raise TypeError("Corr * wrong type") +1093 +1094 def __matmul__(self, y): +1095 if isinstance(y, np.ndarray): +1096 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1097 raise ValueError("Can only multiply correlators by square matrices.") +1098 if not self.N == y.shape[0]: +1099 raise ValueError("matmul: mismatch of matrix dimensions") +1100 newcontent = [] +1101 for t in range(self.T): +1102 if _check_for_none(self, self.content[t]): +1103 newcontent.append(None) +1104 else: +1105 newcontent.append(self.content[t] @ y) +1106 return Corr(newcontent) +1107 elif isinstance(y, Corr): +1108 if not self.N == y.N: +1109 raise ValueError("matmul: mismatch of matrix dimensions") +1110 newcontent = [] +1111 for t in range(self.T): +1112 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1113 newcontent.append(None) +1114 else: +1115 newcontent.append(self.content[t] @ y.content[t]) +1116 return Corr(newcontent) +1117 +1118 else: +1119 return NotImplemented +1120 +1121 def __rmatmul__(self, y): +1122 if isinstance(y, np.ndarray): +1123 if y.ndim != 2 or y.shape[0] != y.shape[1]: +1124 raise ValueError("Can only multiply correlators by square matrices.") +1125 if not self.N == y.shape[0]: +1126 raise ValueError("matmul: mismatch of matrix dimensions") +1127 newcontent = [] +1128 for t in range(self.T): +1129 if _check_for_none(self, self.content[t]): +1130 newcontent.append(None) +1131 else: +1132 newcontent.append(y @ self.content[t]) +1133 return Corr(newcontent) +1134 else: +1135 return NotImplemented +1136 +1137 def __truediv__(self, y): +1138 if isinstance(y, Corr): +1139 if not ((self.N == 1 or y.N == 1 or self.N == y.N) and self.T == y.T): +1140 raise Exception("Multiplication of Corr object requires N=N or N=1 and T=T") +1141 newcontent = [] +1142 for t in range(self.T): +1143 if _check_for_none(self, self.content[t]) or _check_for_none(y, y.content[t]): +1144 newcontent.append(None) +1145 else: +1146 newcontent.append(self.content[t] / y.content[t]) +1147 for t in range(self.T): +1148 if _check_for_none(self, newcontent[t]): +1149 continue +1150 if np.isnan(np.sum(newcontent[t]).value): +1151 newcontent[t] = None +1152 +1153 if all([item is None for item in newcontent]): +1154 raise Exception("Division returns completely undefined correlator") +1155 return Corr(newcontent) +1156 +1157 elif isinstance(y, (Obs, CObs)): +1158 if isinstance(y, Obs): +1159 if y.value == 0: +1160 raise Exception('Division by zero will return undefined correlator') +1161 if isinstance(y, CObs): +1162 if y.is_zero(): +1163 raise Exception('Division by zero will return undefined correlator') +1164 +1165 newcontent = [] +1166 for t in range(self.T): +1167 if _check_for_none(self, self.content[t]): +1168 newcontent.append(None) +1169 else: +1170 newcontent.append(self.content[t] / y) +1171 return Corr(newcontent, prange=self.prange) +1172 +1173 elif isinstance(y, (int, float)): +1174 if y == 0: +1175 raise Exception('Division by zero will return undefined correlator') +1176 newcontent = [] +1177 for t in range(self.T): +1178 if _check_for_none(self, self.content[t]): +1179 newcontent.append(None) +1180 else: +1181 newcontent.append(self.content[t] / y) +1182 return Corr(newcontent, prange=self.prange) +1183 elif isinstance(y, np.ndarray): +1184 if y.shape == (self.T,): +1185 return Corr(list((np.array(self.content).T / y).T)) +1186 else: +1187 raise ValueError("operands could not be broadcast together") +1188 else: +1189 raise TypeError('Corr / wrong type') +1190 +1191 def __neg__(self): +1192 newcontent = [None if _check_for_none(self, item) else -1. * item for item in self.content] +1193 return Corr(newcontent, prange=self.prange) 1194 -1195 def arcsin(self): -1196 return self._apply_func_to_corr(np.arcsin) +1195 def __sub__(self, y): +1196 return self + (-y) 1197 -1198 def arccos(self): -1199 return self._apply_func_to_corr(np.arccos) -1200 -1201 def arctan(self): -1202 return self._apply_func_to_corr(np.arctan) -1203 -1204 def arcsinh(self): -1205 return self._apply_func_to_corr(np.arcsinh) -1206 -1207 def arccosh(self): -1208 return self._apply_func_to_corr(np.arccosh) -1209 -1210 def arctanh(self): -1211 return self._apply_func_to_corr(np.arctanh) +1198 def __pow__(self, y): +1199 if isinstance(y, (Obs, int, float, CObs)): +1200 newcontent = [None if _check_for_none(self, item) else item**y for item in self.content] +1201 return Corr(newcontent, prange=self.prange) +1202 else: +1203 raise TypeError('Type of exponent not supported') +1204 +1205 def __abs__(self): +1206 newcontent = [None if _check_for_none(self, item) else np.abs(item) for item in self.content] +1207 return Corr(newcontent, prange=self.prange) +1208 +1209 # The numpy functions: +1210 def sqrt(self): +1211 return self ** 0.5 1212 -1213 # Right hand side operations (require tweak in main module to work) -1214 def __radd__(self, y): -1215 return self + y +1213 def log(self): +1214 newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content] +1215 return Corr(newcontent, prange=self.prange) 1216 -1217 def __rsub__(self, y): -1218 return -self + y -1219 -1220 def __rmul__(self, y): -1221 return self * y -1222 -1223 def __rtruediv__(self, y): -1224 return (self / y) ** (-1) -1225 -1226 @property -1227 def real(self): -1228 def return_real(obs_OR_cobs): -1229 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1230 return np.vectorize(lambda x: x.real)(obs_OR_cobs) -1231 else: -1232 return obs_OR_cobs +1217 def exp(self): +1218 newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content] +1219 return Corr(newcontent, prange=self.prange) +1220 +1221 def _apply_func_to_corr(self, func): +1222 newcontent = [None if _check_for_none(self, item) else func(item) for item in self.content] +1223 for t in range(self.T): +1224 if _check_for_none(self, newcontent[t]): +1225 continue +1226 tmp_sum = np.sum(newcontent[t]) +1227 if hasattr(tmp_sum, "value"): +1228 if np.isnan(tmp_sum.value): +1229 newcontent[t] = None +1230 if all([item is None for item in newcontent]): +1231 raise Exception('Operation returns undefined correlator') +1232 return Corr(newcontent) 1233 -1234 return self._apply_func_to_corr(return_real) -1235 -1236 @property -1237 def imag(self): -1238 def return_imag(obs_OR_cobs): -1239 if isinstance(obs_OR_cobs.flatten()[0], CObs): -1240 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) -1241 else: -1242 return obs_OR_cobs * 0 # So it stays the right type -1243 -1244 return self._apply_func_to_corr(return_imag) +1234 def sin(self): +1235 return self._apply_func_to_corr(np.sin) +1236 +1237 def cos(self): +1238 return self._apply_func_to_corr(np.cos) +1239 +1240 def tan(self): +1241 return self._apply_func_to_corr(np.tan) +1242 +1243 def sinh(self): +1244 return self._apply_func_to_corr(np.sinh) 1245 -1246 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): -1247 r''' Project large correlation matrix to lowest states +1246 def cosh(self): +1247 return self._apply_func_to_corr(np.cosh) 1248 -1249 This method can be used to reduce the size of an (N x N) correlation matrix -1250 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise -1251 is still small. -1252 -1253 Parameters -1254 ---------- -1255 Ntrunc: int -1256 Rank of the target matrix. -1257 tproj: int -1258 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. -1259 The default value is 3. -1260 t0proj: int -1261 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly -1262 discouraged for O(a) improved theories, since the correctness of the procedure -1263 cannot be granted in this case. The default value is 2. -1264 basematrix : Corr -1265 Correlation matrix that is used to determine the eigenvectors of the -1266 lowest states based on a GEVP. basematrix is taken to be the Corr itself if -1267 is is not specified. -1268 -1269 Notes -1270 ----- -1271 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving -1272 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ -1273 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the -1274 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via -1275 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large -1276 correlation matrix and to remove some noise that is added by irrelevant operators. -1277 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated -1278 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. -1279 ''' -1280 -1281 if self.N == 1: -1282 raise Exception('Method cannot be applied to one-dimensional correlators.') -1283 if basematrix is None: -1284 basematrix = self -1285 if Ntrunc >= basematrix.N: -1286 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) -1287 if basematrix.N != self.N: -1288 raise Exception('basematrix and targetmatrix have to be of the same size.') -1289 -1290 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] -1291 -1292 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) -1293 rmat = [] -1294 for t in range(basematrix.T): -1295 for i in range(Ntrunc): -1296 for j in range(Ntrunc): -1297 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] -1298 rmat.append(np.copy(tmpmat)) -1299 -1300 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] -1301 return Corr(newcontent) +1249 def tanh(self): +1250 return self._apply_func_to_corr(np.tanh) +1251 +1252 def arcsin(self): +1253 return self._apply_func_to_corr(np.arcsin) +1254 +1255 def arccos(self): +1256 return self._apply_func_to_corr(np.arccos) +1257 +1258 def arctan(self): +1259 return self._apply_func_to_corr(np.arctan) +1260 +1261 def arcsinh(self): +1262 return self._apply_func_to_corr(np.arcsinh) +1263 +1264 def arccosh(self): +1265 return self._apply_func_to_corr(np.arccosh) +1266 +1267 def arctanh(self): +1268 return self._apply_func_to_corr(np.arctanh) +1269 +1270 # Right hand side operations (require tweak in main module to work) +1271 def __radd__(self, y): +1272 return self + y +1273 +1274 def __rsub__(self, y): +1275 return -self + y +1276 +1277 def __rmul__(self, y): +1278 return self * y +1279 +1280 def __rtruediv__(self, y): +1281 return (self / y) ** (-1) +1282 +1283 @property +1284 def real(self): +1285 def return_real(obs_OR_cobs): +1286 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1287 return np.vectorize(lambda x: x.real)(obs_OR_cobs) +1288 else: +1289 return obs_OR_cobs +1290 +1291 return self._apply_func_to_corr(return_real) +1292 +1293 @property +1294 def imag(self): +1295 def return_imag(obs_OR_cobs): +1296 if isinstance(obs_OR_cobs.flatten()[0], CObs): +1297 return np.vectorize(lambda x: x.imag)(obs_OR_cobs) +1298 else: +1299 return obs_OR_cobs * 0 # So it stays the right type +1300 +1301 return self._apply_func_to_corr(return_imag) +1302 +1303 def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None): +1304 r''' Project large correlation matrix to lowest states +1305 +1306 This method can be used to reduce the size of an (N x N) correlation matrix +1307 to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise +1308 is still small. +1309 +1310 Parameters +1311 ---------- +1312 Ntrunc: int +1313 Rank of the target matrix. +1314 tproj: int +1315 Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method. +1316 The default value is 3. +1317 t0proj: int +1318 Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly +1319 discouraged for O(a) improved theories, since the correctness of the procedure +1320 cannot be granted in this case. The default value is 2. +1321 basematrix : Corr +1322 Correlation matrix that is used to determine the eigenvectors of the +1323 lowest states based on a GEVP. basematrix is taken to be the Corr itself if +1324 is is not specified. +1325 +1326 Notes +1327 ----- +1328 We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving +1329 the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$ +1330 and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the +1331 resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via +1332 $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large +1333 correlation matrix and to remove some noise that is added by irrelevant operators. +1334 This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated +1335 bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$. +1336 ''' +1337 +1338 if self.N == 1: +1339 raise Exception('Method cannot be applied to one-dimensional correlators.') +1340 if basematrix is None: +1341 basematrix = self +1342 if Ntrunc >= basematrix.N: +1343 raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N)) +1344 if basematrix.N != self.N: +1345 raise Exception('basematrix and targetmatrix have to be of the same size.') +1346 +1347 evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc] +1348 +1349 tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object) +1350 rmat = [] +1351 for t in range(basematrix.T): +1352 for i in range(Ntrunc): +1353 for j in range(Ntrunc): +1354 tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j] +1355 rmat.append(np.copy(tmpmat)) +1356 +1357 newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)] +1358 return Corr(newcontent) @@ -3303,7 +3420,7 @@ timeslice and the error on each timeslice.

    221    def anti_symmetric(self):
 222        """Anti-symmetrize the correlator around x0=0."""
 223        if self.N != 1:
-224            raise Exception('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
+224            raise TypeError('anti_symmetric cannot be safely applied to multi-dimensional correlators.')
 225        if self.T % 2 != 0:
 226            raise Exception("Can not symmetrize odd T")
 227
@@ -3343,7 +3460,7 @@ timeslice and the error on each timeslice.
    
             
    243    def is_matrix_symmetric(self):
 244        """Checks whether a correlator matrices is symmetric on every timeslice."""
 245        if self.N == 1:
-246            raise Exception("Only works for correlator matrices.")
+246            raise TypeError("Only works for correlator matrices.")
 247        for t in range(self.T):
 248            if self[t] is None:
 249                continue
@@ -3361,6 +3478,36 @@ timeslice and the error on each timeslice.
    
 
    
 
 
+
    +
    + +
    + + def + trace(self): + + + +
    + + 
    258    def trace(self):
+259        """Calculates the per-timeslice trace of a correlator matrix."""
+260        if self.N == 1:
+261            raise ValueError("Only works for correlator matrices.")
+262        newcontent = []
+263        for t in range(self.T):
+264            if _check_for_none(self, self.content[t]):
+265                newcontent.append(None)
+266            else:
+267                newcontent.append(np.trace(self.content[t]))
+268        return Corr(newcontent)
+
    + + +

    Calculates the per-timeslice trace of a correlator matrix.

    +
    + +
    @@ -3373,15 +3520,15 @@ timeslice and the error on each timeslice.

    - 
    258    def matrix_symmetric(self):
-259        """Symmetrizes the correlator matrices on every timeslice."""
-260        if self.N == 1:
-261            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
-262        if self.is_matrix_symmetric():
-263            return 1.0 * self
-264        else:
-265            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
-266            return 0.5 * (Corr(transposed) + self)
+            
    270    def matrix_symmetric(self):
+271        """Symmetrizes the correlator matrices on every timeslice."""
+272        if self.N == 1:
+273            raise Exception("Trying to symmetrize a correlator matrix, that already has N=1.")
+274        if self.is_matrix_symmetric():
+275            return 1.0 * self
+276        else:
+277            transposed = [None if _check_for_none(self, G) else G.T for G in self.content]
+278            return 0.5 * (Corr(transposed) + self)
 
    
 
 
@@ -3401,84 +3548,84 @@ timeslice and the error on each timeslice.
    - 
    268    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
-269        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
-270
-271        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
-272        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
-273        ```python
-274        C.GEVP(t0=2)[0]  # Ground state vector(s)
-275        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
-276        ```
-277
-278        Parameters
-279        ----------
-280        t0 : int
-281            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
-282        ts : int
-283            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
-284            If sort="Eigenvector" it gives a reference point for the sorting method.
-285        sort : string
-286            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.
-287            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
-288            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
-289              The reference state is identified by its eigenvalue at $t=t_s$.
-290
-291        Other Parameters
-292        ----------------
-293        state : int
-294           Returns only the vector(s) for a specified state. The lowest state is zero.
-295        '''
-296
-297        if self.N == 1:
-298            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
-299        if ts is not None:
-300            if (ts <= t0):
-301                raise Exception("ts has to be larger than t0.")
+            
    280    def GEVP(self, t0, ts=None, sort="Eigenvalue", **kwargs):
+281        r'''Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
+282
+283        The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the
+284        largest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
+285        ```python
+286        C.GEVP(t0=2)[0]  # Ground state vector(s)
+287        C.GEVP(t0=2)[:3]  # Vectors for the lowest three states
+288        ```
+289
+290        Parameters
+291        ----------
+292        t0 : int
+293            The time t0 for the right hand side of the GEVP according to $G(t)v_i=\lambda_i G(t_0)v_i$
+294        ts : int
+295            fixed time $G(t_s)v_i=\lambda_i G(t_0)v_i$ if sort=None.
+296            If sort="Eigenvector" it gives a reference point for the sorting method.
+297        sort : string
+298            If this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.
+299            - "Eigenvalue": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
+300            - "Eigenvector": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.
+301              The reference state is identified by its eigenvalue at $t=t_s$.
 302
-303        if "sorted_list" in kwargs:
-304            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
-305            sort = kwargs.get("sorted_list")
-306
-307        if self.is_matrix_symmetric():
-308            symmetric_corr = self
-309        else:
-310            symmetric_corr = self.matrix_symmetric()
-311
-312        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
-313        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
+303        Other Parameters
+304        ----------------
+305        state : int
+306           Returns only the vector(s) for a specified state. The lowest state is zero.
+307        '''
+308
+309        if self.N == 1:
+310            raise Exception("GEVP methods only works on correlator matrices and not single correlators.")
+311        if ts is not None:
+312            if (ts <= t0):
+313                raise Exception("ts has to be larger than t0.")
 314
-315        if sort is None:
-316            if (ts is None):
-317                raise Exception("ts is required if sort=None.")
-318            if (self.content[t0] is None) or (self.content[ts] is None):
-319                raise Exception("Corr not defined at t0/ts.")
-320            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
-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                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
-330                    all_vecs.append(_GEVP_solver(Gt, G0))
-331                except Exception:
-332                    all_vecs.append(None)
-333            if sort == "Eigenvector":
-334                if ts is None:
-335                    raise Exception("ts is required for the Eigenvector sorting method.")
-336                all_vecs = _sort_vectors(all_vecs, ts)
-337
-338            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
-339        else:
-340            raise Exception("Unkown value for 'sort'.")
-341
-342        if "state" in kwargs:
-343            return reordered_vecs[kwargs.get("state")]
-344        else:
-345            return reordered_vecs
+315        if "sorted_list" in kwargs:
+316            warnings.warn("Argument 'sorted_list' is deprecated, use 'sort' instead.", DeprecationWarning)
+317            sort = kwargs.get("sorted_list")
+318
+319        if self.is_matrix_symmetric():
+320            symmetric_corr = self
+321        else:
+322            symmetric_corr = self.matrix_symmetric()
+323
+324        G0 = np.vectorize(lambda x: x.value)(symmetric_corr[t0])
+325        np.linalg.cholesky(G0)  # Check if matrix G0 is positive-semidefinite.
+326
+327        if sort is None:
+328            if (ts is None):
+329                raise Exception("ts is required if sort=None.")
+330            if (self.content[t0] is None) or (self.content[ts] is None):
+331                raise Exception("Corr not defined at t0/ts.")
+332            Gt = np.vectorize(lambda x: x.value)(symmetric_corr[ts])
+333            reordered_vecs = _GEVP_solver(Gt, G0)
+334
+335        elif sort in ["Eigenvalue", "Eigenvector"]:
+336            if sort == "Eigenvalue" and ts is not None:
+337                warnings.warn("ts has no effect when sorting by eigenvalue is chosen.", RuntimeWarning)
+338            all_vecs = [None] * (t0 + 1)
+339            for t in range(t0 + 1, self.T):
+340                try:
+341                    Gt = np.vectorize(lambda x: x.value)(symmetric_corr[t])
+342                    all_vecs.append(_GEVP_solver(Gt, G0))
+343                except Exception:
+344                    all_vecs.append(None)
+345            if sort == "Eigenvector":
+346                if ts is None:
+347                    raise Exception("ts is required for the Eigenvector sorting method.")
+348                all_vecs = _sort_vectors(all_vecs, ts)
+349
+350            reordered_vecs = [[v[s] if v is not None else None for v in all_vecs] for s in range(self.N)]
+351        else:
+352            raise Exception("Unkown value for 'sort'.")
+353
+354        if "state" in kwargs:
+355            return reordered_vecs[kwargs.get("state")]
+356        else:
+357            return reordered_vecs
 
    
 
 
@@ -3531,18 +3678,18 @@ Returns only the vector(s) for a specified state. The lowest state is zero.
    - 
    347    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
-348        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
-349
-350        Parameters
-351        ----------
-352        state : int
-353            The state one is interested in ordered by energy. The lowest state is zero.
-354
-355        All other parameters are identical to the ones of Corr.GEVP.
-356        """
-357        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
-358        return self.projected(vec)
+            
    359    def Eigenvalue(self, t0, ts=None, state=0, sort="Eigenvalue"):
+360        """Determines the eigenvalue of the GEVP by solving and projecting the correlator
+361
+362        Parameters
+363        ----------
+364        state : int
+365            The state one is interested in ordered by energy. The lowest state is zero.
+366
+367        All other parameters are identical to the ones of Corr.GEVP.
+368        """
+369        vec = self.GEVP(t0, ts=ts, sort=sort)[state]
+370        return self.projected(vec)
 
    
 
 
@@ -3570,46 +3717,46 @@ The state one is interested in ordered by energy. The lowest state is zero.
    - 
    360    def Hankel(self, N, periodic=False):
-361        """Constructs an NxN Hankel matrix
-362
-363        C(t) c(t+1) ... c(t+n-1)
-364        C(t+1) c(t+2) ... c(t+n)
-365        .................
-366        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
-367
-368        Parameters
-369        ----------
-370        N : int
-371            Dimension of the Hankel matrix
-372        periodic : bool, optional
-373            determines whether the matrix is extended periodically
-374        """
-375
-376        if self.N != 1:
-377            raise Exception("Multi-operator Prony not implemented!")
-378
-379        array = np.empty([N, N], dtype="object")
-380        new_content = []
-381        for t in range(self.T):
-382            new_content.append(array.copy())
-383
-384        def wrap(i):
-385            while i >= self.T:
-386                i -= self.T
-387            return i
-388
-389        for t in range(self.T):
-390            for i in range(N):
-391                for j in range(N):
-392                    if periodic:
-393                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
-394                    elif (t + i + j) >= self.T:
-395                        new_content[t] = None
-396                    else:
-397                        new_content[t][i, j] = self.content[t + i + j][0]
-398
-399        return Corr(new_content)
+            
    372    def Hankel(self, N, periodic=False):
+373        """Constructs an NxN Hankel matrix
+374
+375        C(t) c(t+1) ... c(t+n-1)
+376        C(t+1) c(t+2) ... c(t+n)
+377        .................
+378        C(t+(n-1)) c(t+n) ... c(t+2(n-1))
+379
+380        Parameters
+381        ----------
+382        N : int
+383            Dimension of the Hankel matrix
+384        periodic : bool, optional
+385            determines whether the matrix is extended periodically
+386        """
+387
+388        if self.N != 1:
+389            raise Exception("Multi-operator Prony not implemented!")
+390
+391        array = np.empty([N, N], dtype="object")
+392        new_content = []
+393        for t in range(self.T):
+394            new_content.append(array.copy())
+395
+396        def wrap(i):
+397            while i >= self.T:
+398                i -= self.T
+399            return i
+400
+401        for t in range(self.T):
+402            for i in range(N):
+403                for j in range(N):
+404                    if periodic:
+405                        new_content[t][i, j] = self.content[wrap(t + i + j)][0]
+406                    elif (t + i + j) >= self.T:
+407                        new_content[t] = None
+408                    else:
+409                        new_content[t][i, j] = self.content[t + i + j][0]
+410
+411        return Corr(new_content)
 
    
 
 
@@ -3643,15 +3790,15 @@ determines whether the matrix is extended periodically
    - 
    401    def roll(self, dt):
-402        """Periodically shift the correlator by dt timeslices
-403
-404        Parameters
-405        ----------
-406        dt : int
-407            number of timeslices
-408        """
-409        return Corr(list(np.roll(np.array(self.content, dtype=object), dt)))
+            
    413    def roll(self, dt):
+414        """Periodically shift the correlator by dt timeslices
+415
+416        Parameters
+417        ----------
+418        dt : int
+419            number of timeslices
+420        """
+421        return Corr(list(np.roll(np.array(self.content, dtype=object), dt, axis=0)))
 
    
 
 
@@ -3678,9 +3825,9 @@ number of timeslices
    - 
    411    def reverse(self):
-412        """Reverse the time ordering of the Corr"""
-413        return Corr(self.content[:: -1])
+            
    423    def reverse(self):
+424        """Reverse the time ordering of the Corr"""
+425        return Corr(self.content[:: -1])
 
    
 
 
@@ -3700,23 +3847,23 @@ number of timeslices
    - 
    415    def thin(self, spacing=2, offset=0):
-416        """Thin out a correlator to suppress correlations
-417
-418        Parameters
-419        ----------
-420        spacing : int
-421            Keep only every 'spacing'th entry of the correlator
-422        offset : int
-423            Offset the equal spacing
-424        """
-425        new_content = []
-426        for t in range(self.T):
-427            if (offset + t) % spacing != 0:
-428                new_content.append(None)
-429            else:
-430                new_content.append(self.content[t])
-431        return Corr(new_content)
+            
    427    def thin(self, spacing=2, offset=0):
+428        """Thin out a correlator to suppress correlations
+429
+430        Parameters
+431        ----------
+432        spacing : int
+433            Keep only every 'spacing'th entry of the correlator
+434        offset : int
+435            Offset the equal spacing
+436        """
+437        new_content = []
+438        for t in range(self.T):
+439            if (offset + t) % spacing != 0:
+440                new_content.append(None)
+441            else:
+442                new_content.append(self.content[t])
+443        return Corr(new_content)
 
    
 
 
@@ -3745,34 +3892,34 @@ Offset the equal spacing
    - 
    433    def correlate(self, partner):
-434        """Correlate the correlator with another correlator or Obs
-435
-436        Parameters
-437        ----------
-438        partner : Obs or Corr
-439            partner to correlate the correlator with.
-440            Can either be an Obs which is correlated with all entries of the
-441            correlator or a Corr of same length.
-442        """
-443        if self.N != 1:
-444            raise Exception("Only one-dimensional correlators can be safely correlated.")
-445        new_content = []
-446        for x0, t_slice in enumerate(self.content):
-447            if _check_for_none(self, t_slice):
-448                new_content.append(None)
-449            else:
-450                if isinstance(partner, Corr):
-451                    if _check_for_none(partner, partner.content[x0]):
-452                        new_content.append(None)
-453                    else:
-454                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
-455                elif isinstance(partner, Obs):  # Should this include CObs?
-456                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
-457                else:
-458                    raise Exception("Can only correlate with an Obs or a Corr.")
-459
-460        return Corr(new_content)
+            
    445    def correlate(self, partner):
+446        """Correlate the correlator with another correlator or Obs
+447
+448        Parameters
+449        ----------
+450        partner : Obs or Corr
+451            partner to correlate the correlator with.
+452            Can either be an Obs which is correlated with all entries of the
+453            correlator or a Corr of same length.
+454        """
+455        if self.N != 1:
+456            raise Exception("Only one-dimensional correlators can be safely correlated.")
+457        new_content = []
+458        for x0, t_slice in enumerate(self.content):
+459            if _check_for_none(self, t_slice):
+460                new_content.append(None)
+461            else:
+462                if isinstance(partner, Corr):
+463                    if _check_for_none(partner, partner.content[x0]):
+464                        new_content.append(None)
+465                    else:
+466                        new_content.append(np.array([correlate(o, partner.content[x0][0]) for o in t_slice]))
+467                elif isinstance(partner, Obs):  # Should this include CObs?
+468                    new_content.append(np.array([correlate(o, partner) for o in t_slice]))
+469                else:
+470                    raise Exception("Can only correlate with an Obs or a Corr.")
+471
+472        return Corr(new_content)
 
    
 
 
@@ -3801,28 +3948,28 @@ correlator or a Corr of same length.
    - 
    462    def reweight(self, weight, **kwargs):
-463        """Reweight the correlator.
-464
-465        Parameters
-466        ----------
-467        weight : Obs
-468            Reweighting factor. An Observable that has to be defined on a superset of the
-469            configurations in obs[i].idl for all i.
-470        all_configs : bool
-471            if True, the reweighted observables are normalized by the average of
-472            the reweighting factor on all configurations in weight.idl and not
-473            on the configurations in obs[i].idl.
-474        """
-475        if self.N != 1:
-476            raise Exception("Reweighting only implemented for one-dimensional correlators.")
-477        new_content = []
-478        for t_slice in self.content:
-479            if _check_for_none(self, t_slice):
-480                new_content.append(None)
-481            else:
-482                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
-483        return Corr(new_content)
+            
    474    def reweight(self, weight, **kwargs):
+475        """Reweight the correlator.
+476
+477        Parameters
+478        ----------
+479        weight : Obs
+480            Reweighting factor. An Observable that has to be defined on a superset of the
+481            configurations in obs[i].idl for all i.
+482        all_configs : bool
+483            if True, the reweighted observables are normalized by the average of
+484            the reweighting factor on all configurations in weight.idl and not
+485            on the configurations in obs[i].idl.
+486        """
+487        if self.N != 1:
+488            raise Exception("Reweighting only implemented for one-dimensional correlators.")
+489        new_content = []
+490        for t_slice in self.content:
+491            if _check_for_none(self, t_slice):
+492                new_content.append(None)
+493            else:
+494                new_content.append(np.array(reweight(weight, t_slice, **kwargs)))
+495        return Corr(new_content)
 
    
 
 
@@ -3854,35 +4001,35 @@ on the configurations in obs[i].idl.
    - 
    485    def T_symmetry(self, partner, parity=+1):
-486        """Return the time symmetry average of the correlator and its partner
-487
-488        Parameters
-489        ----------
-490        partner : Corr
-491            Time symmetry partner of the Corr
-492        partity : int
-493            Parity quantum number of the correlator, can be +1 or -1
-494        """
-495        if self.N != 1:
-496            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
-497        if not isinstance(partner, Corr):
-498            raise Exception("T partner has to be a Corr object.")
-499        if parity not in [+1, -1]:
-500            raise Exception("Parity has to be +1 or -1.")
-501        T_partner = parity * partner.reverse()
-502
-503        t_slices = []
-504        test = (self - T_partner)
-505        test.gamma_method()
-506        for x0, t_slice in enumerate(test.content):
-507            if t_slice is not None:
-508                if not t_slice[0].is_zero_within_error(5):
-509                    t_slices.append(x0)
-510        if t_slices:
-511            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
-512
-513        return (self + T_partner) / 2
+            
    497    def T_symmetry(self, partner, parity=+1):
+498        """Return the time symmetry average of the correlator and its partner
+499
+500        Parameters
+501        ----------
+502        partner : Corr
+503            Time symmetry partner of the Corr
+504        partity : int
+505            Parity quantum number of the correlator, can be +1 or -1
+506        """
+507        if self.N != 1:
+508            raise Exception("T_symmetry only implemented for one-dimensional correlators.")
+509        if not isinstance(partner, Corr):
+510            raise Exception("T partner has to be a Corr object.")
+511        if parity not in [+1, -1]:
+512            raise Exception("Parity has to be +1 or -1.")
+513        T_partner = parity * partner.reverse()
+514
+515        t_slices = []
+516        test = (self - T_partner)
+517        test.gamma_method()
+518        for x0, t_slice in enumerate(test.content):
+519            if t_slice is not None:
+520                if not t_slice[0].is_zero_within_error(5):
+521                    t_slices.append(x0)
+522        if t_slices:
+523            warnings.warn("T symmetry partners do not agree within 5 sigma on time slices " + str(t_slices) + ".", RuntimeWarning)
+524
+525        return (self + T_partner) / 2
 
    
 
 
@@ -3911,70 +4058,70 @@ Parity quantum number of the correlator, can be +1 or -1
    - 
    515    def deriv(self, variant="symmetric"):
-516        """Return the first derivative of the correlator with respect to x0.
-517
-518        Parameters
-519        ----------
-520        variant : str
-521            decides which definition of the finite differences derivative is used.
-522            Available choice: symmetric, forward, backward, improved, log, default: symmetric
-523        """
-524        if self.N != 1:
-525            raise Exception("deriv only implemented for one-dimensional correlators.")
-526        if variant == "symmetric":
-527            newcontent = []
-528            for t in range(1, self.T - 1):
-529                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-530                    newcontent.append(None)
-531                else:
-532                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
-533            if (all([x is None for x in newcontent])):
-534                raise Exception('Derivative is undefined at all timeslices')
-535            return Corr(newcontent, padding=[1, 1])
-536        elif variant == "forward":
-537            newcontent = []
-538            for t in range(self.T - 1):
-539                if (self.content[t] is None) or (self.content[t + 1] is None):
-540                    newcontent.append(None)
-541                else:
-542                    newcontent.append(self.content[t + 1] - self.content[t])
-543            if (all([x is None for x in newcontent])):
-544                raise Exception("Derivative is undefined at all timeslices")
-545            return Corr(newcontent, padding=[0, 1])
-546        elif variant == "backward":
-547            newcontent = []
-548            for t in range(1, self.T):
-549                if (self.content[t - 1] is None) or (self.content[t] is None):
-550                    newcontent.append(None)
-551                else:
-552                    newcontent.append(self.content[t] - self.content[t - 1])
-553            if (all([x is None for x in newcontent])):
-554                raise Exception("Derivative is undefined at all timeslices")
-555            return Corr(newcontent, padding=[1, 0])
-556        elif variant == "improved":
-557            newcontent = []
-558            for t in range(2, self.T - 2):
-559                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):
-560                    newcontent.append(None)
-561                else:
-562                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
-563            if (all([x is None for x in newcontent])):
-564                raise Exception('Derivative is undefined at all timeslices')
-565            return Corr(newcontent, padding=[2, 2])
-566        elif variant == 'log':
-567            newcontent = []
-568            for t in range(self.T):
-569                if (self.content[t] is None) or (self.content[t] <= 0):
-570                    newcontent.append(None)
-571                else:
-572                    newcontent.append(np.log(self.content[t]))
-573            if (all([x is None for x in newcontent])):
-574                raise Exception("Log is undefined at all timeslices")
-575            logcorr = Corr(newcontent)
-576            return self * logcorr.deriv('symmetric')
-577        else:
-578            raise Exception("Unknown variant.")
+            
    527    def deriv(self, variant="symmetric"):
+528        """Return the first derivative of the correlator with respect to x0.
+529
+530        Parameters
+531        ----------
+532        variant : str
+533            decides which definition of the finite differences derivative is used.
+534            Available choice: symmetric, forward, backward, improved, log, default: symmetric
+535        """
+536        if self.N != 1:
+537            raise Exception("deriv only implemented for one-dimensional correlators.")
+538        if variant == "symmetric":
+539            newcontent = []
+540            for t in range(1, self.T - 1):
+541                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+542                    newcontent.append(None)
+543                else:
+544                    newcontent.append(0.5 * (self.content[t + 1] - self.content[t - 1]))
+545            if (all([x is None for x in newcontent])):
+546                raise Exception('Derivative is undefined at all timeslices')
+547            return Corr(newcontent, padding=[1, 1])
+548        elif variant == "forward":
+549            newcontent = []
+550            for t in range(self.T - 1):
+551                if (self.content[t] is None) or (self.content[t + 1] is None):
+552                    newcontent.append(None)
+553                else:
+554                    newcontent.append(self.content[t + 1] - self.content[t])
+555            if (all([x is None for x in newcontent])):
+556                raise Exception("Derivative is undefined at all timeslices")
+557            return Corr(newcontent, padding=[0, 1])
+558        elif variant == "backward":
+559            newcontent = []
+560            for t in range(1, self.T):
+561                if (self.content[t - 1] is None) or (self.content[t] is None):
+562                    newcontent.append(None)
+563                else:
+564                    newcontent.append(self.content[t] - self.content[t - 1])
+565            if (all([x is None for x in newcontent])):
+566                raise Exception("Derivative is undefined at all timeslices")
+567            return Corr(newcontent, padding=[1, 0])
+568        elif variant == "improved":
+569            newcontent = []
+570            for t in range(2, self.T - 2):
+571                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+572                    newcontent.append(None)
+573                else:
+574                    newcontent.append((1 / 12) * (self.content[t - 2] - 8 * self.content[t - 1] + 8 * self.content[t + 1] - self.content[t + 2]))
+575            if (all([x is None for x in newcontent])):
+576                raise Exception('Derivative is undefined at all timeslices')
+577            return Corr(newcontent, padding=[2, 2])
+578        elif variant == 'log':
+579            newcontent = []
+580            for t in range(self.T):
+581                if (self.content[t] is None) or (self.content[t] <= 0):
+582                    newcontent.append(None)
+583                else:
+584                    newcontent.append(np.log(self.content[t]))
+585            if (all([x is None for x in newcontent])):
+586                raise Exception("Log is undefined at all timeslices")
+587            logcorr = Corr(newcontent)
+588            return self * logcorr.deriv('symmetric')
+589        else:
+590            raise Exception("Unknown variant.")
 
    
 
 
@@ -4002,68 +4149,68 @@ Available choice: symmetric, forward, backward, improved, log, default: symmetri
    - 
    580    def second_deriv(self, variant="symmetric"):
-581        r"""Return the second derivative of the correlator with respect to x0.
-582
-583        Parameters
-584        ----------
-585        variant : str
-586            decides which definition of the finite differences derivative is used.
-587            Available choice:
-588                - symmetric (default)
-589                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
-590                - big_symmetric
-591                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
-592                - improved
-593                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
-594                - log
-595                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
-596        """
-597        if self.N != 1:
-598            raise Exception("second_deriv only implemented for one-dimensional correlators.")
-599        if variant == "symmetric":
-600            newcontent = []
-601            for t in range(1, self.T - 1):
-602                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
-603                    newcontent.append(None)
-604                else:
-605                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
-606            if (all([x is None for x in newcontent])):
-607                raise Exception("Derivative is undefined at all timeslices")
-608            return Corr(newcontent, padding=[1, 1])
-609        elif variant == "big_symmetric":
-610            newcontent = []
-611            for t in range(2, self.T - 2):
-612                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
-613                    newcontent.append(None)
-614                else:
-615                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
-616            if (all([x is None for x in newcontent])):
-617                raise Exception("Derivative is undefined at all timeslices")
-618            return Corr(newcontent, padding=[2, 2])
-619        elif variant == "improved":
-620            newcontent = []
-621            for t in range(2, self.T - 2):
-622                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):
-623                    newcontent.append(None)
-624                else:
-625                    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]))
-626            if (all([x is None for x in newcontent])):
-627                raise Exception("Derivative is undefined at all timeslices")
-628            return Corr(newcontent, padding=[2, 2])
-629        elif variant == 'log':
-630            newcontent = []
-631            for t in range(self.T):
-632                if (self.content[t] is None) or (self.content[t] <= 0):
-633                    newcontent.append(None)
-634                else:
-635                    newcontent.append(np.log(self.content[t]))
-636            if (all([x is None for x in newcontent])):
-637                raise Exception("Log is undefined at all timeslices")
-638            logcorr = Corr(newcontent)
-639            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
-640        else:
-641            raise Exception("Unknown variant.")
+            
    592    def second_deriv(self, variant="symmetric"):
+593        r"""Return the second derivative of the correlator with respect to x0.
+594
+595        Parameters
+596        ----------
+597        variant : str
+598            decides which definition of the finite differences derivative is used.
+599            Available choice:
+600                - symmetric (default)
+601                    $$\tilde{\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$
+602                - big_symmetric
+603                    $$\partial^2_0 f(x_0) = \frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$
+604                - improved
+605                    $$\partial^2_0 f(x_0) = \frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$
+606                - log
+607                    $$f(x) = \tilde{\partial}^2_0 log(f(x_0))+(\tilde{\partial}_0 log(f(x_0)))^2$$
+608        """
+609        if self.N != 1:
+610            raise Exception("second_deriv only implemented for one-dimensional correlators.")
+611        if variant == "symmetric":
+612            newcontent = []
+613            for t in range(1, self.T - 1):
+614                if (self.content[t - 1] is None) or (self.content[t + 1] is None):
+615                    newcontent.append(None)
+616                else:
+617                    newcontent.append((self.content[t + 1] - 2 * self.content[t] + self.content[t - 1]))
+618            if (all([x is None for x in newcontent])):
+619                raise Exception("Derivative is undefined at all timeslices")
+620            return Corr(newcontent, padding=[1, 1])
+621        elif variant == "big_symmetric":
+622            newcontent = []
+623            for t in range(2, self.T - 2):
+624                if (self.content[t - 2] is None) or (self.content[t + 2] is None):
+625                    newcontent.append(None)
+626                else:
+627                    newcontent.append((self.content[t + 2] - 2 * self.content[t] + self.content[t - 2]) / 4)
+628            if (all([x is None for x in newcontent])):
+629                raise Exception("Derivative is undefined at all timeslices")
+630            return Corr(newcontent, padding=[2, 2])
+631        elif variant == "improved":
+632            newcontent = []
+633            for t in range(2, self.T - 2):
+634                if (self.content[t - 2] is None) or (self.content[t - 1] is None) or (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 2] is None):
+635                    newcontent.append(None)
+636                else:
+637                    newcontent.append((1 / 12) * (-self.content[t + 2] + 16 * self.content[t + 1] - 30 * self.content[t] + 16 * self.content[t - 1] - self.content[t - 2]))
+638            if (all([x is None for x in newcontent])):
+639                raise Exception("Derivative is undefined at all timeslices")
+640            return Corr(newcontent, padding=[2, 2])
+641        elif variant == 'log':
+642            newcontent = []
+643            for t in range(self.T):
+644                if (self.content[t] is None) or (self.content[t] <= 0):
+645                    newcontent.append(None)
+646                else:
+647                    newcontent.append(np.log(self.content[t]))
+648            if (all([x is None for x in newcontent])):
+649                raise Exception("Log is undefined at all timeslices")
+650            logcorr = Corr(newcontent)
+651            return self * (logcorr.second_deriv('symmetric') + (logcorr.deriv('symmetric'))**2)
+652        else:
+653            raise Exception("Unknown variant.")
 
    
 
 
@@ -4099,89 +4246,89 @@ Available choice:
    - 
    643    def m_eff(self, variant='log', guess=1.0):
-644        """Returns the effective mass of the correlator as correlator object
-645
-646        Parameters
-647        ----------
-648        variant : str
-649            log : uses the standard effective mass log(C(t) / C(t+1))
-650            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.
-651            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.
-652            See, e.g., arXiv:1205.5380
-653            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
-654            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
-655        guess : float
-656            guess for the root finder, only relevant for the root variant
-657        """
-658        if self.N != 1:
-659            raise Exception('Correlator must be projected before getting m_eff')
-660        if variant == 'log':
-661            newcontent = []
-662            for t in range(self.T - 1):
-663                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
-664                    newcontent.append(None)
-665                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-666                    newcontent.append(None)
-667                else:
-668                    newcontent.append(self.content[t] / self.content[t + 1])
-669            if (all([x is None for x in newcontent])):
-670                raise Exception('m_eff is undefined at all timeslices')
-671
-672            return np.log(Corr(newcontent, padding=[0, 1]))
-673
-674        elif variant == 'logsym':
-675            newcontent = []
-676            for t in range(1, self.T - 1):
-677                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+            
    655    def m_eff(self, variant='log', guess=1.0):
+656        """Returns the effective mass of the correlator as correlator object
+657
+658        Parameters
+659        ----------
+660        variant : str
+661            log : uses the standard effective mass log(C(t) / C(t+1))
+662            cosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.
+663            sinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.
+664            See, e.g., arXiv:1205.5380
+665            arccosh : Uses the explicit form of the symmetrized correlator (not recommended)
+666            logsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
+667        guess : float
+668            guess for the root finder, only relevant for the root variant
+669        """
+670        if self.N != 1:
+671            raise Exception('Correlator must be projected before getting m_eff')
+672        if variant == 'log':
+673            newcontent = []
+674            for t in range(self.T - 1):
+675                if ((self.content[t] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+676                    newcontent.append(None)
+677                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
 678                    newcontent.append(None)
-679                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
-680                    newcontent.append(None)
-681                else:
-682                    newcontent.append(self.content[t - 1] / self.content[t + 1])
-683            if (all([x is None for x in newcontent])):
-684                raise Exception('m_eff is undefined at all timeslices')
+679                else:
+680                    newcontent.append(self.content[t] / self.content[t + 1])
+681            if (all([x is None for x in newcontent])):
+682                raise Exception('m_eff is undefined at all timeslices')
+683
+684            return np.log(Corr(newcontent, padding=[0, 1]))
 685
-686            return np.log(Corr(newcontent, padding=[1, 1])) / 2
-687
-688        elif variant in ['periodic', 'cosh', 'sinh']:
-689            if variant in ['periodic', 'cosh']:
-690                func = anp.cosh
-691            else:
-692                func = anp.sinh
-693
-694            def root_function(x, d):
-695                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
-696
-697            newcontent = []
-698            for t in range(self.T - 1):
-699                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
-700                    newcontent.append(None)
-701                # Fill the two timeslices in the middle of the lattice with their predecessors
-702                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
-703                    newcontent.append(newcontent[-1])
-704                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
-705                    newcontent.append(None)
-706                else:
-707                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
-708            if (all([x is None for x in newcontent])):
-709                raise Exception('m_eff is undefined at all timeslices')
-710
-711            return Corr(newcontent, padding=[0, 1])
-712
-713        elif variant == 'arccosh':
-714            newcontent = []
-715            for t in range(1, self.T - 1):
-716                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):
+686        elif variant == 'logsym':
+687            newcontent = []
+688            for t in range(1, self.T - 1):
+689                if ((self.content[t - 1] is None) or (self.content[t + 1] is None)) or (self.content[t + 1][0].value == 0):
+690                    newcontent.append(None)
+691                elif self.content[t - 1][0].value / self.content[t + 1][0].value < 0:
+692                    newcontent.append(None)
+693                else:
+694                    newcontent.append(self.content[t - 1] / self.content[t + 1])
+695            if (all([x is None for x in newcontent])):
+696                raise Exception('m_eff is undefined at all timeslices')
+697
+698            return np.log(Corr(newcontent, padding=[1, 1])) / 2
+699
+700        elif variant in ['periodic', 'cosh', 'sinh']:
+701            if variant in ['periodic', 'cosh']:
+702                func = anp.cosh
+703            else:
+704                func = anp.sinh
+705
+706            def root_function(x, d):
+707                return func(x * (t - self.T / 2)) / func(x * (t + 1 - self.T / 2)) - d
+708
+709            newcontent = []
+710            for t in range(self.T - 1):
+711                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t + 1][0].value == 0):
+712                    newcontent.append(None)
+713                # Fill the two timeslices in the middle of the lattice with their predecessors
+714                elif variant == 'sinh' and t in [self.T / 2, self.T / 2 - 1]:
+715                    newcontent.append(newcontent[-1])
+716                elif self.content[t][0].value / self.content[t + 1][0].value < 0:
 717                    newcontent.append(None)
 718                else:
-719                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+719                    newcontent.append(np.abs(find_root(self.content[t][0] / self.content[t + 1][0], root_function, guess=guess)))
 720            if (all([x is None for x in newcontent])):
-721                raise Exception("m_eff is undefined at all timeslices")
-722            return np.arccosh(Corr(newcontent, padding=[1, 1]))
-723
-724        else:
-725            raise Exception('Unknown variant.')
+721                raise Exception('m_eff is undefined at all timeslices')
+722
+723            return Corr(newcontent, padding=[0, 1])
+724
+725        elif variant == 'arccosh':
+726            newcontent = []
+727            for t in range(1, self.T - 1):
+728                if (self.content[t] is None) or (self.content[t + 1] is None) or (self.content[t - 1] is None) or (self.content[t][0].value == 0):
+729                    newcontent.append(None)
+730                else:
+731                    newcontent.append((self.content[t + 1] + self.content[t - 1]) / (2 * self.content[t]))
+732            if (all([x is None for x in newcontent])):
+733                raise Exception("m_eff is undefined at all timeslices")
+734            return np.arccosh(Corr(newcontent, padding=[1, 1]))
+735
+736        else:
+737            raise Exception('Unknown variant.')
 
    
 
 
@@ -4215,39 +4362,39 @@ guess for the root finder, only relevant for the root variant
    - 
    727    def fit(self, function, fitrange=None, silent=False, **kwargs):
-728        r'''Fits function to the data
-729
-730        Parameters
-731        ----------
-732        function : obj
-733            function to fit to the data. See fits.least_squares for details.
-734        fitrange : list
-735            Two element list containing the timeslices on which the fit is supposed to start and stop.
-736            Caution: This range is inclusive as opposed to standard python indexing.
-737            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
-738            If not specified, self.prange or all timeslices are used.
-739        silent : bool
-740            Decides whether output is printed to the standard output.
-741        '''
-742        if self.N != 1:
-743            raise Exception("Correlator must be projected before fitting")
-744
-745        if fitrange is None:
-746            if self.prange:
-747                fitrange = self.prange
-748            else:
-749                fitrange = [0, self.T - 1]
-750        else:
-751            if not isinstance(fitrange, list):
-752                raise Exception("fitrange has to be a list with two elements")
-753            if len(fitrange) != 2:
-754                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
-755
-756        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
-757        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
-758        result = least_squares(xs, ys, function, silent=silent, **kwargs)
-759        return result
+            
    739    def fit(self, function, fitrange=None, silent=False, **kwargs):
+740        r'''Fits function to the data
+741
+742        Parameters
+743        ----------
+744        function : obj
+745            function to fit to the data. See fits.least_squares for details.
+746        fitrange : list
+747            Two element list containing the timeslices on which the fit is supposed to start and stop.
+748            Caution: This range is inclusive as opposed to standard python indexing.
+749            `fitrange=[4, 6]` corresponds to the three entries 4, 5 and 6.
+750            If not specified, self.prange or all timeslices are used.
+751        silent : bool
+752            Decides whether output is printed to the standard output.
+753        '''
+754        if self.N != 1:
+755            raise Exception("Correlator must be projected before fitting")
+756
+757        if fitrange is None:
+758            if self.prange:
+759                fitrange = self.prange
+760            else:
+761                fitrange = [0, self.T - 1]
+762        else:
+763            if not isinstance(fitrange, list):
+764                raise Exception("fitrange has to be a list with two elements")
+765            if len(fitrange) != 2:
+766                raise Exception("fitrange has to have exactly two elements [fit_start, fit_stop]")
+767
+768        xs = np.array([x for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
+769        ys = np.array([self.content[x][0] for x in range(fitrange[0], fitrange[1] + 1) if not self.content[x] is None])
+770        result = least_squares(xs, ys, function, silent=silent, **kwargs)
+771        return result
 
    
 
 
@@ -4281,42 +4428,42 @@ Decides whether output is printed to the standard output.
    - 
    761    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
-762        """ Extract a plateau value from a Corr object
-763
-764        Parameters
-765        ----------
-766        plateau_range : list
-767            list with two entries, indicating the first and the last timeslice
-768            of the plateau region.
-769        method : str
-770            method to extract the plateau.
-771                'fit' fits a constant to the plateau region
-772                'avg', 'average' or 'mean' just average over the given timeslices.
-773        auto_gamma : bool
-774            apply gamma_method with default parameters to the Corr. Defaults to None
-775        """
-776        if not plateau_range:
-777            if self.prange:
-778                plateau_range = self.prange
-779            else:
-780                raise Exception("no plateau range provided")
-781        if self.N != 1:
-782            raise Exception("Correlator must be projected before getting a plateau.")
-783        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
-784            raise Exception("plateau is undefined at all timeslices in plateaurange.")
-785        if auto_gamma:
-786            self.gamma_method()
-787        if method == "fit":
-788            def const_func(a, t):
-789                return a[0]
-790            return self.fit(const_func, plateau_range)[0]
-791        elif method in ["avg", "average", "mean"]:
-792            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
-793            return returnvalue
-794
-795        else:
-796            raise Exception("Unsupported plateau method: " + method)
+            
    773    def plateau(self, plateau_range=None, method="fit", auto_gamma=False):
+774        """ Extract a plateau value from a Corr object
+775
+776        Parameters
+777        ----------
+778        plateau_range : list
+779            list with two entries, indicating the first and the last timeslice
+780            of the plateau region.
+781        method : str
+782            method to extract the plateau.
+783                'fit' fits a constant to the plateau region
+784                'avg', 'average' or 'mean' just average over the given timeslices.
+785        auto_gamma : bool
+786            apply gamma_method with default parameters to the Corr. Defaults to None
+787        """
+788        if not plateau_range:
+789            if self.prange:
+790                plateau_range = self.prange
+791            else:
+792                raise Exception("no plateau range provided")
+793        if self.N != 1:
+794            raise Exception("Correlator must be projected before getting a plateau.")
+795        if (all([self.content[t] is None for t in range(plateau_range[0], plateau_range[1] + 1)])):
+796            raise Exception("plateau is undefined at all timeslices in plateaurange.")
+797        if auto_gamma:
+798            self.gamma_method()
+799        if method == "fit":
+800            def const_func(a, t):
+801                return a[0]
+802            return self.fit(const_func, plateau_range)[0]
+803        elif method in ["avg", "average", "mean"]:
+804            returnvalue = np.mean([item[0] for item in self.content[plateau_range[0]:plateau_range[1] + 1] if item is not None])
+805            return returnvalue
+806
+807        else:
+808            raise Exception("Unsupported plateau method: " + method)
 
    
 
 
@@ -4350,17 +4497,17 @@ apply gamma_method with default parameters to the Corr. Defaults to None
    - 
    798    def set_prange(self, prange):
-799        """Sets the attribute prange of the Corr object."""
-800        if not len(prange) == 2:
-801            raise Exception("prange must be a list or array with two values")
-802        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
-803            raise Exception("Start and end point must be integers")
-804        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
-805            raise Exception("Start and end point must define a range in the interval 0,T")
-806
-807        self.prange = prange
-808        return
+            
    810    def set_prange(self, prange):
+811        """Sets the attribute prange of the Corr object."""
+812        if not len(prange) == 2:
+813            raise Exception("prange must be a list or array with two values")
+814        if not ((isinstance(prange[0], int)) and (isinstance(prange[1], int))):
+815            raise Exception("Start and end point must be integers")
+816        if not (0 <= prange[0] <= self.T and 0 <= prange[1] <= self.T and prange[0] < prange[1]):
+817            raise Exception("Start and end point must define a range in the interval 0,T")
+818
+819        self.prange = prange
+820        return
 
    
 
 
@@ -4380,130 +4527,130 @@ apply gamma_method with default parameters to the Corr. Defaults to None
    - 
    810    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
-811        """Plots the correlator using the tag of the correlator as label if available.
-812
-813        Parameters
-814        ----------
-815        x_range : list
-816            list of two values, determining the range of the x-axis e.g. [4, 8].
-817        comp : Corr or list of Corr
-818            Correlator or list of correlators which are plotted for comparison.
-819            The tags of these correlators are used as labels if available.
-820        logscale : bool
-821            Sets y-axis to logscale.
-822        plateau : Obs
-823            Plateau value to be visualized in the figure.
-824        fit_res : Fit_result
-825            Fit_result object to be visualized.
-826        fit_key : str
-827            Key for the fit function in Fit_result.fit_function (for combined fits).
-828        ylabel : str
-829            Label for the y-axis.
-830        save : str
-831            path to file in which the figure should be saved.
-832        auto_gamma : bool
-833            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
-834        hide_sigma : float
-835            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
-836        references : list
-837            List of floating point values that are displayed as horizontal lines for reference.
-838        title : string
-839            Optional title of the figure.
-840        """
-841        if self.N != 1:
-842            raise Exception("Correlator must be projected before plotting")
-843
-844        if auto_gamma:
-845            self.gamma_method()
-846
-847        if x_range is None:
-848            x_range = [0, self.T - 1]
-849
-850        fig = plt.figure()
-851        ax1 = fig.add_subplot(111)
-852
-853        x, y, y_err = self.plottable()
-854        if hide_sigma:
-855            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-856        else:
-857            hide_from = None
-858        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
-859        if logscale:
-860            ax1.set_yscale('log')
-861        else:
-862            if y_range is None:
-863                try:
-864                    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)])
-865                    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)])
-866                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
-867                except Exception:
-868                    pass
-869            else:
-870                ax1.set_ylim(y_range)
-871        if comp:
-872            if isinstance(comp, (Corr, list)):
-873                for corr in comp if isinstance(comp, list) else [comp]:
-874                    if auto_gamma:
-875                        corr.gamma_method()
-876                    x, y, y_err = corr.plottable()
-877                    if hide_sigma:
-878                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
-879                    else:
-880                        hide_from = None
-881                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
-882            else:
-883                raise Exception("'comp' must be a correlator or a list of correlators.")
-884
-885        if plateau:
-886            if isinstance(plateau, Obs):
-887                if auto_gamma:
-888                    plateau.gamma_method()
-889                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
-890                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
-891            else:
-892                raise Exception("'plateau' must be an Obs")
-893
-894        if references:
-895            if isinstance(references, list):
-896                for ref in references:
-897                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
-898            else:
-899                raise Exception("'references' must be a list of floating pint values.")
-900
-901        if self.prange:
-902            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
-903            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
-904
-905        if fit_res:
-906            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
-907            if isinstance(fit_res.fit_function, dict):
-908                if fit_key:
-909                    ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
-910                else:
-911                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
-912            else:
-913                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
-914
-915        ax1.set_xlabel(r'$x_0 / a$')
-916        if ylabel:
-917            ax1.set_ylabel(ylabel)
-918        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
-919
-920        handles, labels = ax1.get_legend_handles_labels()
-921        if labels:
-922            ax1.legend()
-923
-924        if title:
-925            plt.title(title)
+            
    822    def show(self, x_range=None, comp=None, y_range=None, logscale=False, plateau=None, fit_res=None, fit_key=None, ylabel=None, save=None, auto_gamma=False, hide_sigma=None, references=None, title=None):
+823        """Plots the correlator using the tag of the correlator as label if available.
+824
+825        Parameters
+826        ----------
+827        x_range : list
+828            list of two values, determining the range of the x-axis e.g. [4, 8].
+829        comp : Corr or list of Corr
+830            Correlator or list of correlators which are plotted for comparison.
+831            The tags of these correlators are used as labels if available.
+832        logscale : bool
+833            Sets y-axis to logscale.
+834        plateau : Obs
+835            Plateau value to be visualized in the figure.
+836        fit_res : Fit_result
+837            Fit_result object to be visualized.
+838        fit_key : str
+839            Key for the fit function in Fit_result.fit_function (for combined fits).
+840        ylabel : str
+841            Label for the y-axis.
+842        save : str
+843            path to file in which the figure should be saved.
+844        auto_gamma : bool
+845            Apply the gamma method with standard parameters to all correlators and plateau values before plotting.
+846        hide_sigma : float
+847            Hides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
+848        references : list
+849            List of floating point values that are displayed as horizontal lines for reference.
+850        title : string
+851            Optional title of the figure.
+852        """
+853        if self.N != 1:
+854            raise Exception("Correlator must be projected before plotting")
+855
+856        if auto_gamma:
+857            self.gamma_method()
+858
+859        if x_range is None:
+860            x_range = [0, self.T - 1]
+861
+862        fig = plt.figure()
+863        ax1 = fig.add_subplot(111)
+864
+865        x, y, y_err = self.plottable()
+866        if hide_sigma:
+867            hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+868        else:
+869            hide_from = None
+870        ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=self.tag)
+871        if logscale:
+872            ax1.set_yscale('log')
+873        else:
+874            if y_range is None:
+875                try:
+876                    y_min = min([(x[0].value - x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+877                    y_max = max([(x[0].value + x[0].dvalue) for x in self.content[x_range[0]: x_range[1] + 1] if (x is not None) and x[0].dvalue < 2 * np.abs(x[0].value)])
+878                    ax1.set_ylim([y_min - 0.1 * (y_max - y_min), y_max + 0.1 * (y_max - y_min)])
+879                except Exception:
+880                    pass
+881            else:
+882                ax1.set_ylim(y_range)
+883        if comp:
+884            if isinstance(comp, (Corr, list)):
+885                for corr in comp if isinstance(comp, list) else [comp]:
+886                    if auto_gamma:
+887                        corr.gamma_method()
+888                    x, y, y_err = corr.plottable()
+889                    if hide_sigma:
+890                        hide_from = np.argmax((hide_sigma * np.array(y_err[1:])) > np.abs(y[1:])) - 1
+891                    else:
+892                        hide_from = None
+893                    ax1.errorbar(x[:hide_from], y[:hide_from], y_err[:hide_from], label=corr.tag, mfc=plt.rcParams['axes.facecolor'])
+894            else:
+895                raise Exception("'comp' must be a correlator or a list of correlators.")
+896
+897        if plateau:
+898            if isinstance(plateau, Obs):
+899                if auto_gamma:
+900                    plateau.gamma_method()
+901                ax1.axhline(y=plateau.value, linewidth=2, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--', label=str(plateau))
+902                ax1.axhspan(plateau.value - plateau.dvalue, plateau.value + plateau.dvalue, alpha=0.25, color=plt.rcParams['text.color'], ls='-')
+903            else:
+904                raise Exception("'plateau' must be an Obs")
+905
+906        if references:
+907            if isinstance(references, list):
+908                for ref in references:
+909                    ax1.axhline(y=ref, linewidth=1, color=plt.rcParams['text.color'], alpha=0.6, marker=',', ls='--')
+910            else:
+911                raise Exception("'references' must be a list of floating pint values.")
+912
+913        if self.prange:
+914            ax1.axvline(self.prange[0], 0, 1, ls='-', marker=',', color="black", zorder=0)
+915            ax1.axvline(self.prange[1], 0, 1, ls='-', marker=',', color="black", zorder=0)
+916
+917        if fit_res:
+918            x_samples = np.arange(x_range[0], x_range[1] + 1, 0.05)
+919            if isinstance(fit_res.fit_function, dict):
+920                if fit_key:
+921                    ax1.plot(x_samples, fit_res.fit_function[fit_key]([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
+922                else:
+923                    raise ValueError("Please provide a 'fit_key' for visualizing combined fits.")
+924            else:
+925                ax1.plot(x_samples, fit_res.fit_function([o.value for o in fit_res.fit_parameters], x_samples), ls='-', marker=',', lw=2)
 926
-927        plt.draw()
-928
-929        if save:
-930            if isinstance(save, str):
-931                fig.savefig(save, bbox_inches='tight')
-932            else:
-933                raise Exception("'save' has to be a string.")
+927        ax1.set_xlabel(r'$x_0 / a$')
+928        if ylabel:
+929            ax1.set_ylabel(ylabel)
+930        ax1.set_xlim([x_range[0] - 0.5, x_range[1] + 0.5])
+931
+932        handles, labels = ax1.get_legend_handles_labels()
+933        if labels:
+934            ax1.legend()
+935
+936        if title:
+937            plt.title(title)
+938
+939        plt.draw()
+940
+941        if save:
+942            if isinstance(save, str):
+943                fig.savefig(save, bbox_inches='tight')
+944            else:
+945                raise Exception("'save' has to be a string.")
 
    
 
 
@@ -4553,34 +4700,34 @@ Optional title of the figure.
    - 
    935    def spaghetti_plot(self, logscale=True):
-936        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
-937
-938        Parameters
-939        ----------
-940        logscale : bool
-941            Determines whether the scale of the y-axis is logarithmic or standard.
-942        """
-943        if self.N != 1:
-944            raise Exception("Correlator needs to be projected first.")
-945
-946        mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist]))
-947        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
-948
-949        for name in mc_names:
-950            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
-951
-952            fig = plt.figure()
-953            ax = fig.add_subplot(111)
-954            for dat in data:
-955                ax.plot(x0_vals, dat, ls='-', marker='')
-956
-957            if logscale is True:
-958                ax.set_yscale('log')
-959
-960            ax.set_xlabel(r'$x_0 / a$')
-961            plt.title(name)
-962            plt.draw()
+            
    947    def spaghetti_plot(self, logscale=True):
+948        """Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
+949
+950        Parameters
+951        ----------
+952        logscale : bool
+953            Determines whether the scale of the y-axis is logarithmic or standard.
+954        """
+955        if self.N != 1:
+956            raise Exception("Correlator needs to be projected first.")
+957
+958        mc_names = list(set([item for sublist in [sum(map(o[0].e_content.get, o[0].mc_names), []) for o in self.content if o is not None] for item in sublist]))
+959        x0_vals = [n for (n, o) in zip(np.arange(self.T), self.content) if o is not None]
+960
+961        for name in mc_names:
+962            data = np.array([o[0].deltas[name] + o[0].r_values[name] for o in self.content if o is not None]).T
+963
+964            fig = plt.figure()
+965            ax = fig.add_subplot(111)
+966            for dat in data:
+967                ax.plot(x0_vals, dat, ls='-', marker='')
+968
+969            if logscale is True:
+970                ax.set_yscale('log')
+971
+972            ax.set_xlabel(r'$x_0 / a$')
+973            plt.title(name)
+974            plt.draw()
 
    
 
 
@@ -4607,29 +4754,29 @@ Determines whether the scale of the y-axis is logarithmic or standard.
    - 
    964    def dump(self, filename, datatype="json.gz", **kwargs):
-965        """Dumps the Corr into a file of chosen type
-966        Parameters
-967        ----------
-968        filename : str
-969            Name of the file to be saved.
-970        datatype : str
-971            Format of the exported file. Supported formats include
-972            "json.gz" and "pickle"
-973        path : str
-974            specifies a custom path for the file (default '.')
-975        """
-976        if datatype == "json.gz":
-977            from .input.json import dump_to_json
-978            if 'path' in kwargs:
-979                file_name = kwargs.get('path') + '/' + filename
-980            else:
-981                file_name = filename
-982            dump_to_json(self, file_name)
-983        elif datatype == "pickle":
-984            dump_object(self, filename, **kwargs)
-985        else:
-986            raise Exception("Unknown datatype " + str(datatype))
+            
    976    def dump(self, filename, datatype="json.gz", **kwargs):
+977        """Dumps the Corr into a file of chosen type
+978        Parameters
+979        ----------
+980        filename : str
+981            Name of the file to be saved.
+982        datatype : str
+983            Format of the exported file. Supported formats include
+984            "json.gz" and "pickle"
+985        path : str
+986            specifies a custom path for the file (default '.')
+987        """
+988        if datatype == "json.gz":
+989            from .input.json import dump_to_json
+990            if 'path' in kwargs:
+991                file_name = kwargs.get('path') + '/' + filename
+992            else:
+993                file_name = filename
+994            dump_to_json(self, file_name)
+995        elif datatype == "pickle":
+996            dump_object(self, filename, **kwargs)
+997        else:
+998            raise Exception("Unknown datatype " + str(datatype))
 
    
 
 
@@ -4661,8 +4808,8 @@ specifies a custom path for the file (default '.')
    - 
    988    def print(self, print_range=None):
-989        print(self.__repr__(print_range))
+            
    1000    def print(self, print_range=None):
+1001        print(self.__repr__(print_range))
 
    
 
 
@@ -4680,8 +4827,8 @@ specifies a custom path for the file (default '.')
    - 
    1153    def sqrt(self):
-1154        return self ** 0.5
+            
    1210    def sqrt(self):
+1211        return self ** 0.5
 
    
 
 
@@ -4699,9 +4846,9 @@ specifies a custom path for the file (default '.')
    - 
    1156    def log(self):
-1157        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
-1158        return Corr(newcontent, prange=self.prange)
+            
    1213    def log(self):
+1214        newcontent = [None if _check_for_none(self, item) else np.log(item) for item in self.content]
+1215        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4719,9 +4866,9 @@ specifies a custom path for the file (default '.')
    - 
    1160    def exp(self):
-1161        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
-1162        return Corr(newcontent, prange=self.prange)
+            
    1217    def exp(self):
+1218        newcontent = [None if _check_for_none(self, item) else np.exp(item) for item in self.content]
+1219        return Corr(newcontent, prange=self.prange)
 
    
 
 
@@ -4739,8 +4886,8 @@ specifies a custom path for the file (default '.')
    - 
    1177    def sin(self):
-1178        return self._apply_func_to_corr(np.sin)
+            
    1234    def sin(self):
+1235        return self._apply_func_to_corr(np.sin)
 
    
 
 
@@ -4758,8 +4905,8 @@ specifies a custom path for the file (default '.')
    - 
    1180    def cos(self):
-1181        return self._apply_func_to_corr(np.cos)
+            
    1237    def cos(self):
+1238        return self._apply_func_to_corr(np.cos)
 
    
 
 
@@ -4777,8 +4924,8 @@ specifies a custom path for the file (default '.')
    - 
    1183    def tan(self):
-1184        return self._apply_func_to_corr(np.tan)
+            
    1240    def tan(self):
+1241        return self._apply_func_to_corr(np.tan)
 
    
 
 
@@ -4796,8 +4943,8 @@ specifies a custom path for the file (default '.')
    - 
    1186    def sinh(self):
-1187        return self._apply_func_to_corr(np.sinh)
+            
    1243    def sinh(self):
+1244        return self._apply_func_to_corr(np.sinh)
 
    
 
 
@@ -4815,8 +4962,8 @@ specifies a custom path for the file (default '.')
    - 
    1189    def cosh(self):
-1190        return self._apply_func_to_corr(np.cosh)
+            
    1246    def cosh(self):
+1247        return self._apply_func_to_corr(np.cosh)
 
    
 
 
@@ -4834,8 +4981,8 @@ specifies a custom path for the file (default '.')
    - 
    1192    def tanh(self):
-1193        return self._apply_func_to_corr(np.tanh)
+            
    1249    def tanh(self):
+1250        return self._apply_func_to_corr(np.tanh)
 
    
 
 
@@ -4853,8 +5000,8 @@ specifies a custom path for the file (default '.')
    - 
    1195    def arcsin(self):
-1196        return self._apply_func_to_corr(np.arcsin)
+            
    1252    def arcsin(self):
+1253        return self._apply_func_to_corr(np.arcsin)
 
    
 
 
@@ -4872,8 +5019,8 @@ specifies a custom path for the file (default '.')
    - 
    1198    def arccos(self):
-1199        return self._apply_func_to_corr(np.arccos)
+            
    1255    def arccos(self):
+1256        return self._apply_func_to_corr(np.arccos)
 
    
 
 
@@ -4891,8 +5038,8 @@ specifies a custom path for the file (default '.')
    - 
    1201    def arctan(self):
-1202        return self._apply_func_to_corr(np.arctan)
+            
    1258    def arctan(self):
+1259        return self._apply_func_to_corr(np.arctan)
 
    
 
 
@@ -4910,8 +5057,8 @@ specifies a custom path for the file (default '.')
    - 
    1204    def arcsinh(self):
-1205        return self._apply_func_to_corr(np.arcsinh)
+            
    1261    def arcsinh(self):
+1262        return self._apply_func_to_corr(np.arcsinh)
 
    
 
 
@@ -4929,8 +5076,8 @@ specifies a custom path for the file (default '.')
    - 
    1207    def arccosh(self):
-1208        return self._apply_func_to_corr(np.arccosh)
+            
    1264    def arccosh(self):
+1265        return self._apply_func_to_corr(np.arccosh)
 
    
 
 
@@ -4948,8 +5095,8 @@ specifies a custom path for the file (default '.')
    - 
    1210    def arctanh(self):
-1211        return self._apply_func_to_corr(np.arctanh)
+            
    1267    def arctanh(self):
+1268        return self._apply_func_to_corr(np.arctanh)
 
    
 
 
@@ -4989,62 +5136,62 @@ specifies a custom path for the file (default '.')
    - 
    1246    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
-1247        r''' Project large correlation matrix to lowest states
-1248
-1249        This method can be used to reduce the size of an (N x N) correlation matrix
-1250        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
-1251        is still small.
-1252
-1253        Parameters
-1254        ----------
-1255        Ntrunc: int
-1256            Rank of the target matrix.
-1257        tproj: int
-1258            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
-1259            The default value is 3.
-1260        t0proj: int
-1261            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
-1262            discouraged for O(a) improved theories, since the correctness of the procedure
-1263            cannot be granted in this case. The default value is 2.
-1264        basematrix : Corr
-1265            Correlation matrix that is used to determine the eigenvectors of the
-1266            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
-1267            is is not specified.
-1268
-1269        Notes
-1270        -----
-1271        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
-1272        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
-1273        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
-1274        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
-1275        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
-1276        correlation matrix and to remove some noise that is added by irrelevant operators.
-1277        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
-1278        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
-1279        '''
-1280
-1281        if self.N == 1:
-1282            raise Exception('Method cannot be applied to one-dimensional correlators.')
-1283        if basematrix is None:
-1284            basematrix = self
-1285        if Ntrunc >= basematrix.N:
-1286            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
-1287        if basematrix.N != self.N:
-1288            raise Exception('basematrix and targetmatrix have to be of the same size.')
-1289
-1290        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
-1291
-1292        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
-1293        rmat = []
-1294        for t in range(basematrix.T):
-1295            for i in range(Ntrunc):
-1296                for j in range(Ntrunc):
-1297                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
-1298            rmat.append(np.copy(tmpmat))
-1299
-1300        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
-1301        return Corr(newcontent)
+            
    1303    def prune(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):
+1304        r''' Project large correlation matrix to lowest states
+1305
+1306        This method can be used to reduce the size of an (N x N) correlation matrix
+1307        to (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise
+1308        is still small.
+1309
+1310        Parameters
+1311        ----------
+1312        Ntrunc: int
+1313            Rank of the target matrix.
+1314        tproj: int
+1315            Time where the eigenvectors are evaluated, corresponds to ts in the GEVP method.
+1316            The default value is 3.
+1317        t0proj: int
+1318            Time where the correlation matrix is inverted. Choosing t0proj=1 is strongly
+1319            discouraged for O(a) improved theories, since the correctness of the procedure
+1320            cannot be granted in this case. The default value is 2.
+1321        basematrix : Corr
+1322            Correlation matrix that is used to determine the eigenvectors of the
+1323            lowest states based on a GEVP. basematrix is taken to be the Corr itself if
+1324            is is not specified.
+1325
+1326        Notes
+1327        -----
+1328        We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving
+1329        the GEVP $$C(t) v_n(t, t_0) = \lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \equiv t_\mathrm{proj}$
+1330        and $t_0 \equiv t_{0, \mathrm{proj}}$. The target matrix is projected onto the subspace of the
+1331        resulting eigenvectors $v_n, n=1,\dots,N_\mathrm{trunc}$ via
+1332        $$G^\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large
+1333        correlation matrix and to remove some noise that is added by irrelevant operators.
+1334        This may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated
+1335        bound $t_0 \leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
+1336        '''
+1337
+1338        if self.N == 1:
+1339            raise Exception('Method cannot be applied to one-dimensional correlators.')
+1340        if basematrix is None:
+1341            basematrix = self
+1342        if Ntrunc >= basematrix.N:
+1343            raise Exception('Cannot truncate using Ntrunc <= %d' % (basematrix.N))
+1344        if basematrix.N != self.N:
+1345            raise Exception('basematrix and targetmatrix have to be of the same size.')
+1346
+1347        evecs = basematrix.GEVP(t0proj, tproj, sort=None)[:Ntrunc]
+1348
+1349        tmpmat = np.empty((Ntrunc, Ntrunc), dtype=object)
+1350        rmat = []
+1351        for t in range(basematrix.T):
+1352            for i in range(Ntrunc):
+1353                for j in range(Ntrunc):
+1354                    tmpmat[i][j] = evecs[i].T @ self[t] @ evecs[j]
+1355            rmat.append(np.copy(tmpmat))
+1356
+1357        newcontent = [None if (self.content[t] is None) else rmat[t] for t in range(self.T)]
+1358        return Corr(newcontent)
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index 25217270..fe669075 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
    \n\n
    \n
    python -m pip install git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
    \n\n
    For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
    \n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
    \n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
    \n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
    \n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
      \n\n
      def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at 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\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
    \n\n
    It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
    \n\n
    A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
      • \n
    • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • root (Obs):\nThe root of the data series.
      • \n
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • w0 (Obs):\nExtracted w0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • files (List[str]): A list of files to read data from.
        • \n
      • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
    \n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
    Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
    \n\n
    The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\nfunction to integrate, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(p, x):\n   return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
      \n
      \n\n
      where x is the integration variable.
      • \n
    • p (list of floats or Obs):\nparameters of the function func.
      • \n
    • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
      • \n
    • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
      • \n
    • All parameters of scipy.integrate.quad
      • \n
    \n\n
    Returns
    \n\n
      \n
    • y (Obs):\nThe integral of func from a to b.
      • \n
    • abserr (float):\nAn estimate of the absolute error in the result.
      • \n
    • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
      • \n
    • message: A convergence message.
      • \n
    • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
      • \n
    \n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
    \n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
    \n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
    \n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
    Export bootstrap samples from the Obs
    \n\n
    Parameters
    \n\n
      \n
    • samples (int):\nNumber of bootstrap samples to generate.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
      • \n
    • save_rng (str):\nSave the random numbers to a file if a path is specified.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
      • \n
    \n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
    Imports bootstrap samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
      • \n
    \n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "kind": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. Comput.Phys.Commun. 288 (2023) 108750.
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Installation
    \n\n
    Install the most recent release using pip and pypi:
    \n\n
    \n
    python -m pip install pyerrors     # Fresh install\npython -m pip install -U pyerrors  # Update\n
    \n
    \n\n
    Install the most recent release using conda and conda-forge:
    \n\n
    \n
    conda install -c conda-forge pyerrors  # Fresh install\nconda update -c conda-forge pyerrors   # Update\n
    \n
    \n\n
    Install the current develop version:
    \n\n
    \n
    python -m pip install git+https://github.com/fjosw/pyerrors.git@develop\n
    \n
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See Multiple ensembles/replica for details.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The gamma_method is not automatically called after every intermediate step in order to prevent computational overhead.
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Observables from the same Monte Carlo chain have to be initialized with the same name for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.\nDirect visualizations of the performed fits can be triggered via resplot=True or qqplot=True.
    \n\n
    For all available options including combined fits to multiple datasets see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "
    Calculates the per-timeslice trace of a correlator matrix.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • fit_key (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tfit_key=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "
    \n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "
    \n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "
    \n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "
    \n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k) of the epsilon tensor of rank 3
      • \n
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n\n
    Returns
    \n\n
      \n
    • elem (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4
      • \n
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "
    \n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).\n    ```
    \n\n
    Parameters
    \n\n
      \n
    • For an uncombined fit:
      • \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • OR For a combined fit:
      • \n
    • x (dict):\ndict of lists.
      • \n
    • y (dict):\ndict of lists of Obs.
      • \n
    • funcs (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n       \"b\": func_b}
      \n\n
      def func_a(a, x):\n   return a[1] * anp.exp(-a[0] * x)
      \n\n
      def func_b(a, x):\n   return a[2] * anp.exp(-a[0] * x)
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • tol (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm < edm_max)
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy.
    \n\n
    Returns
    \n\n
      \n
    • output (Fit_result):\nParameters and information on the fitted result.
      • \n
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • fit_parameters (list[Obs]):\nLIist of fitted observables.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, o_y, func, p, title=''):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n\n
    For uncorrelated data the residuals are expected to be distributed ~N(0,1).
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(x, y, func, fit_res, title=''):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n\n
    Returns
    \n\n
      \n
    • err (np.array(Obs)):\nError band for an array of sample values x
      • \n
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (List[Obs]):\nExtracted data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • success (int):\nreturns 0 is successful
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (dict):\nExtracted meson data
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML formatted string of the input data
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(content, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (list[Obs]):\nImported data
      • \n
    • or
      • \n
    • res (dict):\nImported data and meta-data
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • xml_str (str):\nXML string generated from the data
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at 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\n
    Returns
    \n\n
      \n
    • corr (Corr):\nCorrelator of the source sink combination in question.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "
    Read hadrons FlowObservables hdf5 file and extract t0
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • obs (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    \n", "signature": "(\tpath,\tfilestem,\tens_id,\tobs='Clover energy density',\tfit_range=5,\tidl=None,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (dict):\nextracted DistillationContration data
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Npr_matrix):\nread Cobs-matrix
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict[Npr_matrix]):\nextracted Bilinears
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result_dict (dict):\nextracted fourquark matrizes
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • json_string (str):\nString for export to .json(.gz) file
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Null
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nreconstructed list of observables from the json string
      • \n
    • or
      • \n
    • result (Obs):\nonly one observable if the list only has one entry
      • \n
    • or
      • \n
    • result (dict):\nif full_output=True
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (Obs / list / Corr):\nRead data
      • \n
    • or
      • \n
    • data (dict):\nRead data and meta-data
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "
    Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).
    \n\n
    It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.
    \n\n
    A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • t2E_dict (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)
      • \n
    • observable (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • root (Obs):\nThe root of the data series.
      • \n
    \n", "signature": "(t2E_dict, fit_range, plot_fit=False, observable='t0'):", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of observables read
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • rwms (Obs):\nReweighting factors read
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • t0 (Obs):\nExtracted t0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "
    Extract w0/a from given .ms.dat files. Returns w0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • postfix (str):\nPostfix of measurement file (Default: ms)
      • \n
    • c (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of w0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n\n
    Returns
    \n\n
      \n
    • w0 (Obs):\nExtracted w0
      • \n
    \n", "signature": "(\tpath,\tprefix,\tdtr_read,\txmin,\tspatial_extent,\tfit_range=5,\tpostfix='ms',\tc=0.3,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (Obs):\nRead topological charge
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • reto (Obs):\nprojection to the topological charge sector defined by target
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • files (List[str]): A list of files to read data from.
        • \n
      • idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • data (pandas.DataFrame):\nDataframe with the content of the sqlite database.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf files from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n\n
    Returns
    \n\n
      \n
    • result (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\tsilent=False,\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    \n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "
    Sorts a list of names of replika with searches for r and id in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • ll (list):\nlist to sort
      • \n
    \n\n
    Returns
    \n\n
      \n
    • ll (list):\nsorted list
      • \n
    \n", "signature": "(ll):", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n\n
    Returns
    \n\n
      \n
    • miss_str (str):\nstring with integers of which idls are missing
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "
    \n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "
    Performs a (one-dimensional) numeric integration of f(p, x) from a to b.
    \n\n
    The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\nfunction to integrate, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(p, x):\n   return p[0] + p[1] * x + p[2] * anp.sinh(x)\n
      \n
      \n\n
      where x is the integration variable.
      • \n
    • p (list of floats or Obs):\nparameters of the function func.
      • \n
    • a (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).
      • \n
    • b (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).
      • \n
    • All parameters of scipy.integrate.quad
      • \n
    \n\n
    Returns
    \n\n
      \n
    • y (Obs):\nThe integral of func from a to b.
      • \n
    • abserr (float):\nAn estimate of the absolute error in the result.
      • \n
    • infodict (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.
      • \n
    • message: A convergence message.
      • \n
    • explain: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']
      • \n
    \n", "signature": "(func, p, a, b, **kwargs):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "
    Print information about version of python, pyerrors and dependencies.
    \n", "signature": "():", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "
    pyerrors wrapper for the errorbars method of matplotlib
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nA list of x-values which can be Obs.
      • \n
    • y (list):\nA list of y-values which can be Obs.
      • \n
    • axes ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.
      • \n
    \n", "signature": "(\tx,\ty,\taxes=<module 'matplotlib.pyplot' from '/opt/hostedtoolcache/Python/3.10.12/x64/lib/python3.10/site-packages/matplotlib/pyplot.py'>,\t**kwargs):", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n\n
    Returns
    \n\n
      \n
    • None
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n\n
    Returns
    \n\n
      \n
    • object (Obs):\nLoaded Object
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nGenerated Observable
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • corr_obs (list[Obs]):\nGenerated observable list
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n\n
    Returns
    \n\n
      \n
    • energy_levels (list[Obs]):\nExtracted energy levels
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "
    \n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "
    \n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "
    \n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "
    \n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "
    Export bootstrap samples from the Obs
    \n\n
    Parameters
    \n\n
      \n
    • samples (int):\nNumber of bootstrap samples to generate.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.
      • \n
    • save_rng (str):\nSave the random numbers to a file if a path is specified.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).
      • \n
    \n", "signature": "(self, samples=500, random_numbers=None, save_rng=None):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "
    Imports bootstrap samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • boots (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    • random_numbers (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.
      • \n
    \n", "signature": "(boots, name, random_numbers):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • res (Obs):\nObs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
    \n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 8312}, "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": 40, "bases": 0, "doc": 94}, "pyerrors.correlators.Corr.tag": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.content": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.T": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, 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