diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html index eeba5e51..072bff10 100644 --- a/docs/pyerrors/obs.html +++ b/docs/pyerrors/obs.html @@ -61,6 +61,9 @@
  • gamma_method
    • +
  • + gm +
  • details
    • @@ -553,1326 +556,1328 @@ 349 self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue 350 return 351 - 352 def _calc_gamma(self, deltas, idx, shape, w_max, fft): - 353 """Calculate Gamma_{AA} from the deltas, which are defined on idx. - 354 idx is assumed to be a contiguous range (possibly with a stepsize != 1) - 355 - 356 Parameters - 357 ---------- - 358 deltas : list - 359 List of fluctuations - 360 idx : list - 361 List or range of configurations on which the deltas are defined. - 362 shape : int - 363 Number of configurations in idx. - 364 w_max : int - 365 Upper bound for the summation window. - 366 fft : bool - 367 determines whether the fft algorithm is used for the computation - 368 of the autocorrelation function. - 369 """ - 370 gamma = np.zeros(w_max) - 371 deltas = _expand_deltas(deltas, idx, shape) - 372 new_shape = len(deltas) - 373 if fft: - 374 max_gamma = min(new_shape, w_max) - 375 # The padding for the fft has to be even - 376 padding = new_shape + max_gamma + (new_shape + max_gamma) % 2 - 377 gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma] - 378 else: - 379 for n in range(w_max): - 380 if new_shape - n >= 0: - 381 gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape]) - 382 - 383 return gamma + 352 gm = gamma_method + 353 + 354 def _calc_gamma(self, deltas, idx, shape, w_max, fft): + 355 """Calculate Gamma_{AA} from the deltas, which are defined on idx. + 356 idx is assumed to be a contiguous range (possibly with a stepsize != 1) + 357 + 358 Parameters + 359 ---------- + 360 deltas : list + 361 List of fluctuations + 362 idx : list + 363 List or range of configurations on which the deltas are defined. + 364 shape : int + 365 Number of configurations in idx. + 366 w_max : int + 367 Upper bound for the summation window. + 368 fft : bool + 369 determines whether the fft algorithm is used for the computation + 370 of the autocorrelation function. + 371 """ + 372 gamma = np.zeros(w_max) + 373 deltas = _expand_deltas(deltas, idx, shape) + 374 new_shape = len(deltas) + 375 if fft: + 376 max_gamma = min(new_shape, w_max) + 377 # The padding for the fft has to be even + 378 padding = new_shape + max_gamma + (new_shape + max_gamma) % 2 + 379 gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma] + 380 else: + 381 for n in range(w_max): + 382 if new_shape - n >= 0: + 383 gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape]) 384 - 385 def details(self, ens_content=True): - 386 """Output detailed properties of the Obs. - 387 - 388 Parameters - 389 ---------- - 390 ens_content : bool - 391 print details about the ensembles and replica if true. - 392 """ - 393 if self.tag is not None: - 394 print("Description:", self.tag) - 395 if not hasattr(self, 'e_dvalue'): - 396 print('Result\t %3.8e' % (self.value)) - 397 else: - 398 if self.value == 0.0: - 399 percentage = np.nan - 400 else: - 401 percentage = np.abs(self._dvalue / self.value) * 100 - 402 print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage)) - 403 if len(self.e_names) > 1: - 404 print(' Ensemble errors:') - 405 e_content = self.e_content - 406 for e_name in self.mc_names: - 407 if isinstance(self.idl[e_content[e_name][0]], range): - 408 gap = self.idl[e_content[e_name][0]].step - 409 else: - 410 gap = np.min(np.diff(self.idl[e_content[e_name][0]])) - 411 - 412 if len(self.e_names) > 1: - 413 print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name])) - 414 tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name]) - 415 tau_string += f" in units of {gap} config" - 416 if gap > 1: - 417 tau_string += "s" - 418 if self.tau_exp[e_name] > 0: - 419 tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name]) - 420 else: - 421 tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name]) - 422 print(tau_string) - 423 for e_name in self.cov_names: - 424 print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name])) - 425 if ens_content is True: - 426 if len(self.e_names) == 1: - 427 print(self.N, 'samples in', len(self.e_names), 'ensemble:') - 428 else: - 429 print(self.N, 'samples in', len(self.e_names), 'ensembles:') - 430 my_string_list = [] - 431 for key, value in sorted(self.e_content.items()): - 432 if key not in self.covobs: - 433 my_string = ' ' + "\u00B7 Ensemble '" + key + "' " - 434 if len(value) == 1: - 435 my_string += f': {self.shape[value[0]]} configurations' - 436 if isinstance(self.idl[value[0]], range): - 437 my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')' - 438 else: - 439 my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})' - 440 else: - 441 sublist = [] - 442 for v in value: - 443 my_substring = ' ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' " - 444 my_substring += f': {self.shape[v]} configurations' - 445 if isinstance(self.idl[v], range): - 446 my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')' - 447 else: - 448 my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})' - 449 sublist.append(my_substring) - 450 - 451 my_string += '\n' + '\n'.join(sublist) - 452 else: - 453 my_string = ' ' + "\u00B7 Covobs '" + key + "' " - 454 my_string_list.append(my_string) - 455 print('\n'.join(my_string_list)) - 456 - 457 def reweight(self, weight): - 458 """Reweight the obs with given rewighting factors. - 459 - 460 Parameters - 461 ---------- - 462 weight : Obs - 463 Reweighting factor. An Observable that has to be defined on a superset of the - 464 configurations in obs[i].idl for all i. - 465 all_configs : bool - 466 if True, the reweighted observables are normalized by the average of - 467 the reweighting factor on all configurations in weight.idl and not - 468 on the configurations in obs[i].idl. Default False. - 469 """ - 470 return reweight(weight, [self])[0] - 471 - 472 def is_zero_within_error(self, sigma=1): - 473 """Checks whether the observable is zero within 'sigma' standard errors. - 474 - 475 Parameters - 476 ---------- - 477 sigma : int - 478 Number of standard errors used for the check. - 479 - 480 Works only properly when the gamma method was run. - 481 """ - 482 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue - 483 - 484 def is_zero(self, atol=1e-10): - 485 """Checks whether the observable is zero within a given tolerance. - 486 - 487 Parameters - 488 ---------- - 489 atol : float - 490 Absolute tolerance (for details see numpy documentation). - 491 """ - 492 return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values()) - 493 - 494 def plot_tauint(self, save=None): - 495 """Plot integrated autocorrelation time for each ensemble. - 496 - 497 Parameters - 498 ---------- - 499 save : str - 500 saves the figure to a file named 'save' if. - 501 """ - 502 if not hasattr(self, 'e_dvalue'): - 503 raise Exception('Run the gamma method first.') - 504 - 505 for e, e_name in enumerate(self.mc_names): - 506 fig = plt.figure() - 507 plt.xlabel(r'$W$') - 508 plt.ylabel(r'$\tau_\mathrm{int}$') - 509 length = int(len(self.e_n_tauint[e_name])) - 510 if self.tau_exp[e_name] > 0: - 511 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] - 512 x_help = np.arange(2 * self.tau_exp[e_name]) - 513 y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base - 514 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) - 515 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') - 516 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], - 517 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) - 518 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 - 519 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) - 520 else: - 521 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) - 522 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) - 523 - 524 plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label) - 525 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') - 526 plt.legend() - 527 plt.xlim(-0.5, xmax) - 528 ylim = plt.ylim() - 529 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) - 530 plt.draw() - 531 if save: - 532 fig.savefig(save + "_" + str(e)) - 533 - 534 def plot_rho(self, save=None): - 535 """Plot normalized autocorrelation function time for each ensemble. - 536 - 537 Parameters - 538 ---------- - 539 save : str - 540 saves the figure to a file named 'save' if. - 541 """ - 542 if not hasattr(self, 'e_dvalue'): - 543 raise Exception('Run the gamma method first.') - 544 for e, e_name in enumerate(self.mc_names): - 545 fig = plt.figure() - 546 plt.xlabel('W') - 547 plt.ylabel('rho') - 548 length = int(len(self.e_drho[e_name])) - 549 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) - 550 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') - 551 if self.tau_exp[e_name] > 0: - 552 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], - 553 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) - 554 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 - 555 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) - 556 else: - 557 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) - 558 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) - 559 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) - 560 plt.xlim(-0.5, xmax) - 561 plt.draw() - 562 if save: - 563 fig.savefig(save + "_" + str(e)) - 564 - 565 def plot_rep_dist(self): - 566 """Plot replica distribution for each ensemble with more than one replicum.""" - 567 if not hasattr(self, 'e_dvalue'): - 568 raise Exception('Run the gamma method first.') - 569 for e, e_name in enumerate(self.mc_names): - 570 if len(self.e_content[e_name]) == 1: - 571 print('No replica distribution for a single replicum (', e_name, ')') - 572 continue - 573 r_length = [] - 574 sub_r_mean = 0 - 575 for r, r_name in enumerate(self.e_content[e_name]): - 576 r_length.append(len(self.deltas[r_name])) - 577 sub_r_mean += self.shape[r_name] * self.r_values[r_name] - 578 e_N = np.sum(r_length) - 579 sub_r_mean /= e_N - 580 arr = np.zeros(len(self.e_content[e_name])) - 581 for r, r_name in enumerate(self.e_content[e_name]): - 582 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) - 583 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) - 584 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') - 585 plt.draw() - 586 - 587 def plot_history(self, expand=True): - 588 """Plot derived Monte Carlo history for each ensemble - 589 - 590 Parameters - 591 ---------- - 592 expand : bool - 593 show expanded history for irregular Monte Carlo chains (default: True). - 594 """ - 595 for e, e_name in enumerate(self.mc_names): - 596 plt.figure() - 597 r_length = [] - 598 tmp = [] - 599 tmp_expanded = [] - 600 for r, r_name in enumerate(self.e_content[e_name]): - 601 tmp.append(self.deltas[r_name] + self.r_values[r_name]) - 602 if expand: - 603 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) - 604 r_length.append(len(tmp_expanded[-1])) - 605 else: - 606 r_length.append(len(tmp[-1])) - 607 e_N = np.sum(r_length) - 608 x = np.arange(e_N) - 609 y_test = np.concatenate(tmp, axis=0) - 610 if expand: - 611 y = np.concatenate(tmp_expanded, axis=0) - 612 else: - 613 y = y_test - 614 plt.errorbar(x, y, fmt='.', markersize=3) - 615 plt.xlim(-0.5, e_N - 0.5) - 616 plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})') - 617 plt.draw() - 618 - 619 def plot_piechart(self, save=None): - 620 """Plot piechart which shows the fractional contribution of each - 621 ensemble to the error and returns a dictionary containing the fractions. - 622 - 623 Parameters - 624 ---------- - 625 save : str - 626 saves the figure to a file named 'save' if. - 627 """ - 628 if not hasattr(self, 'e_dvalue'): - 629 raise Exception('Run the gamma method first.') - 630 if np.isclose(0.0, self._dvalue, atol=1e-15): - 631 raise Exception('Error is 0.0') - 632 labels = self.e_names - 633 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 - 634 fig1, ax1 = plt.subplots() - 635 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) - 636 ax1.axis('equal') - 637 plt.draw() - 638 if save: - 639 fig1.savefig(save) - 640 - 641 return dict(zip(self.e_names, sizes)) + 385 return gamma + 386 + 387 def details(self, ens_content=True): + 388 """Output detailed properties of the Obs. + 389 + 390 Parameters + 391 ---------- + 392 ens_content : bool + 393 print details about the ensembles and replica if true. + 394 """ + 395 if self.tag is not None: + 396 print("Description:", self.tag) + 397 if not hasattr(self, 'e_dvalue'): + 398 print('Result\t %3.8e' % (self.value)) + 399 else: + 400 if self.value == 0.0: + 401 percentage = np.nan + 402 else: + 403 percentage = np.abs(self._dvalue / self.value) * 100 + 404 print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage)) + 405 if len(self.e_names) > 1: + 406 print(' Ensemble errors:') + 407 e_content = self.e_content + 408 for e_name in self.mc_names: + 409 if isinstance(self.idl[e_content[e_name][0]], range): + 410 gap = self.idl[e_content[e_name][0]].step + 411 else: + 412 gap = np.min(np.diff(self.idl[e_content[e_name][0]])) + 413 + 414 if len(self.e_names) > 1: + 415 print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name])) + 416 tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name]) + 417 tau_string += f" in units of {gap} config" + 418 if gap > 1: + 419 tau_string += "s" + 420 if self.tau_exp[e_name] > 0: + 421 tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name]) + 422 else: + 423 tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name]) + 424 print(tau_string) + 425 for e_name in self.cov_names: + 426 print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name])) + 427 if ens_content is True: + 428 if len(self.e_names) == 1: + 429 print(self.N, 'samples in', len(self.e_names), 'ensemble:') + 430 else: + 431 print(self.N, 'samples in', len(self.e_names), 'ensembles:') + 432 my_string_list = [] + 433 for key, value in sorted(self.e_content.items()): + 434 if key not in self.covobs: + 435 my_string = ' ' + "\u00B7 Ensemble '" + key + "' " + 436 if len(value) == 1: + 437 my_string += f': {self.shape[value[0]]} configurations' + 438 if isinstance(self.idl[value[0]], range): + 439 my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')' + 440 else: + 441 my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})' + 442 else: + 443 sublist = [] + 444 for v in value: + 445 my_substring = ' ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' " + 446 my_substring += f': {self.shape[v]} configurations' + 447 if isinstance(self.idl[v], range): + 448 my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')' + 449 else: + 450 my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})' + 451 sublist.append(my_substring) + 452 + 453 my_string += '\n' + '\n'.join(sublist) + 454 else: + 455 my_string = ' ' + "\u00B7 Covobs '" + key + "' " + 456 my_string_list.append(my_string) + 457 print('\n'.join(my_string_list)) + 458 + 459 def reweight(self, weight): + 460 """Reweight the obs with given rewighting factors. + 461 + 462 Parameters + 463 ---------- + 464 weight : Obs + 465 Reweighting factor. An Observable that has to be defined on a superset of the + 466 configurations in obs[i].idl for all i. + 467 all_configs : bool + 468 if True, the reweighted observables are normalized by the average of + 469 the reweighting factor on all configurations in weight.idl and not + 470 on the configurations in obs[i].idl. Default False. + 471 """ + 472 return reweight(weight, [self])[0] + 473 + 474 def is_zero_within_error(self, sigma=1): + 475 """Checks whether the observable is zero within 'sigma' standard errors. + 476 + 477 Parameters + 478 ---------- + 479 sigma : int + 480 Number of standard errors used for the check. + 481 + 482 Works only properly when the gamma method was run. + 483 """ + 484 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue + 485 + 486 def is_zero(self, atol=1e-10): + 487 """Checks whether the observable is zero within a given tolerance. + 488 + 489 Parameters + 490 ---------- + 491 atol : float + 492 Absolute tolerance (for details see numpy documentation). + 493 """ + 494 return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values()) + 495 + 496 def plot_tauint(self, save=None): + 497 """Plot integrated autocorrelation time for each ensemble. + 498 + 499 Parameters + 500 ---------- + 501 save : str + 502 saves the figure to a file named 'save' if. + 503 """ + 504 if not hasattr(self, 'e_dvalue'): + 505 raise Exception('Run the gamma method first.') + 506 + 507 for e, e_name in enumerate(self.mc_names): + 508 fig = plt.figure() + 509 plt.xlabel(r'$W$') + 510 plt.ylabel(r'$\tau_\mathrm{int}$') + 511 length = int(len(self.e_n_tauint[e_name])) + 512 if self.tau_exp[e_name] > 0: + 513 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] + 514 x_help = np.arange(2 * self.tau_exp[e_name]) + 515 y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base + 516 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) + 517 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') + 518 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], + 519 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) + 520 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 + 521 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) + 522 else: + 523 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) + 524 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) + 525 + 526 plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label) + 527 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') + 528 plt.legend() + 529 plt.xlim(-0.5, xmax) + 530 ylim = plt.ylim() + 531 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) + 532 plt.draw() + 533 if save: + 534 fig.savefig(save + "_" + str(e)) + 535 + 536 def plot_rho(self, save=None): + 537 """Plot normalized autocorrelation function time for each ensemble. + 538 + 539 Parameters + 540 ---------- + 541 save : str + 542 saves the figure to a file named 'save' if. + 543 """ + 544 if not hasattr(self, 'e_dvalue'): + 545 raise Exception('Run the gamma method first.') + 546 for e, e_name in enumerate(self.mc_names): + 547 fig = plt.figure() + 548 plt.xlabel('W') + 549 plt.ylabel('rho') + 550 length = int(len(self.e_drho[e_name])) + 551 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) + 552 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') + 553 if self.tau_exp[e_name] > 0: + 554 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], + 555 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) + 556 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 + 557 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) + 558 else: + 559 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) + 560 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) + 561 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) + 562 plt.xlim(-0.5, xmax) + 563 plt.draw() + 564 if save: + 565 fig.savefig(save + "_" + str(e)) + 566 + 567 def plot_rep_dist(self): + 568 """Plot replica distribution for each ensemble with more than one replicum.""" + 569 if not hasattr(self, 'e_dvalue'): + 570 raise Exception('Run the gamma method first.') + 571 for e, e_name in enumerate(self.mc_names): + 572 if len(self.e_content[e_name]) == 1: + 573 print('No replica distribution for a single replicum (', e_name, ')') + 574 continue + 575 r_length = [] + 576 sub_r_mean = 0 + 577 for r, r_name in enumerate(self.e_content[e_name]): + 578 r_length.append(len(self.deltas[r_name])) + 579 sub_r_mean += self.shape[r_name] * self.r_values[r_name] + 580 e_N = np.sum(r_length) + 581 sub_r_mean /= e_N + 582 arr = np.zeros(len(self.e_content[e_name])) + 583 for r, r_name in enumerate(self.e_content[e_name]): + 584 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) + 585 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) + 586 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') + 587 plt.draw() + 588 + 589 def plot_history(self, expand=True): + 590 """Plot derived Monte Carlo history for each ensemble + 591 + 592 Parameters + 593 ---------- + 594 expand : bool + 595 show expanded history for irregular Monte Carlo chains (default: True). + 596 """ + 597 for e, e_name in enumerate(self.mc_names): + 598 plt.figure() + 599 r_length = [] + 600 tmp = [] + 601 tmp_expanded = [] + 602 for r, r_name in enumerate(self.e_content[e_name]): + 603 tmp.append(self.deltas[r_name] + self.r_values[r_name]) + 604 if expand: + 605 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) + 606 r_length.append(len(tmp_expanded[-1])) + 607 else: + 608 r_length.append(len(tmp[-1])) + 609 e_N = np.sum(r_length) + 610 x = np.arange(e_N) + 611 y_test = np.concatenate(tmp, axis=0) + 612 if expand: + 613 y = np.concatenate(tmp_expanded, axis=0) + 614 else: + 615 y = y_test + 616 plt.errorbar(x, y, fmt='.', markersize=3) + 617 plt.xlim(-0.5, e_N - 0.5) + 618 plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})') + 619 plt.draw() + 620 + 621 def plot_piechart(self, save=None): + 622 """Plot piechart which shows the fractional contribution of each + 623 ensemble to the error and returns a dictionary containing the fractions. + 624 + 625 Parameters + 626 ---------- + 627 save : str + 628 saves the figure to a file named 'save' if. + 629 """ + 630 if not hasattr(self, 'e_dvalue'): + 631 raise Exception('Run the gamma method first.') + 632 if np.isclose(0.0, self._dvalue, atol=1e-15): + 633 raise Exception('Error is 0.0') + 634 labels = self.e_names + 635 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 + 636 fig1, ax1 = plt.subplots() + 637 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) + 638 ax1.axis('equal') + 639 plt.draw() + 640 if save: + 641 fig1.savefig(save) 642 - 643 def dump(self, filename, datatype="json.gz", description="", **kwargs): - 644 """Dump the Obs to a file 'name' of chosen format. - 645 - 646 Parameters - 647 ---------- - 648 filename : str - 649 name of the file to be saved. - 650 datatype : str - 651 Format of the exported file. Supported formats include - 652 "json.gz" and "pickle" - 653 description : str - 654 Description for output file, only relevant for json.gz format. - 655 path : str - 656 specifies a custom path for the file (default '.') - 657 """ - 658 if 'path' in kwargs: - 659 file_name = kwargs.get('path') + '/' + filename - 660 else: - 661 file_name = filename - 662 - 663 if datatype == "json.gz": - 664 from .input.json import dump_to_json - 665 dump_to_json([self], file_name, description=description) - 666 elif datatype == "pickle": - 667 with open(file_name + '.p', 'wb') as fb: - 668 pickle.dump(self, fb) - 669 else: - 670 raise Exception("Unknown datatype " + str(datatype)) - 671 - 672 def export_jackknife(self): - 673 """Export jackknife samples from the Obs - 674 - 675 Returns - 676 ------- - 677 numpy.ndarray - 678 Returns a numpy array of length N + 1 where N is the number of samples - 679 for the given ensemble and replicum. The zeroth entry of the array contains - 680 the mean value of the Obs, entries 1 to N contain the N jackknife samples - 681 derived from the Obs. The current implementation only works for observables - 682 defined on exactly one ensemble and replicum. The derived jackknife samples - 683 should agree with samples from a full jackknife analysis up to O(1/N). - 684 """ - 685 - 686 if len(self.names) != 1: - 687 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") - 688 - 689 name = self.names[0] - 690 full_data = self.deltas[name] + self.r_values[name] - 691 n = full_data.size - 692 mean = self.value - 693 tmp_jacks = np.zeros(n + 1) - 694 tmp_jacks[0] = mean - 695 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) - 696 return tmp_jacks - 697 - 698 def __float__(self): - 699 return float(self.value) - 700 - 701 def __repr__(self): - 702 return 'Obs[' + str(self) + ']' - 703 - 704 def __str__(self): - 705 return _format_uncertainty(self.value, self._dvalue) - 706 - 707 def __hash__(self): - 708 hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),) - 709 hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()]) - 710 hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()]) - 711 hash_tuple += tuple([o.encode() for o in self.names]) - 712 m = hashlib.md5() - 713 [m.update(o) for o in hash_tuple] - 714 return int(m.hexdigest(), 16) & 0xFFFFFFFF - 715 - 716 # Overload comparisons - 717 def __lt__(self, other): - 718 return self.value < other - 719 - 720 def __le__(self, other): - 721 return self.value <= other - 722 - 723 def __gt__(self, other): - 724 return self.value > other - 725 - 726 def __ge__(self, other): - 727 return self.value >= other - 728 - 729 def __eq__(self, other): - 730 return (self - other).is_zero() - 731 - 732 def __ne__(self, other): - 733 return not (self - other).is_zero() - 734 - 735 # Overload math operations - 736 def __add__(self, y): - 737 if isinstance(y, Obs): - 738 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) - 739 else: - 740 if isinstance(y, np.ndarray): - 741 return np.array([self + o for o in y]) - 742 elif y.__class__.__name__ in ['Corr', 'CObs']: - 743 return NotImplemented - 744 else: - 745 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) - 746 - 747 def __radd__(self, y): - 748 return self + y - 749 - 750 def __mul__(self, y): - 751 if isinstance(y, Obs): - 752 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) - 753 else: - 754 if isinstance(y, np.ndarray): - 755 return np.array([self * o for o in y]) - 756 elif isinstance(y, complex): - 757 return CObs(self * y.real, self * y.imag) - 758 elif y.__class__.__name__ in ['Corr', 'CObs']: - 759 return NotImplemented - 760 else: - 761 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) - 762 - 763 def __rmul__(self, y): - 764 return self * y - 765 - 766 def __sub__(self, y): - 767 if isinstance(y, Obs): - 768 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) - 769 else: - 770 if isinstance(y, np.ndarray): - 771 return np.array([self - o for o in y]) - 772 elif y.__class__.__name__ in ['Corr', 'CObs']: - 773 return NotImplemented - 774 else: - 775 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) - 776 - 777 def __rsub__(self, y): - 778 return -1 * (self - y) - 779 - 780 def __pos__(self): - 781 return self - 782 - 783 def __neg__(self): - 784 return -1 * self - 785 - 786 def __truediv__(self, y): - 787 if isinstance(y, Obs): - 788 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) - 789 else: - 790 if isinstance(y, np.ndarray): - 791 return np.array([self / o for o in y]) - 792 elif y.__class__.__name__ in ['Corr', 'CObs']: - 793 return NotImplemented - 794 else: - 795 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) - 796 - 797 def __rtruediv__(self, y): - 798 if isinstance(y, Obs): - 799 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) - 800 else: - 801 if isinstance(y, np.ndarray): - 802 return np.array([o / self for o in y]) - 803 elif y.__class__.__name__ in ['Corr', 'CObs']: - 804 return NotImplemented - 805 else: - 806 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) - 807 - 808 def __pow__(self, y): - 809 if isinstance(y, Obs): - 810 return derived_observable(lambda x: x[0] ** x[1], [self, y]) - 811 else: - 812 return derived_observable(lambda x: x[0] ** y, [self]) - 813 - 814 def __rpow__(self, y): - 815 if isinstance(y, Obs): - 816 return derived_observable(lambda x: x[0] ** x[1], [y, self]) - 817 else: - 818 return derived_observable(lambda x: y ** x[0], [self]) - 819 - 820 def __abs__(self): - 821 return derived_observable(lambda x: anp.abs(x[0]), [self]) - 822 - 823 # Overload numpy functions - 824 def sqrt(self): - 825 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) - 826 - 827 def log(self): - 828 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) - 829 - 830 def exp(self): - 831 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) - 832 - 833 def sin(self): - 834 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) - 835 - 836 def cos(self): - 837 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) - 838 - 839 def tan(self): - 840 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) - 841 - 842 def arcsin(self): - 843 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) - 844 - 845 def arccos(self): - 846 return derived_observable(lambda x: anp.arccos(x[0]), [self]) - 847 - 848 def arctan(self): - 849 return derived_observable(lambda x: anp.arctan(x[0]), [self]) - 850 - 851 def sinh(self): - 852 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) - 853 - 854 def cosh(self): - 855 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) - 856 - 857 def tanh(self): - 858 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) - 859 - 860 def arcsinh(self): - 861 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) - 862 - 863 def arccosh(self): - 864 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) - 865 - 866 def arctanh(self): - 867 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) - 868 - 869 - 870class CObs: - 871 """Class for a complex valued observable.""" - 872 __slots__ = ['_real', '_imag', 'tag'] - 873 - 874 def __init__(self, real, imag=0.0): - 875 self._real = real - 876 self._imag = imag - 877 self.tag = None - 878 - 879 @property - 880 def real(self): - 881 return self._real - 882 - 883 @property - 884 def imag(self): - 885 return self._imag - 886 - 887 def gamma_method(self, **kwargs): - 888 """Executes the gamma_method for the real and the imaginary part.""" - 889 if isinstance(self.real, Obs): - 890 self.real.gamma_method(**kwargs) - 891 if isinstance(self.imag, Obs): - 892 self.imag.gamma_method(**kwargs) - 893 - 894 def is_zero(self): - 895 """Checks whether both real and imaginary part are zero within machine precision.""" - 896 return self.real == 0.0 and self.imag == 0.0 - 897 - 898 def conjugate(self): - 899 return CObs(self.real, -self.imag) - 900 - 901 def __add__(self, other): - 902 if isinstance(other, np.ndarray): - 903 return other + self - 904 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 905 return CObs(self.real + other.real, - 906 self.imag + other.imag) - 907 else: - 908 return CObs(self.real + other, self.imag) - 909 - 910 def __radd__(self, y): - 911 return self + y - 912 - 913 def __sub__(self, other): - 914 if isinstance(other, np.ndarray): - 915 return -1 * (other - self) - 916 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 917 return CObs(self.real - other.real, self.imag - other.imag) - 918 else: - 919 return CObs(self.real - other, self.imag) - 920 - 921 def __rsub__(self, other): - 922 return -1 * (self - other) - 923 - 924 def __mul__(self, other): - 925 if isinstance(other, np.ndarray): - 926 return other * self - 927 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 928 if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]): - 929 return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3], - 930 [self.real, other.real, self.imag, other.imag], - 931 man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]), - 932 derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3], - 933 [self.real, other.real, self.imag, other.imag], - 934 man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value])) - 935 elif getattr(other, 'imag', 0) != 0: - 936 return CObs(self.real * other.real - self.imag * other.imag, - 937 self.imag * other.real + self.real * other.imag) - 938 else: - 939 return CObs(self.real * other.real, self.imag * other.real) - 940 else: - 941 return CObs(self.real * other, self.imag * other) - 942 - 943 def __rmul__(self, other): - 944 return self * other - 945 - 946 def __truediv__(self, other): - 947 if isinstance(other, np.ndarray): - 948 return 1 / (other / self) - 949 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 950 r = other.real ** 2 + other.imag ** 2 - 951 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r) - 952 else: - 953 return CObs(self.real / other, self.imag / other) - 954 - 955 def __rtruediv__(self, other): - 956 r = self.real ** 2 + self.imag ** 2 - 957 if hasattr(other, 'real') and hasattr(other, 'imag'): - 958 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r) - 959 else: - 960 return CObs(self.real * other / r, -self.imag * other / r) - 961 - 962 def __abs__(self): - 963 return np.sqrt(self.real**2 + self.imag**2) - 964 - 965 def __pos__(self): - 966 return self - 967 - 968 def __neg__(self): - 969 return -1 * self - 970 - 971 def __eq__(self, other): - 972 return self.real == other.real and self.imag == other.imag - 973 - 974 def __str__(self): - 975 return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)' - 976 - 977 def __repr__(self): - 978 return 'CObs[' + str(self) + ']' - 979 - 980 - 981def _format_uncertainty(value, dvalue): - 982 """Creates a string of a value and its error in paranthesis notation, e.g., 13.02(45)""" - 983 if dvalue == 0.0: - 984 return str(value) - 985 fexp = np.floor(np.log10(dvalue)) - 986 if fexp < 0.0: - 987 return '{:{form}}({:2.0f})'.format(value, dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') - 988 elif fexp == 0.0: - 989 return '{:.1f}({:1.1f})'.format(value, dvalue) - 990 else: - 991 return '{:.0f}({:2.0f})'.format(value, dvalue) - 992 - 993 - 994def _expand_deltas(deltas, idx, shape): - 995 """Expand deltas defined on idx to a regular, contiguous range, where holes are filled by 0. - 996 If idx is of type range, the deltas are not changed - 997 - 998 Parameters - 999 ---------- -1000 deltas : list -1001 List of fluctuations -1002 idx : list -1003 List or range of configs on which the deltas are defined, has to be sorted in ascending order. -1004 shape : int -1005 Number of configs in idx. -1006 """ -1007 if isinstance(idx, range): -1008 return deltas -1009 else: -1010 ret = np.zeros(idx[-1] - idx[0] + 1) -1011 for i in range(shape): -1012 ret[idx[i] - idx[0]] = deltas[i] -1013 return ret -1014 -1015 -1016def _merge_idx(idl): -1017 """Returns the union of all lists in idl as sorted list -1018 -1019 Parameters -1020 ---------- -1021 idl : list -1022 List of lists or ranges. -1023 """ -1024 -1025 # Use groupby to efficiently check whether all elements of idl are identical -1026 try: -1027 g = groupby(idl) -1028 if next(g, True) and not next(g, False): -1029 return idl[0] -1030 except Exception: -1031 pass -1032 -1033 if np.all([type(idx) is range for idx in idl]): -1034 if len(set([idx[0] for idx in idl])) == 1: -1035 idstart = min([idx.start for idx in idl]) -1036 idstop = max([idx.stop for idx in idl]) -1037 idstep = min([idx.step for idx in idl]) -1038 return range(idstart, idstop, idstep) -1039 -1040 return sorted(set().union(*idl)) + 643 return dict(zip(self.e_names, sizes)) + 644 + 645 def dump(self, filename, datatype="json.gz", description="", **kwargs): + 646 """Dump the Obs to a file 'name' of chosen format. + 647 + 648 Parameters + 649 ---------- + 650 filename : str + 651 name of the file to be saved. + 652 datatype : str + 653 Format of the exported file. Supported formats include + 654 "json.gz" and "pickle" + 655 description : str + 656 Description for output file, only relevant for json.gz format. + 657 path : str + 658 specifies a custom path for the file (default '.') + 659 """ + 660 if 'path' in kwargs: + 661 file_name = kwargs.get('path') + '/' + filename + 662 else: + 663 file_name = filename + 664 + 665 if datatype == "json.gz": + 666 from .input.json import dump_to_json + 667 dump_to_json([self], file_name, description=description) + 668 elif datatype == "pickle": + 669 with open(file_name + '.p', 'wb') as fb: + 670 pickle.dump(self, fb) + 671 else: + 672 raise Exception("Unknown datatype " + str(datatype)) + 673 + 674 def export_jackknife(self): + 675 """Export jackknife samples from the Obs + 676 + 677 Returns + 678 ------- + 679 numpy.ndarray + 680 Returns a numpy array of length N + 1 where N is the number of samples + 681 for the given ensemble and replicum. The zeroth entry of the array contains + 682 the mean value of the Obs, entries 1 to N contain the N jackknife samples + 683 derived from the Obs. The current implementation only works for observables + 684 defined on exactly one ensemble and replicum. The derived jackknife samples + 685 should agree with samples from a full jackknife analysis up to O(1/N). + 686 """ + 687 + 688 if len(self.names) != 1: + 689 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") + 690 + 691 name = self.names[0] + 692 full_data = self.deltas[name] + self.r_values[name] + 693 n = full_data.size + 694 mean = self.value + 695 tmp_jacks = np.zeros(n + 1) + 696 tmp_jacks[0] = mean + 697 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) + 698 return tmp_jacks + 699 + 700 def __float__(self): + 701 return float(self.value) + 702 + 703 def __repr__(self): + 704 return 'Obs[' + str(self) + ']' + 705 + 706 def __str__(self): + 707 return _format_uncertainty(self.value, self._dvalue) + 708 + 709 def __hash__(self): + 710 hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),) + 711 hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()]) + 712 hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()]) + 713 hash_tuple += tuple([o.encode() for o in self.names]) + 714 m = hashlib.md5() + 715 [m.update(o) for o in hash_tuple] + 716 return int(m.hexdigest(), 16) & 0xFFFFFFFF + 717 + 718 # Overload comparisons + 719 def __lt__(self, other): + 720 return self.value < other + 721 + 722 def __le__(self, other): + 723 return self.value <= other + 724 + 725 def __gt__(self, other): + 726 return self.value > other + 727 + 728 def __ge__(self, other): + 729 return self.value >= other + 730 + 731 def __eq__(self, other): + 732 return (self - other).is_zero() + 733 + 734 def __ne__(self, other): + 735 return not (self - other).is_zero() + 736 + 737 # Overload math operations + 738 def __add__(self, y): + 739 if isinstance(y, Obs): + 740 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) + 741 else: + 742 if isinstance(y, np.ndarray): + 743 return np.array([self + o for o in y]) + 744 elif y.__class__.__name__ in ['Corr', 'CObs']: + 745 return NotImplemented + 746 else: + 747 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) + 748 + 749 def __radd__(self, y): + 750 return self + y + 751 + 752 def __mul__(self, y): + 753 if isinstance(y, Obs): + 754 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) + 755 else: + 756 if isinstance(y, np.ndarray): + 757 return np.array([self * o for o in y]) + 758 elif isinstance(y, complex): + 759 return CObs(self * y.real, self * y.imag) + 760 elif y.__class__.__name__ in ['Corr', 'CObs']: + 761 return NotImplemented + 762 else: + 763 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) + 764 + 765 def __rmul__(self, y): + 766 return self * y + 767 + 768 def __sub__(self, y): + 769 if isinstance(y, Obs): + 770 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) + 771 else: + 772 if isinstance(y, np.ndarray): + 773 return np.array([self - o for o in y]) + 774 elif y.__class__.__name__ in ['Corr', 'CObs']: + 775 return NotImplemented + 776 else: + 777 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) + 778 + 779 def __rsub__(self, y): + 780 return -1 * (self - y) + 781 + 782 def __pos__(self): + 783 return self + 784 + 785 def __neg__(self): + 786 return -1 * self + 787 + 788 def __truediv__(self, y): + 789 if isinstance(y, Obs): + 790 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) + 791 else: + 792 if isinstance(y, np.ndarray): + 793 return np.array([self / o for o in y]) + 794 elif y.__class__.__name__ in ['Corr', 'CObs']: + 795 return NotImplemented + 796 else: + 797 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) + 798 + 799 def __rtruediv__(self, y): + 800 if isinstance(y, Obs): + 801 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) + 802 else: + 803 if isinstance(y, np.ndarray): + 804 return np.array([o / self for o in y]) + 805 elif y.__class__.__name__ in ['Corr', 'CObs']: + 806 return NotImplemented + 807 else: + 808 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) + 809 + 810 def __pow__(self, y): + 811 if isinstance(y, Obs): + 812 return derived_observable(lambda x: x[0] ** x[1], [self, y]) + 813 else: + 814 return derived_observable(lambda x: x[0] ** y, [self]) + 815 + 816 def __rpow__(self, y): + 817 if isinstance(y, Obs): + 818 return derived_observable(lambda x: x[0] ** x[1], [y, self]) + 819 else: + 820 return derived_observable(lambda x: y ** x[0], [self]) + 821 + 822 def __abs__(self): + 823 return derived_observable(lambda x: anp.abs(x[0]), [self]) + 824 + 825 # Overload numpy functions + 826 def sqrt(self): + 827 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) + 828 + 829 def log(self): + 830 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) + 831 + 832 def exp(self): + 833 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) + 834 + 835 def sin(self): + 836 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) + 837 + 838 def cos(self): + 839 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) + 840 + 841 def tan(self): + 842 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) + 843 + 844 def arcsin(self): + 845 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) + 846 + 847 def arccos(self): + 848 return derived_observable(lambda x: anp.arccos(x[0]), [self]) + 849 + 850 def arctan(self): + 851 return derived_observable(lambda x: anp.arctan(x[0]), [self]) + 852 + 853 def sinh(self): + 854 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) + 855 + 856 def cosh(self): + 857 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) + 858 + 859 def tanh(self): + 860 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) + 861 + 862 def arcsinh(self): + 863 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) + 864 + 865 def arccosh(self): + 866 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) + 867 + 868 def arctanh(self): + 869 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) + 870 + 871 + 872class CObs: + 873 """Class for a complex valued observable.""" + 874 __slots__ = ['_real', '_imag', 'tag'] + 875 + 876 def __init__(self, real, imag=0.0): + 877 self._real = real + 878 self._imag = imag + 879 self.tag = None + 880 + 881 @property + 882 def real(self): + 883 return self._real + 884 + 885 @property + 886 def imag(self): + 887 return self._imag + 888 + 889 def gamma_method(self, **kwargs): + 890 """Executes the gamma_method for the real and the imaginary part.""" + 891 if isinstance(self.real, Obs): + 892 self.real.gamma_method(**kwargs) + 893 if isinstance(self.imag, Obs): + 894 self.imag.gamma_method(**kwargs) + 895 + 896 def is_zero(self): + 897 """Checks whether both real and imaginary part are zero within machine precision.""" + 898 return self.real == 0.0 and self.imag == 0.0 + 899 + 900 def conjugate(self): + 901 return CObs(self.real, -self.imag) + 902 + 903 def __add__(self, other): + 904 if isinstance(other, np.ndarray): + 905 return other + self + 906 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 907 return CObs(self.real + other.real, + 908 self.imag + other.imag) + 909 else: + 910 return CObs(self.real + other, self.imag) + 911 + 912 def __radd__(self, y): + 913 return self + y + 914 + 915 def __sub__(self, other): + 916 if isinstance(other, np.ndarray): + 917 return -1 * (other - self) + 918 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 919 return CObs(self.real - other.real, self.imag - other.imag) + 920 else: + 921 return CObs(self.real - other, self.imag) + 922 + 923 def __rsub__(self, other): + 924 return -1 * (self - other) + 925 + 926 def __mul__(self, other): + 927 if isinstance(other, np.ndarray): + 928 return other * self + 929 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 930 if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]): + 931 return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3], + 932 [self.real, other.real, self.imag, other.imag], + 933 man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]), + 934 derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3], + 935 [self.real, other.real, self.imag, other.imag], + 936 man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value])) + 937 elif getattr(other, 'imag', 0) != 0: + 938 return CObs(self.real * other.real - self.imag * other.imag, + 939 self.imag * other.real + self.real * other.imag) + 940 else: + 941 return CObs(self.real * other.real, self.imag * other.real) + 942 else: + 943 return CObs(self.real * other, self.imag * other) + 944 + 945 def __rmul__(self, other): + 946 return self * other + 947 + 948 def __truediv__(self, other): + 949 if isinstance(other, np.ndarray): + 950 return 1 / (other / self) + 951 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 952 r = other.real ** 2 + other.imag ** 2 + 953 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r) + 954 else: + 955 return CObs(self.real / other, self.imag / other) + 956 + 957 def __rtruediv__(self, other): + 958 r = self.real ** 2 + self.imag ** 2 + 959 if hasattr(other, 'real') and hasattr(other, 'imag'): + 960 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r) + 961 else: + 962 return CObs(self.real * other / r, -self.imag * other / r) + 963 + 964 def __abs__(self): + 965 return np.sqrt(self.real**2 + self.imag**2) + 966 + 967 def __pos__(self): + 968 return self + 969 + 970 def __neg__(self): + 971 return -1 * self + 972 + 973 def __eq__(self, other): + 974 return self.real == other.real and self.imag == other.imag + 975 + 976 def __str__(self): + 977 return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)' + 978 + 979 def __repr__(self): + 980 return 'CObs[' + str(self) + ']' + 981 + 982 + 983def _format_uncertainty(value, dvalue): + 984 """Creates a string of a value and its error in paranthesis notation, e.g., 13.02(45)""" + 985 if dvalue == 0.0: + 986 return str(value) + 987 fexp = np.floor(np.log10(dvalue)) + 988 if fexp < 0.0: + 989 return '{:{form}}({:2.0f})'.format(value, dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') + 990 elif fexp == 0.0: + 991 return '{:.1f}({:1.1f})'.format(value, dvalue) + 992 else: + 993 return '{:.0f}({:2.0f})'.format(value, dvalue) + 994 + 995 + 996def _expand_deltas(deltas, idx, shape): + 997 """Expand deltas defined on idx to a regular, contiguous range, where holes are filled by 0. + 998 If idx is of type range, the deltas are not changed + 999 +1000 Parameters +1001 ---------- +1002 deltas : list +1003 List of fluctuations +1004 idx : list +1005 List or range of configs on which the deltas are defined, has to be sorted in ascending order. +1006 shape : int +1007 Number of configs in idx. +1008 """ +1009 if isinstance(idx, range): +1010 return deltas +1011 else: +1012 ret = np.zeros(idx[-1] - idx[0] + 1) +1013 for i in range(shape): +1014 ret[idx[i] - idx[0]] = deltas[i] +1015 return ret +1016 +1017 +1018def _merge_idx(idl): +1019 """Returns the union of all lists in idl as sorted list +1020 +1021 Parameters +1022 ---------- +1023 idl : list +1024 List of lists or ranges. +1025 """ +1026 +1027 # Use groupby to efficiently check whether all elements of idl are identical +1028 try: +1029 g = groupby(idl) +1030 if next(g, True) and not next(g, False): +1031 return idl[0] +1032 except Exception: +1033 pass +1034 +1035 if np.all([type(idx) is range for idx in idl]): +1036 if len(set([idx[0] for idx in idl])) == 1: +1037 idstart = min([idx.start for idx in idl]) +1038 idstop = max([idx.stop for idx in idl]) +1039 idstep = min([idx.step for idx in idl]) +1040 return range(idstart, idstop, idstep) 1041 -1042 -1043def _intersection_idx(idl): -1044 """Returns the intersection of all lists in idl as sorted list -1045 -1046 Parameters -1047 ---------- -1048 idl : list -1049 List of lists or ranges. -1050 """ -1051 -1052 def _lcm(*args): -1053 """Returns the lowest common multiple of args. -1054 -1055 From python 3.9 onwards the math library contains an lcm function.""" -1056 return reduce(lambda a, b: a * b // gcd(a, b), args) -1057 -1058 # Use groupby to efficiently check whether all elements of idl are identical -1059 try: -1060 g = groupby(idl) -1061 if next(g, True) and not next(g, False): -1062 return idl[0] -1063 except Exception: -1064 pass -1065 -1066 if np.all([type(idx) is range for idx in idl]): -1067 if len(set([idx[0] for idx in idl])) == 1: -1068 idstart = max([idx.start for idx in idl]) -1069 idstop = min([idx.stop for idx in idl]) -1070 idstep = _lcm(*[idx.step for idx in idl]) -1071 return range(idstart, idstop, idstep) -1072 -1073 return sorted(set.intersection(*[set(o) for o in idl])) +1042 return sorted(set().union(*idl)) +1043 +1044 +1045def _intersection_idx(idl): +1046 """Returns the intersection of all lists in idl as sorted list +1047 +1048 Parameters +1049 ---------- +1050 idl : list +1051 List of lists or ranges. +1052 """ +1053 +1054 def _lcm(*args): +1055 """Returns the lowest common multiple of args. +1056 +1057 From python 3.9 onwards the math library contains an lcm function.""" +1058 return reduce(lambda a, b: a * b // gcd(a, b), args) +1059 +1060 # Use groupby to efficiently check whether all elements of idl are identical +1061 try: +1062 g = groupby(idl) +1063 if next(g, True) and not next(g, False): +1064 return idl[0] +1065 except Exception: +1066 pass +1067 +1068 if np.all([type(idx) is range for idx in idl]): +1069 if len(set([idx[0] for idx in idl])) == 1: +1070 idstart = max([idx.start for idx in idl]) +1071 idstop = min([idx.stop for idx in idl]) +1072 idstep = _lcm(*[idx.step for idx in idl]) +1073 return range(idstart, idstop, idstep) 1074 -1075 -1076def _expand_deltas_for_merge(deltas, idx, shape, new_idx): -1077 """Expand deltas defined on idx to the list of configs that is defined by new_idx. -1078 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest -1079 common divisor of the step sizes is used as new step size. -1080 -1081 Parameters -1082 ---------- -1083 deltas : list -1084 List of fluctuations -1085 idx : list -1086 List or range of configs on which the deltas are defined. -1087 Has to be a subset of new_idx and has to be sorted in ascending order. -1088 shape : list -1089 Number of configs in idx. -1090 new_idx : list -1091 List of configs that defines the new range, has to be sorted in ascending order. -1092 """ -1093 -1094 if type(idx) is range and type(new_idx) is range: -1095 if idx == new_idx: -1096 return deltas -1097 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) -1098 for i in range(shape): -1099 ret[idx[i] - new_idx[0]] = deltas[i] -1100 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) -1101 -1102 -1103def _filter_zeroes(deltas, idx, eps=Obs.filter_eps): -1104 """Filter out all configurations with vanishing fluctuation such that they do not -1105 contribute to the error estimate anymore. Returns the new deltas and -1106 idx according to the filtering. -1107 A fluctuation is considered to be vanishing, if it is smaller than eps times -1108 the mean of the absolute values of all deltas in one list. -1109 -1110 Parameters -1111 ---------- -1112 deltas : list -1113 List of fluctuations -1114 idx : list -1115 List or ranges of configs on which the deltas are defined. -1116 eps : float -1117 Prefactor that enters the filter criterion. -1118 """ -1119 new_deltas = [] -1120 new_idx = [] -1121 maxd = np.mean(np.fabs(deltas)) -1122 for i in range(len(deltas)): -1123 if abs(deltas[i]) > eps * maxd: -1124 new_deltas.append(deltas[i]) -1125 new_idx.append(idx[i]) -1126 if new_idx: -1127 return np.array(new_deltas), new_idx -1128 else: -1129 return deltas, idx -1130 -1131 -1132def derived_observable(func, data, array_mode=False, **kwargs): -1133 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. -1134 -1135 Parameters -1136 ---------- -1137 func : object -1138 arbitrary function of the form func(data, **kwargs). For the -1139 automatic differentiation to work, all numpy functions have to have -1140 the autograd wrapper (use 'import autograd.numpy as anp'). -1141 data : list -1142 list of Obs, e.g. [obs1, obs2, obs3]. -1143 num_grad : bool -1144 if True, numerical derivatives are used instead of autograd -1145 (default False). To control the numerical differentiation the -1146 kwargs of numdifftools.step_generators.MaxStepGenerator -1147 can be used. -1148 man_grad : list -1149 manually supply a list or an array which contains the jacobian -1150 of func. Use cautiously, supplying the wrong derivative will -1151 not be intercepted. -1152 -1153 Notes -1154 ----- -1155 For simple mathematical operations it can be practical to use anonymous -1156 functions. For the ratio of two observables one can e.g. use -1157 -1158 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) -1159 """ -1160 -1161 data = np.asarray(data) -1162 raveled_data = data.ravel() -1163 -1164 # Workaround for matrix operations containing non Obs data -1165 if not all(isinstance(x, Obs) for x in raveled_data): -1166 for i in range(len(raveled_data)): -1167 if isinstance(raveled_data[i], (int, float)): -1168 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") -1169 -1170 allcov = {} -1171 for o in raveled_data: -1172 for name in o.cov_names: -1173 if name in allcov: -1174 if not np.allclose(allcov[name], o.covobs[name].cov): -1175 raise Exception('Inconsistent covariance matrices for %s!' % (name)) -1176 else: -1177 allcov[name] = o.covobs[name].cov -1178 -1179 n_obs = len(raveled_data) -1180 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) -1181 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) -1182 new_sample_names = sorted(set(new_names) - set(new_cov_names)) -1183 -1184 is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names} -1185 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 -1186 -1187 if data.ndim == 1: -1188 values = np.array([o.value for o in data]) -1189 else: -1190 values = np.vectorize(lambda x: x.value)(data) -1191 -1192 new_values = func(values, **kwargs) +1075 return sorted(set.intersection(*[set(o) for o in idl])) +1076 +1077 +1078def _expand_deltas_for_merge(deltas, idx, shape, new_idx): +1079 """Expand deltas defined on idx to the list of configs that is defined by new_idx. +1080 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest +1081 common divisor of the step sizes is used as new step size. +1082 +1083 Parameters +1084 ---------- +1085 deltas : list +1086 List of fluctuations +1087 idx : list +1088 List or range of configs on which the deltas are defined. +1089 Has to be a subset of new_idx and has to be sorted in ascending order. +1090 shape : list +1091 Number of configs in idx. +1092 new_idx : list +1093 List of configs that defines the new range, has to be sorted in ascending order. +1094 """ +1095 +1096 if type(idx) is range and type(new_idx) is range: +1097 if idx == new_idx: +1098 return deltas +1099 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) +1100 for i in range(shape): +1101 ret[idx[i] - new_idx[0]] = deltas[i] +1102 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) +1103 +1104 +1105def _filter_zeroes(deltas, idx, eps=Obs.filter_eps): +1106 """Filter out all configurations with vanishing fluctuation such that they do not +1107 contribute to the error estimate anymore. Returns the new deltas and +1108 idx according to the filtering. +1109 A fluctuation is considered to be vanishing, if it is smaller than eps times +1110 the mean of the absolute values of all deltas in one list. +1111 +1112 Parameters +1113 ---------- +1114 deltas : list +1115 List of fluctuations +1116 idx : list +1117 List or ranges of configs on which the deltas are defined. +1118 eps : float +1119 Prefactor that enters the filter criterion. +1120 """ +1121 new_deltas = [] +1122 new_idx = [] +1123 maxd = np.mean(np.fabs(deltas)) +1124 for i in range(len(deltas)): +1125 if abs(deltas[i]) > eps * maxd: +1126 new_deltas.append(deltas[i]) +1127 new_idx.append(idx[i]) +1128 if new_idx: +1129 return np.array(new_deltas), new_idx +1130 else: +1131 return deltas, idx +1132 +1133 +1134def derived_observable(func, data, array_mode=False, **kwargs): +1135 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. +1136 +1137 Parameters +1138 ---------- +1139 func : object +1140 arbitrary function of the form func(data, **kwargs). For the +1141 automatic differentiation to work, all numpy functions have to have +1142 the autograd wrapper (use 'import autograd.numpy as anp'). +1143 data : list +1144 list of Obs, e.g. [obs1, obs2, obs3]. +1145 num_grad : bool +1146 if True, numerical derivatives are used instead of autograd +1147 (default False). To control the numerical differentiation the +1148 kwargs of numdifftools.step_generators.MaxStepGenerator +1149 can be used. +1150 man_grad : list +1151 manually supply a list or an array which contains the jacobian +1152 of func. Use cautiously, supplying the wrong derivative will +1153 not be intercepted. +1154 +1155 Notes +1156 ----- +1157 For simple mathematical operations it can be practical to use anonymous +1158 functions. For the ratio of two observables one can e.g. use +1159 +1160 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) +1161 """ +1162 +1163 data = np.asarray(data) +1164 raveled_data = data.ravel() +1165 +1166 # Workaround for matrix operations containing non Obs data +1167 if not all(isinstance(x, Obs) for x in raveled_data): +1168 for i in range(len(raveled_data)): +1169 if isinstance(raveled_data[i], (int, float)): +1170 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") +1171 +1172 allcov = {} +1173 for o in raveled_data: +1174 for name in o.cov_names: +1175 if name in allcov: +1176 if not np.allclose(allcov[name], o.covobs[name].cov): +1177 raise Exception('Inconsistent covariance matrices for %s!' % (name)) +1178 else: +1179 allcov[name] = o.covobs[name].cov +1180 +1181 n_obs = len(raveled_data) +1182 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) +1183 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) +1184 new_sample_names = sorted(set(new_names) - set(new_cov_names)) +1185 +1186 is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names} +1187 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 +1188 +1189 if data.ndim == 1: +1190 values = np.array([o.value for o in data]) +1191 else: +1192 values = np.vectorize(lambda x: x.value)(data) 1193 -1194 multi = int(isinstance(new_values, np.ndarray)) +1194 new_values = func(values, **kwargs) 1195 -1196 new_r_values = {} -1197 new_idl_d = {} -1198 for name in new_sample_names: -1199 idl = [] -1200 tmp_values = np.zeros(n_obs) -1201 for i, item in enumerate(raveled_data): -1202 tmp_values[i] = item.r_values.get(name, item.value) -1203 tmp_idl = item.idl.get(name) -1204 if tmp_idl is not None: -1205 idl.append(tmp_idl) -1206 if multi > 0: -1207 tmp_values = np.array(tmp_values).reshape(data.shape) -1208 new_r_values[name] = func(tmp_values, **kwargs) -1209 new_idl_d[name] = _merge_idx(idl) -1210 if not is_merged[name]: -1211 is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]]))) -1212 -1213 if 'man_grad' in kwargs: -1214 deriv = np.asarray(kwargs.get('man_grad')) -1215 if new_values.shape + data.shape != deriv.shape: -1216 raise Exception('Manual derivative does not have correct shape.') -1217 elif kwargs.get('num_grad') is True: -1218 if multi > 0: -1219 raise Exception('Multi mode currently not supported for numerical derivative') -1220 options = { -1221 'base_step': 0.1, -1222 'step_ratio': 2.5} -1223 for key in options.keys(): -1224 kwarg = kwargs.get(key) -1225 if kwarg is not None: -1226 options[key] = kwarg -1227 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) -1228 if tmp_df.size == 1: -1229 deriv = np.array([tmp_df.real]) -1230 else: -1231 deriv = tmp_df.real -1232 else: -1233 deriv = jacobian(func)(values, **kwargs) -1234 -1235 final_result = np.zeros(new_values.shape, dtype=object) +1196 multi = int(isinstance(new_values, np.ndarray)) +1197 +1198 new_r_values = {} +1199 new_idl_d = {} +1200 for name in new_sample_names: +1201 idl = [] +1202 tmp_values = np.zeros(n_obs) +1203 for i, item in enumerate(raveled_data): +1204 tmp_values[i] = item.r_values.get(name, item.value) +1205 tmp_idl = item.idl.get(name) +1206 if tmp_idl is not None: +1207 idl.append(tmp_idl) +1208 if multi > 0: +1209 tmp_values = np.array(tmp_values).reshape(data.shape) +1210 new_r_values[name] = func(tmp_values, **kwargs) +1211 new_idl_d[name] = _merge_idx(idl) +1212 if not is_merged[name]: +1213 is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]]))) +1214 +1215 if 'man_grad' in kwargs: +1216 deriv = np.asarray(kwargs.get('man_grad')) +1217 if new_values.shape + data.shape != deriv.shape: +1218 raise Exception('Manual derivative does not have correct shape.') +1219 elif kwargs.get('num_grad') is True: +1220 if multi > 0: +1221 raise Exception('Multi mode currently not supported for numerical derivative') +1222 options = { +1223 'base_step': 0.1, +1224 'step_ratio': 2.5} +1225 for key in options.keys(): +1226 kwarg = kwargs.get(key) +1227 if kwarg is not None: +1228 options[key] = kwarg +1229 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) +1230 if tmp_df.size == 1: +1231 deriv = np.array([tmp_df.real]) +1232 else: +1233 deriv = tmp_df.real +1234 else: +1235 deriv = jacobian(func)(values, **kwargs) 1236 -1237 if array_mode is True: +1237 final_result = np.zeros(new_values.shape, dtype=object) 1238 -1239 class _Zero_grad(): -1240 def __init__(self, N): -1241 self.grad = np.zeros((N, 1)) -1242 -1243 new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x])) -1244 d_extracted = {} -1245 g_extracted = {} -1246 for name in new_sample_names: -1247 d_extracted[name] = [] -1248 ens_length = len(new_idl_d[name]) -1249 for i_dat, dat in enumerate(data): -1250 d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, ))) -1251 for name in new_cov_names: -1252 g_extracted[name] = [] -1253 zero_grad = _Zero_grad(new_covobs_lengths[name]) -1254 for i_dat, dat in enumerate(data): -1255 g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1))) -1256 -1257 for i_val, new_val in np.ndenumerate(new_values): -1258 new_deltas = {} -1259 new_grad = {} -1260 if array_mode is True: -1261 for name in new_sample_names: -1262 ens_length = d_extracted[name][0].shape[-1] -1263 new_deltas[name] = np.zeros(ens_length) -1264 for i_dat, dat in enumerate(d_extracted[name]): -1265 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1266 for name in new_cov_names: -1267 new_grad[name] = 0 -1268 for i_dat, dat in enumerate(g_extracted[name]): -1269 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1270 else: -1271 for j_obs, obs in np.ndenumerate(data): -1272 for name in obs.names: -1273 if name in obs.cov_names: -1274 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad -1275 else: -1276 new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name]) -1277 -1278 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} +1239 if array_mode is True: +1240 +1241 class _Zero_grad(): +1242 def __init__(self, N): +1243 self.grad = np.zeros((N, 1)) +1244 +1245 new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x])) +1246 d_extracted = {} +1247 g_extracted = {} +1248 for name in new_sample_names: +1249 d_extracted[name] = [] +1250 ens_length = len(new_idl_d[name]) +1251 for i_dat, dat in enumerate(data): +1252 d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, ))) +1253 for name in new_cov_names: +1254 g_extracted[name] = [] +1255 zero_grad = _Zero_grad(new_covobs_lengths[name]) +1256 for i_dat, dat in enumerate(data): +1257 g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1))) +1258 +1259 for i_val, new_val in np.ndenumerate(new_values): +1260 new_deltas = {} +1261 new_grad = {} +1262 if array_mode is True: +1263 for name in new_sample_names: +1264 ens_length = d_extracted[name][0].shape[-1] +1265 new_deltas[name] = np.zeros(ens_length) +1266 for i_dat, dat in enumerate(d_extracted[name]): +1267 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1268 for name in new_cov_names: +1269 new_grad[name] = 0 +1270 for i_dat, dat in enumerate(g_extracted[name]): +1271 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1272 else: +1273 for j_obs, obs in np.ndenumerate(data): +1274 for name in obs.names: +1275 if name in obs.cov_names: +1276 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad +1277 else: +1278 new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name]) 1279 -1280 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): -1281 raise Exception('The same name has been used for deltas and covobs!') -1282 new_samples = [] -1283 new_means = [] -1284 new_idl = [] -1285 new_names_obs = [] -1286 for name in new_names: -1287 if name not in new_covobs: -1288 if is_merged[name]: -1289 filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name]) -1290 else: -1291 filtered_deltas = new_deltas[name] -1292 filtered_idl_d = new_idl_d[name] -1293 -1294 new_samples.append(filtered_deltas) -1295 new_idl.append(filtered_idl_d) -1296 new_means.append(new_r_values[name][i_val]) -1297 new_names_obs.append(name) -1298 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) -1299 for name in new_covobs: -1300 final_result[i_val].names.append(name) -1301 final_result[i_val]._covobs = new_covobs -1302 final_result[i_val]._value = new_val -1303 final_result[i_val].is_merged = is_merged -1304 final_result[i_val].reweighted = reweighted -1305 -1306 if multi == 0: -1307 final_result = final_result.item() -1308 -1309 return final_result +1280 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} +1281 +1282 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): +1283 raise Exception('The same name has been used for deltas and covobs!') +1284 new_samples = [] +1285 new_means = [] +1286 new_idl = [] +1287 new_names_obs = [] +1288 for name in new_names: +1289 if name not in new_covobs: +1290 if is_merged[name]: +1291 filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name]) +1292 else: +1293 filtered_deltas = new_deltas[name] +1294 filtered_idl_d = new_idl_d[name] +1295 +1296 new_samples.append(filtered_deltas) +1297 new_idl.append(filtered_idl_d) +1298 new_means.append(new_r_values[name][i_val]) +1299 new_names_obs.append(name) +1300 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) +1301 for name in new_covobs: +1302 final_result[i_val].names.append(name) +1303 final_result[i_val]._covobs = new_covobs +1304 final_result[i_val]._value = new_val +1305 final_result[i_val].is_merged = is_merged +1306 final_result[i_val].reweighted = reweighted +1307 +1308 if multi == 0: +1309 final_result = final_result.item() 1310 -1311 -1312def _reduce_deltas(deltas, idx_old, idx_new): -1313 """Extract deltas defined on idx_old on all configs of idx_new. -1314 -1315 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they -1316 are ordered in an ascending order. -1317 -1318 Parameters -1319 ---------- -1320 deltas : list -1321 List of fluctuations -1322 idx_old : list -1323 List or range of configs on which the deltas are defined -1324 idx_new : list -1325 List of configs for which we want to extract the deltas. -1326 Has to be a subset of idx_old. -1327 """ -1328 if not len(deltas) == len(idx_old): -1329 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) -1330 if type(idx_old) is range and type(idx_new) is range: -1331 if idx_old == idx_new: -1332 return deltas -1333 # Use groupby to efficiently check whether all elements of idx_old and idx_new are identical -1334 try: -1335 g = groupby([idx_old, idx_new]) -1336 if next(g, True) and not next(g, False): -1337 return deltas -1338 except Exception: -1339 pass -1340 indices = np.intersect1d(idx_old, idx_new, assume_unique=True, return_indices=True)[1] -1341 if len(indices) < len(idx_new): -1342 raise Exception('Error in _reduce_deltas: Config of idx_new not in idx_old') -1343 return np.array(deltas)[indices] -1344 -1345 -1346def reweight(weight, obs, **kwargs): -1347 """Reweight a list of observables. -1348 -1349 Parameters -1350 ---------- -1351 weight : Obs -1352 Reweighting factor. An Observable that has to be defined on a superset of the -1353 configurations in obs[i].idl for all i. -1354 obs : list -1355 list of Obs, e.g. [obs1, obs2, obs3]. -1356 all_configs : bool -1357 if True, the reweighted observables are normalized by the average of -1358 the reweighting factor on all configurations in weight.idl and not -1359 on the configurations in obs[i].idl. Default False. -1360 """ -1361 result = [] -1362 for i in range(len(obs)): -1363 if len(obs[i].cov_names): -1364 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') -1365 if not set(obs[i].names).issubset(weight.names): -1366 raise Exception('Error: Ensembles do not fit') -1367 for name in obs[i].names: -1368 if not set(obs[i].idl[name]).issubset(weight.idl[name]): -1369 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) -1370 new_samples = [] -1371 w_deltas = {} -1372 for name in sorted(obs[i].names): -1373 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) -1374 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) -1375 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) -1376 -1377 if kwargs.get('all_configs'): -1378 new_weight = weight -1379 else: -1380 new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) -1381 -1382 result.append(tmp_obs / new_weight) -1383 result[-1].reweighted = True -1384 result[-1].is_merged = obs[i].is_merged -1385 -1386 return result +1311 return final_result +1312 +1313 +1314def _reduce_deltas(deltas, idx_old, idx_new): +1315 """Extract deltas defined on idx_old on all configs of idx_new. +1316 +1317 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they +1318 are ordered in an ascending order. +1319 +1320 Parameters +1321 ---------- +1322 deltas : list +1323 List of fluctuations +1324 idx_old : list +1325 List or range of configs on which the deltas are defined +1326 idx_new : list +1327 List of configs for which we want to extract the deltas. +1328 Has to be a subset of idx_old. +1329 """ +1330 if not len(deltas) == len(idx_old): +1331 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) +1332 if type(idx_old) is range and type(idx_new) is range: +1333 if idx_old == idx_new: +1334 return deltas +1335 # Use groupby to efficiently check whether all elements of idx_old and idx_new are identical +1336 try: +1337 g = groupby([idx_old, idx_new]) +1338 if next(g, True) and not next(g, False): +1339 return deltas +1340 except Exception: +1341 pass +1342 indices = np.intersect1d(idx_old, idx_new, assume_unique=True, return_indices=True)[1] +1343 if len(indices) < len(idx_new): +1344 raise Exception('Error in _reduce_deltas: Config of idx_new not in idx_old') +1345 return np.array(deltas)[indices] +1346 +1347 +1348def reweight(weight, obs, **kwargs): +1349 """Reweight a list of observables. +1350 +1351 Parameters +1352 ---------- +1353 weight : Obs +1354 Reweighting factor. An Observable that has to be defined on a superset of the +1355 configurations in obs[i].idl for all i. +1356 obs : list +1357 list of Obs, e.g. [obs1, obs2, obs3]. +1358 all_configs : bool +1359 if True, the reweighted observables are normalized by the average of +1360 the reweighting factor on all configurations in weight.idl and not +1361 on the configurations in obs[i].idl. Default False. +1362 """ +1363 result = [] +1364 for i in range(len(obs)): +1365 if len(obs[i].cov_names): +1366 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') +1367 if not set(obs[i].names).issubset(weight.names): +1368 raise Exception('Error: Ensembles do not fit') +1369 for name in obs[i].names: +1370 if not set(obs[i].idl[name]).issubset(weight.idl[name]): +1371 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) +1372 new_samples = [] +1373 w_deltas = {} +1374 for name in sorted(obs[i].names): +1375 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) +1376 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) +1377 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) +1378 +1379 if kwargs.get('all_configs'): +1380 new_weight = weight +1381 else: +1382 new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) +1383 +1384 result.append(tmp_obs / new_weight) +1385 result[-1].reweighted = True +1386 result[-1].is_merged = obs[i].is_merged 1387 -1388 -1389def correlate(obs_a, obs_b): -1390 """Correlate two observables. -1391 -1392 Parameters -1393 ---------- -1394 obs_a : Obs -1395 First observable -1396 obs_b : Obs -1397 Second observable -1398 -1399 Notes -1400 ----- -1401 Keep in mind to only correlate primary observables which have not been reweighted -1402 yet. The reweighting has to be applied after correlating the observables. -1403 Currently only works if ensembles are identical (this is not strictly necessary). -1404 """ -1405 -1406 if sorted(obs_a.names) != sorted(obs_b.names): -1407 raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}") -1408 if len(obs_a.cov_names) or len(obs_b.cov_names): -1409 raise Exception('Error: Not possible to correlate Obs that contain covobs!') -1410 for name in obs_a.names: -1411 if obs_a.shape[name] != obs_b.shape[name]: -1412 raise Exception('Shapes of ensemble', name, 'do not fit') -1413 if obs_a.idl[name] != obs_b.idl[name]: -1414 raise Exception('idl of ensemble', name, 'do not fit') -1415 -1416 if obs_a.reweighted is True: -1417 warnings.warn("The first observable is already reweighted.", RuntimeWarning) -1418 if obs_b.reweighted is True: -1419 warnings.warn("The second observable is already reweighted.", RuntimeWarning) -1420 -1421 new_samples = [] -1422 new_idl = [] -1423 for name in sorted(obs_a.names): -1424 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) -1425 new_idl.append(obs_a.idl[name]) -1426 -1427 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) -1428 o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names} -1429 o.reweighted = obs_a.reweighted or obs_b.reweighted -1430 return o -1431 -1432 -1433def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): -1434 r'''Calculates the error covariance matrix of a set of observables. -1435 -1436 WARNING: This function should be used with care, especially for observables with support on multiple -1437 ensembles with differing autocorrelations. See the notes below for details. -1438 -1439 The gamma method has to be applied first to all observables. +1388 return result +1389 +1390 +1391def correlate(obs_a, obs_b): +1392 """Correlate two observables. +1393 +1394 Parameters +1395 ---------- +1396 obs_a : Obs +1397 First observable +1398 obs_b : Obs +1399 Second observable +1400 +1401 Notes +1402 ----- +1403 Keep in mind to only correlate primary observables which have not been reweighted +1404 yet. The reweighting has to be applied after correlating the observables. +1405 Currently only works if ensembles are identical (this is not strictly necessary). +1406 """ +1407 +1408 if sorted(obs_a.names) != sorted(obs_b.names): +1409 raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}") +1410 if len(obs_a.cov_names) or len(obs_b.cov_names): +1411 raise Exception('Error: Not possible to correlate Obs that contain covobs!') +1412 for name in obs_a.names: +1413 if obs_a.shape[name] != obs_b.shape[name]: +1414 raise Exception('Shapes of ensemble', name, 'do not fit') +1415 if obs_a.idl[name] != obs_b.idl[name]: +1416 raise Exception('idl of ensemble', name, 'do not fit') +1417 +1418 if obs_a.reweighted is True: +1419 warnings.warn("The first observable is already reweighted.", RuntimeWarning) +1420 if obs_b.reweighted is True: +1421 warnings.warn("The second observable is already reweighted.", RuntimeWarning) +1422 +1423 new_samples = [] +1424 new_idl = [] +1425 for name in sorted(obs_a.names): +1426 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) +1427 new_idl.append(obs_a.idl[name]) +1428 +1429 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) +1430 o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names} +1431 o.reweighted = obs_a.reweighted or obs_b.reweighted +1432 return o +1433 +1434 +1435def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): +1436 r'''Calculates the error covariance matrix of a set of observables. +1437 +1438 WARNING: This function should be used with care, especially for observables with support on multiple +1439 ensembles with differing autocorrelations. See the notes below for details. 1440 -1441 Parameters -1442 ---------- -1443 obs : list or numpy.ndarray -1444 List or one dimensional array of Obs -1445 visualize : bool -1446 If True plots the corresponding normalized correlation matrix (default False). -1447 correlation : bool -1448 If True the correlation matrix instead of the error covariance matrix is returned (default False). -1449 smooth : None or int -1450 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue -1451 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the -1452 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely -1453 small ones. -1454 -1455 Notes -1456 ----- -1457 The error covariance is defined such that it agrees with the squared standard error for two identical observables -1458 $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$ -1459 in the absence of autocorrelation. -1460 The 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 -1461 $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. -1462 For 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. -1463 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ -1464 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). -1465 ''' -1466 -1467 length = len(obs) +1441 The gamma method has to be applied first to all observables. +1442 +1443 Parameters +1444 ---------- +1445 obs : list or numpy.ndarray +1446 List or one dimensional array of Obs +1447 visualize : bool +1448 If True plots the corresponding normalized correlation matrix (default False). +1449 correlation : bool +1450 If True the correlation matrix instead of the error covariance matrix is returned (default False). +1451 smooth : None or int +1452 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue +1453 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the +1454 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely +1455 small ones. +1456 +1457 Notes +1458 ----- +1459 The error covariance is defined such that it agrees with the squared standard error for two identical observables +1460 $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$ +1461 in the absence of autocorrelation. +1462 The 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 +1463 $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. +1464 For 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. +1465 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ +1466 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). +1467 ''' 1468 -1469 max_samples = np.max([o.N for o in obs]) -1470 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: -1471 warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning) -1472 -1473 cov = np.zeros((length, length)) -1474 for i in range(length): -1475 for j in range(i, length): -1476 cov[i, j] = _covariance_element(obs[i], obs[j]) -1477 cov = cov + cov.T - np.diag(np.diag(cov)) -1478 -1479 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) +1469 length = len(obs) +1470 +1471 max_samples = np.max([o.N for o in obs]) +1472 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: +1473 warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning) +1474 +1475 cov = np.zeros((length, length)) +1476 for i in range(length): +1477 for j in range(i, length): +1478 cov[i, j] = _covariance_element(obs[i], obs[j]) +1479 cov = cov + cov.T - np.diag(np.diag(cov)) 1480 -1481 if isinstance(smooth, int): -1482 corr = _smooth_eigenvalues(corr, smooth) -1483 -1484 if visualize: -1485 plt.matshow(corr, vmin=-1, vmax=1) -1486 plt.set_cmap('RdBu') -1487 plt.colorbar() -1488 plt.draw() -1489 -1490 if correlation is True: -1491 return corr -1492 -1493 errors = [o.dvalue for o in obs] -1494 cov = np.diag(errors) @ corr @ np.diag(errors) -1495 -1496 eigenvalues = np.linalg.eigh(cov)[0] -1497 if not np.all(eigenvalues >= 0): -1498 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) -1499 -1500 return cov +1481 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) +1482 +1483 if isinstance(smooth, int): +1484 corr = _smooth_eigenvalues(corr, smooth) +1485 +1486 if visualize: +1487 plt.matshow(corr, vmin=-1, vmax=1) +1488 plt.set_cmap('RdBu') +1489 plt.colorbar() +1490 plt.draw() +1491 +1492 if correlation is True: +1493 return corr +1494 +1495 errors = [o.dvalue for o in obs] +1496 cov = np.diag(errors) @ corr @ np.diag(errors) +1497 +1498 eigenvalues = np.linalg.eigh(cov)[0] +1499 if not np.all(eigenvalues >= 0): +1500 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) 1501 -1502 -1503def _smooth_eigenvalues(corr, E): -1504 """Eigenvalue smoothing as described in hep-lat/9412087 -1505 -1506 corr : np.ndarray -1507 correlation matrix -1508 E : integer -1509 Number of eigenvalues to be left substantially unchanged -1510 """ -1511 if not (2 < E < corr.shape[0] - 1): -1512 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") -1513 vals, vec = np.linalg.eigh(corr) -1514 lambda_min = np.mean(vals[:-E]) -1515 vals[vals < lambda_min] = lambda_min -1516 vals /= np.mean(vals) -1517 return vec @ np.diag(vals) @ vec.T -1518 -1519 -1520def _covariance_element(obs1, obs2): -1521 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" -1522 -1523 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): -1524 deltas1 = _reduce_deltas(deltas1, idx1, new_idx) -1525 deltas2 = _reduce_deltas(deltas2, idx2, new_idx) -1526 return np.sum(deltas1 * deltas2) -1527 -1528 if set(obs1.names).isdisjoint(set(obs2.names)): -1529 return 0.0 -1530 -1531 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): -1532 raise Exception('The gamma method has to be applied to both Obs first.') -1533 -1534 dvalue = 0.0 +1502 return cov +1503 +1504 +1505def _smooth_eigenvalues(corr, E): +1506 """Eigenvalue smoothing as described in hep-lat/9412087 +1507 +1508 corr : np.ndarray +1509 correlation matrix +1510 E : integer +1511 Number of eigenvalues to be left substantially unchanged +1512 """ +1513 if not (2 < E < corr.shape[0] - 1): +1514 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") +1515 vals, vec = np.linalg.eigh(corr) +1516 lambda_min = np.mean(vals[:-E]) +1517 vals[vals < lambda_min] = lambda_min +1518 vals /= np.mean(vals) +1519 return vec @ np.diag(vals) @ vec.T +1520 +1521 +1522def _covariance_element(obs1, obs2): +1523 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" +1524 +1525 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): +1526 deltas1 = _reduce_deltas(deltas1, idx1, new_idx) +1527 deltas2 = _reduce_deltas(deltas2, idx2, new_idx) +1528 return np.sum(deltas1 * deltas2) +1529 +1530 if set(obs1.names).isdisjoint(set(obs2.names)): +1531 return 0.0 +1532 +1533 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): +1534 raise Exception('The gamma method has to be applied to both Obs first.') 1535 -1536 for e_name in obs1.mc_names: +1536 dvalue = 0.0 1537 -1538 if e_name not in obs2.mc_names: -1539 continue -1540 -1541 idl_d = {} -1542 for r_name in obs1.e_content[e_name]: -1543 if r_name not in obs2.e_content[e_name]: -1544 continue -1545 idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]]) -1546 -1547 gamma = 0.0 +1538 for e_name in obs1.mc_names: +1539 +1540 if e_name not in obs2.mc_names: +1541 continue +1542 +1543 idl_d = {} +1544 for r_name in obs1.e_content[e_name]: +1545 if r_name not in obs2.e_content[e_name]: +1546 continue +1547 idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]]) 1548 -1549 for r_name in obs1.e_content[e_name]: -1550 if r_name not in obs2.e_content[e_name]: -1551 continue -1552 if len(idl_d[r_name]) == 0: +1549 gamma = 0.0 +1550 +1551 for r_name in obs1.e_content[e_name]: +1552 if r_name not in obs2.e_content[e_name]: 1553 continue -1554 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) -1555 -1556 if gamma == 0.0: -1557 continue -1558 -1559 gamma_div = 0.0 -1560 for r_name in obs1.e_content[e_name]: -1561 if r_name not in obs2.e_content[e_name]: -1562 continue -1563 if len(idl_d[r_name]) == 0: +1554 if len(idl_d[r_name]) == 0: +1555 continue +1556 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) +1557 +1558 if gamma == 0.0: +1559 continue +1560 +1561 gamma_div = 0.0 +1562 for r_name in obs1.e_content[e_name]: +1563 if r_name not in obs2.e_content[e_name]: 1564 continue -1565 gamma_div += np.sqrt(calc_gamma(obs1.deltas[r_name], obs1.deltas[r_name], obs1.idl[r_name], obs1.idl[r_name], idl_d[r_name]) * calc_gamma(obs2.deltas[r_name], obs2.deltas[r_name], obs2.idl[r_name], obs2.idl[r_name], idl_d[r_name])) -1566 gamma /= gamma_div -1567 -1568 dvalue += gamma +1565 if len(idl_d[r_name]) == 0: +1566 continue +1567 gamma_div += np.sqrt(calc_gamma(obs1.deltas[r_name], obs1.deltas[r_name], obs1.idl[r_name], obs1.idl[r_name], idl_d[r_name]) * calc_gamma(obs2.deltas[r_name], obs2.deltas[r_name], obs2.idl[r_name], obs2.idl[r_name], idl_d[r_name])) +1568 gamma /= gamma_div 1569 -1570 for e_name in obs1.cov_names: +1570 dvalue += gamma 1571 -1572 if e_name not in obs2.cov_names: -1573 continue -1574 -1575 dvalue += float(np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad))) +1572 for e_name in obs1.cov_names: +1573 +1574 if e_name not in obs2.cov_names: +1575 continue 1576 -1577 return dvalue +1577 dvalue += float(np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad))) 1578 -1579 -1580def import_jackknife(jacks, name, idl=None): -1581 """Imports jackknife samples and returns an Obs -1582 -1583 Parameters -1584 ---------- -1585 jacks : numpy.ndarray -1586 numpy array containing the mean value as zeroth entry and -1587 the N jackknife samples as first to Nth entry. -1588 name : str -1589 name of the ensemble the samples are defined on. -1590 """ -1591 length = len(jacks) - 1 -1592 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) -1593 samples = jacks[1:] @ prj -1594 mean = np.mean(samples) -1595 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) -1596 new_obs._value = jacks[0] -1597 return new_obs -1598 -1599 -1600def merge_obs(list_of_obs): -1601 """Combine all observables in list_of_obs into one new observable -1602 -1603 Parameters -1604 ---------- -1605 list_of_obs : list -1606 list of the Obs object to be combined -1607 -1608 Notes -1609 ----- -1610 It is not possible to combine obs which are based on the same replicum -1611 """ -1612 replist = [item for obs in list_of_obs for item in obs.names] -1613 if (len(replist) == len(set(replist))) is False: -1614 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) -1615 if any([len(o.cov_names) for o in list_of_obs]): -1616 raise Exception('Not possible to merge data that contains covobs!') -1617 new_dict = {} -1618 idl_dict = {} -1619 for o in list_of_obs: -1620 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) -1621 for key in set(o.deltas) | set(o.r_values)}) -1622 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) -1623 -1624 names = sorted(new_dict.keys()) -1625 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) -1626 o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names} -1627 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) -1628 return o -1629 -1630 -1631def cov_Obs(means, cov, name, grad=None): -1632 """Create an Obs based on mean(s) and a covariance matrix -1633 -1634 Parameters -1635 ---------- -1636 mean : list of floats or float -1637 N mean value(s) of the new Obs -1638 cov : list or array -1639 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance -1640 name : str -1641 identifier for the covariance matrix -1642 grad : list or array -1643 Gradient of the Covobs wrt. the means belonging to cov. -1644 """ -1645 -1646 def covobs_to_obs(co): -1647 """Make an Obs out of a Covobs -1648 -1649 Parameters -1650 ---------- -1651 co : Covobs -1652 Covobs to be embedded into the Obs -1653 """ -1654 o = Obs([], [], means=[]) -1655 o._value = co.value -1656 o.names.append(co.name) -1657 o._covobs[co.name] = co -1658 o._dvalue = np.sqrt(co.errsq()) -1659 return o -1660 -1661 ol = [] -1662 if isinstance(means, (float, int)): -1663 means = [means] -1664 -1665 for i in range(len(means)): -1666 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) -1667 if ol[0].covobs[name].N != len(means): -1668 raise Exception('You have to provide %d mean values!' % (ol[0].N)) -1669 if len(ol) == 1: -1670 return ol[0] -1671 return ol +1579 return dvalue +1580 +1581 +1582def import_jackknife(jacks, name, idl=None): +1583 """Imports jackknife samples and returns an Obs +1584 +1585 Parameters +1586 ---------- +1587 jacks : numpy.ndarray +1588 numpy array containing the mean value as zeroth entry and +1589 the N jackknife samples as first to Nth entry. +1590 name : str +1591 name of the ensemble the samples are defined on. +1592 """ +1593 length = len(jacks) - 1 +1594 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) +1595 samples = jacks[1:] @ prj +1596 mean = np.mean(samples) +1597 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) +1598 new_obs._value = jacks[0] +1599 return new_obs +1600 +1601 +1602def merge_obs(list_of_obs): +1603 """Combine all observables in list_of_obs into one new observable +1604 +1605 Parameters +1606 ---------- +1607 list_of_obs : list +1608 list of the Obs object to be combined +1609 +1610 Notes +1611 ----- +1612 It is not possible to combine obs which are based on the same replicum +1613 """ +1614 replist = [item for obs in list_of_obs for item in obs.names] +1615 if (len(replist) == len(set(replist))) is False: +1616 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) +1617 if any([len(o.cov_names) for o in list_of_obs]): +1618 raise Exception('Not possible to merge data that contains covobs!') +1619 new_dict = {} +1620 idl_dict = {} +1621 for o in list_of_obs: +1622 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) +1623 for key in set(o.deltas) | set(o.r_values)}) +1624 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) +1625 +1626 names = sorted(new_dict.keys()) +1627 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) +1628 o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names} +1629 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) +1630 return o +1631 +1632 +1633def cov_Obs(means, cov, name, grad=None): +1634 """Create an Obs based on mean(s) and a covariance matrix +1635 +1636 Parameters +1637 ---------- +1638 mean : list of floats or float +1639 N mean value(s) of the new Obs +1640 cov : list or array +1641 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance +1642 name : str +1643 identifier for the covariance matrix +1644 grad : list or array +1645 Gradient of the Covobs wrt. the means belonging to cov. +1646 """ +1647 +1648 def covobs_to_obs(co): +1649 """Make an Obs out of a Covobs +1650 +1651 Parameters +1652 ---------- +1653 co : Covobs +1654 Covobs to be embedded into the Obs +1655 """ +1656 o = Obs([], [], means=[]) +1657 o._value = co.value +1658 o.names.append(co.name) +1659 o._covobs[co.name] = co +1660 o._dvalue = np.sqrt(co.errsq()) +1661 return o +1662 +1663 ol = [] +1664 if isinstance(means, (float, int)): +1665 means = [means] +1666 +1667 for i in range(len(means)): +1668 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) +1669 if ol[0].covobs[name].N != len(means): +1670 raise Exception('You have to provide %d mean values!' % (ol[0].N)) +1671 if len(ol) == 1: +1672 return ol[0] +1673 return ol @@ -2221,522 +2226,524 @@ 350 self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue 351 return 352 -353 def _calc_gamma(self, deltas, idx, shape, w_max, fft): -354 """Calculate Gamma_{AA} from the deltas, which are defined on idx. -355 idx is assumed to be a contiguous range (possibly with a stepsize != 1) -356 -357 Parameters -358 ---------- -359 deltas : list -360 List of fluctuations -361 idx : list -362 List or range of configurations on which the deltas are defined. -363 shape : int -364 Number of configurations in idx. -365 w_max : int -366 Upper bound for the summation window. -367 fft : bool -368 determines whether the fft algorithm is used for the computation -369 of the autocorrelation function. -370 """ -371 gamma = np.zeros(w_max) -372 deltas = _expand_deltas(deltas, idx, shape) -373 new_shape = len(deltas) -374 if fft: -375 max_gamma = min(new_shape, w_max) -376 # The padding for the fft has to be even -377 padding = new_shape + max_gamma + (new_shape + max_gamma) % 2 -378 gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma] -379 else: -380 for n in range(w_max): -381 if new_shape - n >= 0: -382 gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape]) -383 -384 return gamma +353 gm = gamma_method +354 +355 def _calc_gamma(self, deltas, idx, shape, w_max, fft): +356 """Calculate Gamma_{AA} from the deltas, which are defined on idx. +357 idx is assumed to be a contiguous range (possibly with a stepsize != 1) +358 +359 Parameters +360 ---------- +361 deltas : list +362 List of fluctuations +363 idx : list +364 List or range of configurations on which the deltas are defined. +365 shape : int +366 Number of configurations in idx. +367 w_max : int +368 Upper bound for the summation window. +369 fft : bool +370 determines whether the fft algorithm is used for the computation +371 of the autocorrelation function. +372 """ +373 gamma = np.zeros(w_max) +374 deltas = _expand_deltas(deltas, idx, shape) +375 new_shape = len(deltas) +376 if fft: +377 max_gamma = min(new_shape, w_max) +378 # The padding for the fft has to be even +379 padding = new_shape + max_gamma + (new_shape + max_gamma) % 2 +380 gamma[:max_gamma] += np.fft.irfft(np.abs(np.fft.rfft(deltas, padding)) ** 2)[:max_gamma] +381 else: +382 for n in range(w_max): +383 if new_shape - n >= 0: +384 gamma[n] += deltas[0:new_shape - n].dot(deltas[n:new_shape]) 385 -386 def details(self, ens_content=True): -387 """Output detailed properties of the Obs. -388 -389 Parameters -390 ---------- -391 ens_content : bool -392 print details about the ensembles and replica if true. -393 """ -394 if self.tag is not None: -395 print("Description:", self.tag) -396 if not hasattr(self, 'e_dvalue'): -397 print('Result\t %3.8e' % (self.value)) -398 else: -399 if self.value == 0.0: -400 percentage = np.nan -401 else: -402 percentage = np.abs(self._dvalue / self.value) * 100 -403 print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage)) -404 if len(self.e_names) > 1: -405 print(' Ensemble errors:') -406 e_content = self.e_content -407 for e_name in self.mc_names: -408 if isinstance(self.idl[e_content[e_name][0]], range): -409 gap = self.idl[e_content[e_name][0]].step -410 else: -411 gap = np.min(np.diff(self.idl[e_content[e_name][0]])) -412 -413 if len(self.e_names) > 1: -414 print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name])) -415 tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name]) -416 tau_string += f" in units of {gap} config" -417 if gap > 1: -418 tau_string += "s" -419 if self.tau_exp[e_name] > 0: -420 tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name]) -421 else: -422 tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name]) -423 print(tau_string) -424 for e_name in self.cov_names: -425 print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name])) -426 if ens_content is True: -427 if len(self.e_names) == 1: -428 print(self.N, 'samples in', len(self.e_names), 'ensemble:') -429 else: -430 print(self.N, 'samples in', len(self.e_names), 'ensembles:') -431 my_string_list = [] -432 for key, value in sorted(self.e_content.items()): -433 if key not in self.covobs: -434 my_string = ' ' + "\u00B7 Ensemble '" + key + "' " -435 if len(value) == 1: -436 my_string += f': {self.shape[value[0]]} configurations' -437 if isinstance(self.idl[value[0]], range): -438 my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')' -439 else: -440 my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})' -441 else: -442 sublist = [] -443 for v in value: -444 my_substring = ' ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' " -445 my_substring += f': {self.shape[v]} configurations' -446 if isinstance(self.idl[v], range): -447 my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')' -448 else: -449 my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})' -450 sublist.append(my_substring) -451 -452 my_string += '\n' + '\n'.join(sublist) -453 else: -454 my_string = ' ' + "\u00B7 Covobs '" + key + "' " -455 my_string_list.append(my_string) -456 print('\n'.join(my_string_list)) -457 -458 def reweight(self, weight): -459 """Reweight the obs with given rewighting factors. -460 -461 Parameters -462 ---------- -463 weight : Obs -464 Reweighting factor. An Observable that has to be defined on a superset of the -465 configurations in obs[i].idl for all i. -466 all_configs : bool -467 if True, the reweighted observables are normalized by the average of -468 the reweighting factor on all configurations in weight.idl and not -469 on the configurations in obs[i].idl. Default False. -470 """ -471 return reweight(weight, [self])[0] -472 -473 def is_zero_within_error(self, sigma=1): -474 """Checks whether the observable is zero within 'sigma' standard errors. -475 -476 Parameters -477 ---------- -478 sigma : int -479 Number of standard errors used for the check. -480 -481 Works only properly when the gamma method was run. -482 """ -483 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue -484 -485 def is_zero(self, atol=1e-10): -486 """Checks whether the observable is zero within a given tolerance. -487 -488 Parameters -489 ---------- -490 atol : float -491 Absolute tolerance (for details see numpy documentation). -492 """ -493 return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values()) -494 -495 def plot_tauint(self, save=None): -496 """Plot integrated autocorrelation time for each ensemble. -497 -498 Parameters -499 ---------- -500 save : str -501 saves the figure to a file named 'save' if. -502 """ -503 if not hasattr(self, 'e_dvalue'): -504 raise Exception('Run the gamma method first.') -505 -506 for e, e_name in enumerate(self.mc_names): -507 fig = plt.figure() -508 plt.xlabel(r'$W$') -509 plt.ylabel(r'$\tau_\mathrm{int}$') -510 length = int(len(self.e_n_tauint[e_name])) -511 if self.tau_exp[e_name] > 0: -512 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] -513 x_help = np.arange(2 * self.tau_exp[e_name]) -514 y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base -515 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) -516 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') -517 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], -518 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) -519 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 -520 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) -521 else: -522 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) -523 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) -524 -525 plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label) -526 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') -527 plt.legend() -528 plt.xlim(-0.5, xmax) -529 ylim = plt.ylim() -530 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) -531 plt.draw() -532 if save: -533 fig.savefig(save + "_" + str(e)) -534 -535 def plot_rho(self, save=None): -536 """Plot normalized autocorrelation function time for each ensemble. -537 -538 Parameters -539 ---------- -540 save : str -541 saves the figure to a file named 'save' if. -542 """ -543 if not hasattr(self, 'e_dvalue'): -544 raise Exception('Run the gamma method first.') -545 for e, e_name in enumerate(self.mc_names): -546 fig = plt.figure() -547 plt.xlabel('W') -548 plt.ylabel('rho') -549 length = int(len(self.e_drho[e_name])) -550 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) -551 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') -552 if self.tau_exp[e_name] > 0: -553 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], -554 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) -555 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 -556 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) -557 else: -558 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) -559 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) -560 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) -561 plt.xlim(-0.5, xmax) -562 plt.draw() -563 if save: -564 fig.savefig(save + "_" + str(e)) -565 -566 def plot_rep_dist(self): -567 """Plot replica distribution for each ensemble with more than one replicum.""" -568 if not hasattr(self, 'e_dvalue'): -569 raise Exception('Run the gamma method first.') -570 for e, e_name in enumerate(self.mc_names): -571 if len(self.e_content[e_name]) == 1: -572 print('No replica distribution for a single replicum (', e_name, ')') -573 continue -574 r_length = [] -575 sub_r_mean = 0 -576 for r, r_name in enumerate(self.e_content[e_name]): -577 r_length.append(len(self.deltas[r_name])) -578 sub_r_mean += self.shape[r_name] * self.r_values[r_name] -579 e_N = np.sum(r_length) -580 sub_r_mean /= e_N -581 arr = np.zeros(len(self.e_content[e_name])) -582 for r, r_name in enumerate(self.e_content[e_name]): -583 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) -584 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) -585 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') -586 plt.draw() -587 -588 def plot_history(self, expand=True): -589 """Plot derived Monte Carlo history for each ensemble -590 -591 Parameters -592 ---------- -593 expand : bool -594 show expanded history for irregular Monte Carlo chains (default: True). -595 """ -596 for e, e_name in enumerate(self.mc_names): -597 plt.figure() -598 r_length = [] -599 tmp = [] -600 tmp_expanded = [] -601 for r, r_name in enumerate(self.e_content[e_name]): -602 tmp.append(self.deltas[r_name] + self.r_values[r_name]) -603 if expand: -604 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) -605 r_length.append(len(tmp_expanded[-1])) -606 else: -607 r_length.append(len(tmp[-1])) -608 e_N = np.sum(r_length) -609 x = np.arange(e_N) -610 y_test = np.concatenate(tmp, axis=0) -611 if expand: -612 y = np.concatenate(tmp_expanded, axis=0) -613 else: -614 y = y_test -615 plt.errorbar(x, y, fmt='.', markersize=3) -616 plt.xlim(-0.5, e_N - 0.5) -617 plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})') -618 plt.draw() -619 -620 def plot_piechart(self, save=None): -621 """Plot piechart which shows the fractional contribution of each -622 ensemble to the error and returns a dictionary containing the fractions. -623 -624 Parameters -625 ---------- -626 save : str -627 saves the figure to a file named 'save' if. -628 """ -629 if not hasattr(self, 'e_dvalue'): -630 raise Exception('Run the gamma method first.') -631 if np.isclose(0.0, self._dvalue, atol=1e-15): -632 raise Exception('Error is 0.0') -633 labels = self.e_names -634 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 -635 fig1, ax1 = plt.subplots() -636 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) -637 ax1.axis('equal') -638 plt.draw() -639 if save: -640 fig1.savefig(save) -641 -642 return dict(zip(self.e_names, sizes)) +386 return gamma +387 +388 def details(self, ens_content=True): +389 """Output detailed properties of the Obs. +390 +391 Parameters +392 ---------- +393 ens_content : bool +394 print details about the ensembles and replica if true. +395 """ +396 if self.tag is not None: +397 print("Description:", self.tag) +398 if not hasattr(self, 'e_dvalue'): +399 print('Result\t %3.8e' % (self.value)) +400 else: +401 if self.value == 0.0: +402 percentage = np.nan +403 else: +404 percentage = np.abs(self._dvalue / self.value) * 100 +405 print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage)) +406 if len(self.e_names) > 1: +407 print(' Ensemble errors:') +408 e_content = self.e_content +409 for e_name in self.mc_names: +410 if isinstance(self.idl[e_content[e_name][0]], range): +411 gap = self.idl[e_content[e_name][0]].step +412 else: +413 gap = np.min(np.diff(self.idl[e_content[e_name][0]])) +414 +415 if len(self.e_names) > 1: +416 print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name])) +417 tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name]) +418 tau_string += f" in units of {gap} config" +419 if gap > 1: +420 tau_string += "s" +421 if self.tau_exp[e_name] > 0: +422 tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name]) +423 else: +424 tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name]) +425 print(tau_string) +426 for e_name in self.cov_names: +427 print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name])) +428 if ens_content is True: +429 if len(self.e_names) == 1: +430 print(self.N, 'samples in', len(self.e_names), 'ensemble:') +431 else: +432 print(self.N, 'samples in', len(self.e_names), 'ensembles:') +433 my_string_list = [] +434 for key, value in sorted(self.e_content.items()): +435 if key not in self.covobs: +436 my_string = ' ' + "\u00B7 Ensemble '" + key + "' " +437 if len(value) == 1: +438 my_string += f': {self.shape[value[0]]} configurations' +439 if isinstance(self.idl[value[0]], range): +440 my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')' +441 else: +442 my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})' +443 else: +444 sublist = [] +445 for v in value: +446 my_substring = ' ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' " +447 my_substring += f': {self.shape[v]} configurations' +448 if isinstance(self.idl[v], range): +449 my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')' +450 else: +451 my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})' +452 sublist.append(my_substring) +453 +454 my_string += '\n' + '\n'.join(sublist) +455 else: +456 my_string = ' ' + "\u00B7 Covobs '" + key + "' " +457 my_string_list.append(my_string) +458 print('\n'.join(my_string_list)) +459 +460 def reweight(self, weight): +461 """Reweight the obs with given rewighting factors. +462 +463 Parameters +464 ---------- +465 weight : Obs +466 Reweighting factor. An Observable that has to be defined on a superset of the +467 configurations in obs[i].idl for all i. +468 all_configs : bool +469 if True, the reweighted observables are normalized by the average of +470 the reweighting factor on all configurations in weight.idl and not +471 on the configurations in obs[i].idl. Default False. +472 """ +473 return reweight(weight, [self])[0] +474 +475 def is_zero_within_error(self, sigma=1): +476 """Checks whether the observable is zero within 'sigma' standard errors. +477 +478 Parameters +479 ---------- +480 sigma : int +481 Number of standard errors used for the check. +482 +483 Works only properly when the gamma method was run. +484 """ +485 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue +486 +487 def is_zero(self, atol=1e-10): +488 """Checks whether the observable is zero within a given tolerance. +489 +490 Parameters +491 ---------- +492 atol : float +493 Absolute tolerance (for details see numpy documentation). +494 """ +495 return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values()) +496 +497 def plot_tauint(self, save=None): +498 """Plot integrated autocorrelation time for each ensemble. +499 +500 Parameters +501 ---------- +502 save : str +503 saves the figure to a file named 'save' if. +504 """ +505 if not hasattr(self, 'e_dvalue'): +506 raise Exception('Run the gamma method first.') +507 +508 for e, e_name in enumerate(self.mc_names): +509 fig = plt.figure() +510 plt.xlabel(r'$W$') +511 plt.ylabel(r'$\tau_\mathrm{int}$') +512 length = int(len(self.e_n_tauint[e_name])) +513 if self.tau_exp[e_name] > 0: +514 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] +515 x_help = np.arange(2 * self.tau_exp[e_name]) +516 y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base +517 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) +518 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') +519 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], +520 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) +521 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 +522 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) +523 else: +524 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) +525 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) +526 +527 plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label) +528 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') +529 plt.legend() +530 plt.xlim(-0.5, xmax) +531 ylim = plt.ylim() +532 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) +533 plt.draw() +534 if save: +535 fig.savefig(save + "_" + str(e)) +536 +537 def plot_rho(self, save=None): +538 """Plot normalized autocorrelation function time for each ensemble. +539 +540 Parameters +541 ---------- +542 save : str +543 saves the figure to a file named 'save' if. +544 """ +545 if not hasattr(self, 'e_dvalue'): +546 raise Exception('Run the gamma method first.') +547 for e, e_name in enumerate(self.mc_names): +548 fig = plt.figure() +549 plt.xlabel('W') +550 plt.ylabel('rho') +551 length = int(len(self.e_drho[e_name])) +552 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) +553 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') +554 if self.tau_exp[e_name] > 0: +555 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], +556 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) +557 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 +558 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) +559 else: +560 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) +561 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) +562 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) +563 plt.xlim(-0.5, xmax) +564 plt.draw() +565 if save: +566 fig.savefig(save + "_" + str(e)) +567 +568 def plot_rep_dist(self): +569 """Plot replica distribution for each ensemble with more than one replicum.""" +570 if not hasattr(self, 'e_dvalue'): +571 raise Exception('Run the gamma method first.') +572 for e, e_name in enumerate(self.mc_names): +573 if len(self.e_content[e_name]) == 1: +574 print('No replica distribution for a single replicum (', e_name, ')') +575 continue +576 r_length = [] +577 sub_r_mean = 0 +578 for r, r_name in enumerate(self.e_content[e_name]): +579 r_length.append(len(self.deltas[r_name])) +580 sub_r_mean += self.shape[r_name] * self.r_values[r_name] +581 e_N = np.sum(r_length) +582 sub_r_mean /= e_N +583 arr = np.zeros(len(self.e_content[e_name])) +584 for r, r_name in enumerate(self.e_content[e_name]): +585 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) +586 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) +587 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') +588 plt.draw() +589 +590 def plot_history(self, expand=True): +591 """Plot derived Monte Carlo history for each ensemble +592 +593 Parameters +594 ---------- +595 expand : bool +596 show expanded history for irregular Monte Carlo chains (default: True). +597 """ +598 for e, e_name in enumerate(self.mc_names): +599 plt.figure() +600 r_length = [] +601 tmp = [] +602 tmp_expanded = [] +603 for r, r_name in enumerate(self.e_content[e_name]): +604 tmp.append(self.deltas[r_name] + self.r_values[r_name]) +605 if expand: +606 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) +607 r_length.append(len(tmp_expanded[-1])) +608 else: +609 r_length.append(len(tmp[-1])) +610 e_N = np.sum(r_length) +611 x = np.arange(e_N) +612 y_test = np.concatenate(tmp, axis=0) +613 if expand: +614 y = np.concatenate(tmp_expanded, axis=0) +615 else: +616 y = y_test +617 plt.errorbar(x, y, fmt='.', markersize=3) +618 plt.xlim(-0.5, e_N - 0.5) +619 plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})') +620 plt.draw() +621 +622 def plot_piechart(self, save=None): +623 """Plot piechart which shows the fractional contribution of each +624 ensemble to the error and returns a dictionary containing the fractions. +625 +626 Parameters +627 ---------- +628 save : str +629 saves the figure to a file named 'save' if. +630 """ +631 if not hasattr(self, 'e_dvalue'): +632 raise Exception('Run the gamma method first.') +633 if np.isclose(0.0, self._dvalue, atol=1e-15): +634 raise Exception('Error is 0.0') +635 labels = self.e_names +636 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 +637 fig1, ax1 = plt.subplots() +638 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) +639 ax1.axis('equal') +640 plt.draw() +641 if save: +642 fig1.savefig(save) 643 -644 def dump(self, filename, datatype="json.gz", description="", **kwargs): -645 """Dump the Obs to a file 'name' of chosen format. -646 -647 Parameters -648 ---------- -649 filename : str -650 name of the file to be saved. -651 datatype : str -652 Format of the exported file. Supported formats include -653 "json.gz" and "pickle" -654 description : str -655 Description for output file, only relevant for json.gz format. -656 path : str -657 specifies a custom path for the file (default '.') -658 """ -659 if 'path' in kwargs: -660 file_name = kwargs.get('path') + '/' + filename -661 else: -662 file_name = filename -663 -664 if datatype == "json.gz": -665 from .input.json import dump_to_json -666 dump_to_json([self], file_name, description=description) -667 elif datatype == "pickle": -668 with open(file_name + '.p', 'wb') as fb: -669 pickle.dump(self, fb) -670 else: -671 raise Exception("Unknown datatype " + str(datatype)) -672 -673 def export_jackknife(self): -674 """Export jackknife samples from the Obs -675 -676 Returns -677 ------- -678 numpy.ndarray -679 Returns a numpy array of length N + 1 where N is the number of samples -680 for the given ensemble and replicum. The zeroth entry of the array contains -681 the mean value of the Obs, entries 1 to N contain the N jackknife samples -682 derived from the Obs. The current implementation only works for observables -683 defined on exactly one ensemble and replicum. The derived jackknife samples -684 should agree with samples from a full jackknife analysis up to O(1/N). -685 """ -686 -687 if len(self.names) != 1: -688 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") -689 -690 name = self.names[0] -691 full_data = self.deltas[name] + self.r_values[name] -692 n = full_data.size -693 mean = self.value -694 tmp_jacks = np.zeros(n + 1) -695 tmp_jacks[0] = mean -696 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) -697 return tmp_jacks -698 -699 def __float__(self): -700 return float(self.value) -701 -702 def __repr__(self): -703 return 'Obs[' + str(self) + ']' -704 -705 def __str__(self): -706 return _format_uncertainty(self.value, self._dvalue) -707 -708 def __hash__(self): -709 hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),) -710 hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()]) -711 hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()]) -712 hash_tuple += tuple([o.encode() for o in self.names]) -713 m = hashlib.md5() -714 [m.update(o) for o in hash_tuple] -715 return int(m.hexdigest(), 16) & 0xFFFFFFFF -716 -717 # Overload comparisons -718 def __lt__(self, other): -719 return self.value < other -720 -721 def __le__(self, other): -722 return self.value <= other -723 -724 def __gt__(self, other): -725 return self.value > other -726 -727 def __ge__(self, other): -728 return self.value >= other -729 -730 def __eq__(self, other): -731 return (self - other).is_zero() -732 -733 def __ne__(self, other): -734 return not (self - other).is_zero() -735 -736 # Overload math operations -737 def __add__(self, y): -738 if isinstance(y, Obs): -739 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) -740 else: -741 if isinstance(y, np.ndarray): -742 return np.array([self + o for o in y]) -743 elif y.__class__.__name__ in ['Corr', 'CObs']: -744 return NotImplemented -745 else: -746 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) -747 -748 def __radd__(self, y): -749 return self + y -750 -751 def __mul__(self, y): -752 if isinstance(y, Obs): -753 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) -754 else: -755 if isinstance(y, np.ndarray): -756 return np.array([self * o for o in y]) -757 elif isinstance(y, complex): -758 return CObs(self * y.real, self * y.imag) -759 elif y.__class__.__name__ in ['Corr', 'CObs']: -760 return NotImplemented -761 else: -762 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) -763 -764 def __rmul__(self, y): -765 return self * y -766 -767 def __sub__(self, y): -768 if isinstance(y, Obs): -769 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) -770 else: -771 if isinstance(y, np.ndarray): -772 return np.array([self - o for o in y]) -773 elif y.__class__.__name__ in ['Corr', 'CObs']: -774 return NotImplemented -775 else: -776 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) -777 -778 def __rsub__(self, y): -779 return -1 * (self - y) -780 -781 def __pos__(self): -782 return self -783 -784 def __neg__(self): -785 return -1 * self -786 -787 def __truediv__(self, y): -788 if isinstance(y, Obs): -789 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) -790 else: -791 if isinstance(y, np.ndarray): -792 return np.array([self / o for o in y]) -793 elif y.__class__.__name__ in ['Corr', 'CObs']: -794 return NotImplemented -795 else: -796 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) -797 -798 def __rtruediv__(self, y): -799 if isinstance(y, Obs): -800 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) -801 else: -802 if isinstance(y, np.ndarray): -803 return np.array([o / self for o in y]) -804 elif y.__class__.__name__ in ['Corr', 'CObs']: -805 return NotImplemented -806 else: -807 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) -808 -809 def __pow__(self, y): -810 if isinstance(y, Obs): -811 return derived_observable(lambda x: x[0] ** x[1], [self, y]) -812 else: -813 return derived_observable(lambda x: x[0] ** y, [self]) -814 -815 def __rpow__(self, y): -816 if isinstance(y, Obs): -817 return derived_observable(lambda x: x[0] ** x[1], [y, self]) -818 else: -819 return derived_observable(lambda x: y ** x[0], [self]) -820 -821 def __abs__(self): -822 return derived_observable(lambda x: anp.abs(x[0]), [self]) -823 -824 # Overload numpy functions -825 def sqrt(self): -826 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) -827 -828 def log(self): -829 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) -830 -831 def exp(self): -832 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) -833 -834 def sin(self): -835 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) -836 -837 def cos(self): -838 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) -839 -840 def tan(self): -841 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) -842 -843 def arcsin(self): -844 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) -845 -846 def arccos(self): -847 return derived_observable(lambda x: anp.arccos(x[0]), [self]) -848 -849 def arctan(self): -850 return derived_observable(lambda x: anp.arctan(x[0]), [self]) -851 -852 def sinh(self): -853 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) -854 -855 def cosh(self): -856 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) -857 -858 def tanh(self): -859 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) -860 -861 def arcsinh(self): -862 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) -863 -864 def arccosh(self): -865 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) -866 -867 def arctanh(self): -868 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) +644 return dict(zip(self.e_names, sizes)) +645 +646 def dump(self, filename, datatype="json.gz", description="", **kwargs): +647 """Dump the Obs to a file 'name' of chosen format. +648 +649 Parameters +650 ---------- +651 filename : str +652 name of the file to be saved. +653 datatype : str +654 Format of the exported file. Supported formats include +655 "json.gz" and "pickle" +656 description : str +657 Description for output file, only relevant for json.gz format. +658 path : str +659 specifies a custom path for the file (default '.') +660 """ +661 if 'path' in kwargs: +662 file_name = kwargs.get('path') + '/' + filename +663 else: +664 file_name = filename +665 +666 if datatype == "json.gz": +667 from .input.json import dump_to_json +668 dump_to_json([self], file_name, description=description) +669 elif datatype == "pickle": +670 with open(file_name + '.p', 'wb') as fb: +671 pickle.dump(self, fb) +672 else: +673 raise Exception("Unknown datatype " + str(datatype)) +674 +675 def export_jackknife(self): +676 """Export jackknife samples from the Obs +677 +678 Returns +679 ------- +680 numpy.ndarray +681 Returns a numpy array of length N + 1 where N is the number of samples +682 for the given ensemble and replicum. The zeroth entry of the array contains +683 the mean value of the Obs, entries 1 to N contain the N jackknife samples +684 derived from the Obs. The current implementation only works for observables +685 defined on exactly one ensemble and replicum. The derived jackknife samples +686 should agree with samples from a full jackknife analysis up to O(1/N). +687 """ +688 +689 if len(self.names) != 1: +690 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") +691 +692 name = self.names[0] +693 full_data = self.deltas[name] + self.r_values[name] +694 n = full_data.size +695 mean = self.value +696 tmp_jacks = np.zeros(n + 1) +697 tmp_jacks[0] = mean +698 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) +699 return tmp_jacks +700 +701 def __float__(self): +702 return float(self.value) +703 +704 def __repr__(self): +705 return 'Obs[' + str(self) + ']' +706 +707 def __str__(self): +708 return _format_uncertainty(self.value, self._dvalue) +709 +710 def __hash__(self): +711 hash_tuple = (np.array([self.value]).astype(np.float32).data.tobytes(),) +712 hash_tuple += tuple([o.astype(np.float32).data.tobytes() for o in self.deltas.values()]) +713 hash_tuple += tuple([np.array([o.errsq()]).astype(np.float32).data.tobytes() for o in self.covobs.values()]) +714 hash_tuple += tuple([o.encode() for o in self.names]) +715 m = hashlib.md5() +716 [m.update(o) for o in hash_tuple] +717 return int(m.hexdigest(), 16) & 0xFFFFFFFF +718 +719 # Overload comparisons +720 def __lt__(self, other): +721 return self.value < other +722 +723 def __le__(self, other): +724 return self.value <= other +725 +726 def __gt__(self, other): +727 return self.value > other +728 +729 def __ge__(self, other): +730 return self.value >= other +731 +732 def __eq__(self, other): +733 return (self - other).is_zero() +734 +735 def __ne__(self, other): +736 return not (self - other).is_zero() +737 +738 # Overload math operations +739 def __add__(self, y): +740 if isinstance(y, Obs): +741 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) +742 else: +743 if isinstance(y, np.ndarray): +744 return np.array([self + o for o in y]) +745 elif y.__class__.__name__ in ['Corr', 'CObs']: +746 return NotImplemented +747 else: +748 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) +749 +750 def __radd__(self, y): +751 return self + y +752 +753 def __mul__(self, y): +754 if isinstance(y, Obs): +755 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) +756 else: +757 if isinstance(y, np.ndarray): +758 return np.array([self * o for o in y]) +759 elif isinstance(y, complex): +760 return CObs(self * y.real, self * y.imag) +761 elif y.__class__.__name__ in ['Corr', 'CObs']: +762 return NotImplemented +763 else: +764 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) +765 +766 def __rmul__(self, y): +767 return self * y +768 +769 def __sub__(self, y): +770 if isinstance(y, Obs): +771 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) +772 else: +773 if isinstance(y, np.ndarray): +774 return np.array([self - o for o in y]) +775 elif y.__class__.__name__ in ['Corr', 'CObs']: +776 return NotImplemented +777 else: +778 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) +779 +780 def __rsub__(self, y): +781 return -1 * (self - y) +782 +783 def __pos__(self): +784 return self +785 +786 def __neg__(self): +787 return -1 * self +788 +789 def __truediv__(self, y): +790 if isinstance(y, Obs): +791 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) +792 else: +793 if isinstance(y, np.ndarray): +794 return np.array([self / o for o in y]) +795 elif y.__class__.__name__ in ['Corr', 'CObs']: +796 return NotImplemented +797 else: +798 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) +799 +800 def __rtruediv__(self, y): +801 if isinstance(y, Obs): +802 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) +803 else: +804 if isinstance(y, np.ndarray): +805 return np.array([o / self for o in y]) +806 elif y.__class__.__name__ in ['Corr', 'CObs']: +807 return NotImplemented +808 else: +809 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) +810 +811 def __pow__(self, y): +812 if isinstance(y, Obs): +813 return derived_observable(lambda x: x[0] ** x[1], [self, y]) +814 else: +815 return derived_observable(lambda x: x[0] ** y, [self]) +816 +817 def __rpow__(self, y): +818 if isinstance(y, Obs): +819 return derived_observable(lambda x: x[0] ** x[1], [y, self]) +820 else: +821 return derived_observable(lambda x: y ** x[0], [self]) +822 +823 def __abs__(self): +824 return derived_observable(lambda x: anp.abs(x[0]), [self]) +825 +826 # Overload numpy functions +827 def sqrt(self): +828 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) +829 +830 def log(self): +831 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) +832 +833 def exp(self): +834 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) +835 +836 def sin(self): +837 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) +838 +839 def cos(self): +840 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) +841 +842 def tan(self): +843 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) +844 +845 def arcsin(self): +846 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) +847 +848 def arccos(self): +849 return derived_observable(lambda x: anp.arccos(x[0]), [self]) +850 +851 def arctan(self): +852 return derived_observable(lambda x: anp.arctan(x[0]), [self]) +853 +854 def sinh(self): +855 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) +856 +857 def cosh(self): +858 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) +859 +860 def tanh(self): +861 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) +862 +863 def arcsinh(self): +864 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) +865 +866 def arccosh(self): +867 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) +868 +869 def arctanh(self): +870 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) @@ -3074,6 +3081,218 @@ list of ranges or lists on which the samples are defined
    Parameters
    + + + + + +
    + +
    + + def + gm(self, **kwargs): + + + +
    + + 
    178    def gamma_method(self, **kwargs):
+179        """Estimate the error and related properties of the Obs.
+180
+181        Parameters
+182        ----------
+183        S : float
+184            specifies a custom value for the parameter S (default 2.0).
+185            If set to 0 it is assumed that the data exhibits no
+186            autocorrelation. In this case the error estimates coincides
+187            with the sample standard error.
+188        tau_exp : float
+189            positive value triggers the critical slowing down analysis
+190            (default 0.0).
+191        N_sigma : float
+192            number of standard deviations from zero until the tail is
+193            attached to the autocorrelation function (default 1).
+194        fft : bool
+195            determines whether the fft algorithm is used for the computation
+196            of the autocorrelation function (default True)
+197        """
+198
+199        e_content = self.e_content
+200        self.e_dvalue = {}
+201        self.e_ddvalue = {}
+202        self.e_tauint = {}
+203        self.e_dtauint = {}
+204        self.e_windowsize = {}
+205        self.e_n_tauint = {}
+206        self.e_n_dtauint = {}
+207        e_gamma = {}
+208        self.e_rho = {}
+209        self.e_drho = {}
+210        self._dvalue = 0
+211        self.ddvalue = 0
+212
+213        self.S = {}
+214        self.tau_exp = {}
+215        self.N_sigma = {}
+216
+217        if kwargs.get('fft') is False:
+218            fft = False
+219        else:
+220            fft = True
+221
+222        def _parse_kwarg(kwarg_name):
+223            if kwarg_name in kwargs:
+224                tmp = kwargs.get(kwarg_name)
+225                if isinstance(tmp, (int, float)):
+226                    if tmp < 0:
+227                        raise Exception(kwarg_name + ' has to be larger or equal to 0.')
+228                    for e, e_name in enumerate(self.e_names):
+229                        getattr(self, kwarg_name)[e_name] = tmp
+230                else:
+231                    raise TypeError(kwarg_name + ' is not in proper format.')
+232            else:
+233                for e, e_name in enumerate(self.e_names):
+234                    if e_name in getattr(Obs, kwarg_name + '_dict'):
+235                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_dict')[e_name]
+236                    else:
+237                        getattr(self, kwarg_name)[e_name] = getattr(Obs, kwarg_name + '_global')
+238
+239        _parse_kwarg('S')
+240        _parse_kwarg('tau_exp')
+241        _parse_kwarg('N_sigma')
+242
+243        for e, e_name in enumerate(self.mc_names):
+244            r_length = []
+245            for r_name in e_content[e_name]:
+246                if isinstance(self.idl[r_name], range):
+247                    r_length.append(len(self.idl[r_name]))
+248                else:
+249                    r_length.append((self.idl[r_name][-1] - self.idl[r_name][0] + 1))
+250
+251            e_N = np.sum([self.shape[r_name] for r_name in e_content[e_name]])
+252            w_max = max(r_length) // 2
+253            e_gamma[e_name] = np.zeros(w_max)
+254            self.e_rho[e_name] = np.zeros(w_max)
+255            self.e_drho[e_name] = np.zeros(w_max)
+256
+257            for r_name in e_content[e_name]:
+258                e_gamma[e_name] += self._calc_gamma(self.deltas[r_name], self.idl[r_name], self.shape[r_name], w_max, fft)
+259
+260            gamma_div = np.zeros(w_max)
+261            for r_name in e_content[e_name]:
+262                gamma_div += self._calc_gamma(np.ones((self.shape[r_name])), self.idl[r_name], self.shape[r_name], w_max, fft)
+263            gamma_div[gamma_div < 1] = 1.0
+264            e_gamma[e_name] /= gamma_div[:w_max]
+265
+266            if np.abs(e_gamma[e_name][0]) < 10 * np.finfo(float).tiny:  # Prevent division by zero
+267                self.e_tauint[e_name] = 0.5
+268                self.e_dtauint[e_name] = 0.0
+269                self.e_dvalue[e_name] = 0.0
+270                self.e_ddvalue[e_name] = 0.0
+271                self.e_windowsize[e_name] = 0
+272                continue
+273
+274            gaps = []
+275            for r_name in e_content[e_name]:
+276                if isinstance(self.idl[r_name], range):
+277                    gaps.append(1)
+278                else:
+279                    gaps.append(np.min(np.diff(self.idl[r_name])))
+280
+281            if not np.all([gi == gaps[0] for gi in gaps]):
+282                raise Exception(f"Replica for ensemble {e_name} are not equally spaced.", gaps)
+283            else:
+284                gapsize = gaps[0]
+285
+286            self.e_rho[e_name] = e_gamma[e_name][:w_max] / e_gamma[e_name][0]
+287            self.e_n_tauint[e_name] = np.cumsum(np.concatenate(([0.5], self.e_rho[e_name][1:])))
+288            # Make sure no entry of tauint is smaller than 0.5
+289            self.e_n_tauint[e_name][self.e_n_tauint[e_name] <= 0.5] = 0.5 + np.finfo(np.float64).eps
+290            # hep-lat/0306017 eq. (42)
+291            self.e_n_dtauint[e_name] = self.e_n_tauint[e_name] * 2 * np.sqrt(np.abs(np.arange(w_max) / gapsize + 0.5 - self.e_n_tauint[e_name]) / e_N)
+292            self.e_n_dtauint[e_name][0] = 0.0
+293
+294            def _compute_drho(i):
+295                tmp = self.e_rho[e_name][i + 1:w_max] + np.concatenate([self.e_rho[e_name][i - 1::-1], self.e_rho[e_name][1:w_max - 2 * i]]) - 2 * self.e_rho[e_name][i] * self.e_rho[e_name][1:w_max - i]
+296                self.e_drho[e_name][i] = np.sqrt(np.sum(tmp ** 2) / e_N)
+297
+298            _compute_drho(gapsize)
+299            if self.tau_exp[e_name] > 0:
+300                texp = self.tau_exp[e_name]
+301                # Critical slowing down analysis
+302                if w_max // 2 <= 1:
+303                    raise Exception("Need at least 8 samples for tau_exp error analysis")
+304                for n in range(gapsize, w_max // 2, gapsize):
+305                    _compute_drho(n + gapsize)
+306                    if (self.e_rho[e_name][n] - self.N_sigma[e_name] * self.e_drho[e_name][n]) < 0 or n >= w_max // 2 - 2:
+307                        # Bias correction hep-lat/0306017 eq. (49) included
+308                        self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n / gapsize + 1) / e_N) / (1 + 1 / e_N) + texp * np.abs(self.e_rho[e_name][n + 1])  # The absolute makes sure, that the tail contribution is always positive
+309                        self.e_dtauint[e_name] = np.sqrt(self.e_n_dtauint[e_name][n] ** 2 + texp ** 2 * self.e_drho[e_name][n + 1] ** 2)
+310                        # Error of tau_exp neglected so far, missing term: self.e_rho[e_name][n + 1] ** 2 * d_tau_exp ** 2
+311                        self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+312                        self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n / gapsize + 0.5) / e_N)
+313                        self.e_windowsize[e_name] = n
+314                        break
+315            else:
+316                if self.S[e_name] == 0.0:
+317                    self.e_tauint[e_name] = 0.5
+318                    self.e_dtauint[e_name] = 0.0
+319                    self.e_dvalue[e_name] = np.sqrt(e_gamma[e_name][0] / (e_N - 1))
+320                    self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt(0.5 / e_N)
+321                    self.e_windowsize[e_name] = 0
+322                else:
+323                    # Standard automatic windowing procedure
+324                    tau = self.S[e_name] / np.log((2 * self.e_n_tauint[e_name][gapsize::gapsize] + 1) / (2 * self.e_n_tauint[e_name][gapsize::gapsize] - 1))
+325                    g_w = np.exp(- np.arange(1, len(tau) + 1) / tau) - tau / np.sqrt(np.arange(1, len(tau) + 1) * e_N)
+326                    for n in range(1, w_max):
+327                        if n < w_max // 2 - 2:
+328                            _compute_drho(gapsize * n + gapsize)
+329                        if g_w[n - 1] < 0 or n >= w_max - 1:
+330                            n *= gapsize
+331                            self.e_tauint[e_name] = self.e_n_tauint[e_name][n] * (1 + (2 * n / gapsize + 1) / e_N) / (1 + 1 / e_N)  # Bias correction hep-lat/0306017 eq. (49)
+332                            self.e_dtauint[e_name] = self.e_n_dtauint[e_name][n]
+333                            self.e_dvalue[e_name] = np.sqrt(2 * self.e_tauint[e_name] * e_gamma[e_name][0] * (1 + 1 / e_N) / e_N)
+334                            self.e_ddvalue[e_name] = self.e_dvalue[e_name] * np.sqrt((n / gapsize + 0.5) / e_N)
+335                            self.e_windowsize[e_name] = n
+336                            break
+337
+338            self._dvalue += self.e_dvalue[e_name] ** 2
+339            self.ddvalue += (self.e_dvalue[e_name] * self.e_ddvalue[e_name]) ** 2
+340
+341        for e_name in self.cov_names:
+342            self.e_dvalue[e_name] = np.sqrt(self.covobs[e_name].errsq())
+343            self.e_ddvalue[e_name] = 0
+344            self._dvalue += self.e_dvalue[e_name]**2
+345
+346        self._dvalue = np.sqrt(self._dvalue)
+347        if self._dvalue == 0.0:
+348            self.ddvalue = 0.0
+349        else:
+350            self.ddvalue = np.sqrt(self.ddvalue) / self._dvalue
+351        return
+
    + + +

    Estimate the error and related properties of the Obs.

    + +
    Parameters
    +
    - 
    386    def details(self, ens_content=True):
-387        """Output detailed properties of the Obs.
-388
-389        Parameters
-390        ----------
-391        ens_content : bool
-392            print details about the ensembles and replica if true.
-393        """
-394        if self.tag is not None:
-395            print("Description:", self.tag)
-396        if not hasattr(self, 'e_dvalue'):
-397            print('Result\t %3.8e' % (self.value))
-398        else:
-399            if self.value == 0.0:
-400                percentage = np.nan
-401            else:
-402                percentage = np.abs(self._dvalue / self.value) * 100
-403            print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage))
-404            if len(self.e_names) > 1:
-405                print(' Ensemble errors:')
-406            e_content = self.e_content
-407            for e_name in self.mc_names:
-408                if isinstance(self.idl[e_content[e_name][0]], range):
-409                    gap = self.idl[e_content[e_name][0]].step
-410                else:
-411                    gap = np.min(np.diff(self.idl[e_content[e_name][0]]))
-412
-413                if len(self.e_names) > 1:
-414                    print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name]))
-415                tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name])
-416                tau_string += f" in units of {gap} config"
-417                if gap > 1:
-418                    tau_string += "s"
-419                if self.tau_exp[e_name] > 0:
-420                    tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name])
-421                else:
-422                    tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name])
-423                print(tau_string)
-424            for e_name in self.cov_names:
-425                print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name]))
-426        if ens_content is True:
-427            if len(self.e_names) == 1:
-428                print(self.N, 'samples in', len(self.e_names), 'ensemble:')
-429            else:
-430                print(self.N, 'samples in', len(self.e_names), 'ensembles:')
-431            my_string_list = []
-432            for key, value in sorted(self.e_content.items()):
-433                if key not in self.covobs:
-434                    my_string = '  ' + "\u00B7 Ensemble '" + key + "' "
-435                    if len(value) == 1:
-436                        my_string += f': {self.shape[value[0]]} configurations'
-437                        if isinstance(self.idl[value[0]], range):
-438                            my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')'
-439                        else:
-440                            my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})'
-441                    else:
-442                        sublist = []
-443                        for v in value:
-444                            my_substring = '    ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' "
-445                            my_substring += f': {self.shape[v]} configurations'
-446                            if isinstance(self.idl[v], range):
-447                                my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')'
-448                            else:
-449                                my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})'
-450                            sublist.append(my_substring)
-451
-452                        my_string += '\n' + '\n'.join(sublist)
-453                else:
-454                    my_string = '  ' + "\u00B7 Covobs   '" + key + "' "
-455                my_string_list.append(my_string)
-456            print('\n'.join(my_string_list))
+            
    388    def details(self, ens_content=True):
+389        """Output detailed properties of the Obs.
+390
+391        Parameters
+392        ----------
+393        ens_content : bool
+394            print details about the ensembles and replica if true.
+395        """
+396        if self.tag is not None:
+397            print("Description:", self.tag)
+398        if not hasattr(self, 'e_dvalue'):
+399            print('Result\t %3.8e' % (self.value))
+400        else:
+401            if self.value == 0.0:
+402                percentage = np.nan
+403            else:
+404                percentage = np.abs(self._dvalue / self.value) * 100
+405            print('Result\t %3.8e +/- %3.8e +/- %3.8e (%3.3f%%)' % (self.value, self._dvalue, self.ddvalue, percentage))
+406            if len(self.e_names) > 1:
+407                print(' Ensemble errors:')
+408            e_content = self.e_content
+409            for e_name in self.mc_names:
+410                if isinstance(self.idl[e_content[e_name][0]], range):
+411                    gap = self.idl[e_content[e_name][0]].step
+412                else:
+413                    gap = np.min(np.diff(self.idl[e_content[e_name][0]]))
+414
+415                if len(self.e_names) > 1:
+416                    print('', e_name, '\t %3.6e +/- %3.6e' % (self.e_dvalue[e_name], self.e_ddvalue[e_name]))
+417                tau_string = " \N{GREEK SMALL LETTER TAU}_int\t " + _format_uncertainty(self.e_tauint[e_name], self.e_dtauint[e_name])
+418                tau_string += f" in units of {gap} config"
+419                if gap > 1:
+420                    tau_string += "s"
+421                if self.tau_exp[e_name] > 0:
+422                    tau_string = f"{tau_string: <45}" + '\t(\N{GREEK SMALL LETTER TAU}_exp=%3.2f, N_\N{GREEK SMALL LETTER SIGMA}=%1.0i)' % (self.tau_exp[e_name], self.N_sigma[e_name])
+423                else:
+424                    tau_string = f"{tau_string: <45}" + '\t(S=%3.2f)' % (self.S[e_name])
+425                print(tau_string)
+426            for e_name in self.cov_names:
+427                print('', e_name, '\t %3.8e' % (self.e_dvalue[e_name]))
+428        if ens_content is True:
+429            if len(self.e_names) == 1:
+430                print(self.N, 'samples in', len(self.e_names), 'ensemble:')
+431            else:
+432                print(self.N, 'samples in', len(self.e_names), 'ensembles:')
+433            my_string_list = []
+434            for key, value in sorted(self.e_content.items()):
+435                if key not in self.covobs:
+436                    my_string = '  ' + "\u00B7 Ensemble '" + key + "' "
+437                    if len(value) == 1:
+438                        my_string += f': {self.shape[value[0]]} configurations'
+439                        if isinstance(self.idl[value[0]], range):
+440                            my_string += f' (from {self.idl[value[0]].start} to {self.idl[value[0]][-1]}' + int(self.idl[value[0]].step != 1) * f' in steps of {self.idl[value[0]].step}' + ')'
+441                        else:
+442                            my_string += f' (irregular range from {self.idl[value[0]][0]} to {self.idl[value[0]][-1]})'
+443                    else:
+444                        sublist = []
+445                        for v in value:
+446                            my_substring = '    ' + "\u00B7 Replicum '" + v[len(key) + 1:] + "' "
+447                            my_substring += f': {self.shape[v]} configurations'
+448                            if isinstance(self.idl[v], range):
+449                                my_substring += f' (from {self.idl[v].start} to {self.idl[v][-1]}' + int(self.idl[v].step != 1) * f' in steps of {self.idl[v].step}' + ')'
+450                            else:
+451                                my_substring += f' (irregular range from {self.idl[v][0]} to {self.idl[v][-1]})'
+452                            sublist.append(my_substring)
+453
+454                        my_string += '\n' + '\n'.join(sublist)
+455                else:
+456                    my_string = '  ' + "\u00B7 Covobs   '" + key + "' "
+457                my_string_list.append(my_string)
+458            print('\n'.join(my_string_list))
 
    
 
 
@@ -3202,20 +3421,20 @@ print details about the ensembles and replica if true.
    - 
    458    def reweight(self, weight):
-459        """Reweight the obs with given rewighting factors.
-460
-461        Parameters
-462        ----------
-463        weight : Obs
-464            Reweighting factor. An Observable that has to be defined on a superset of the
-465            configurations in obs[i].idl for all i.
-466        all_configs : bool
-467            if True, the reweighted observables are normalized by the average of
-468            the reweighting factor on all configurations in weight.idl and not
-469            on the configurations in obs[i].idl. Default False.
-470        """
-471        return reweight(weight, [self])[0]
+            
    460    def reweight(self, weight):
+461        """Reweight the obs with given rewighting factors.
+462
+463        Parameters
+464        ----------
+465        weight : Obs
+466            Reweighting factor. An Observable that has to be defined on a superset of the
+467            configurations in obs[i].idl for all i.
+468        all_configs : bool
+469            if True, the reweighted observables are normalized by the average of
+470            the reweighting factor on all configurations in weight.idl and not
+471            on the configurations in obs[i].idl. Default False.
+472        """
+473        return reweight(weight, [self])[0]
 
    
 
 
@@ -3247,17 +3466,17 @@ on the configurations in obs[i].idl. Default False.
    - 
    473    def is_zero_within_error(self, sigma=1):
-474        """Checks whether the observable is zero within 'sigma' standard errors.
-475
-476        Parameters
-477        ----------
-478        sigma : int
-479            Number of standard errors used for the check.
-480
-481        Works only properly when the gamma method was run.
-482        """
-483        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
+            
    475    def is_zero_within_error(self, sigma=1):
+476        """Checks whether the observable is zero within 'sigma' standard errors.
+477
+478        Parameters
+479        ----------
+480        sigma : int
+481            Number of standard errors used for the check.
+482
+483        Works only properly when the gamma method was run.
+484        """
+485        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
 
    
 
 
@@ -3285,15 +3504,15 @@ Number of standard errors used for the check.
    - 
    485    def is_zero(self, atol=1e-10):
-486        """Checks whether the observable is zero within a given tolerance.
-487
-488        Parameters
-489        ----------
-490        atol : float
-491            Absolute tolerance (for details see numpy documentation).
-492        """
-493        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
+            
    487    def is_zero(self, atol=1e-10):
+488        """Checks whether the observable is zero within a given tolerance.
+489
+490        Parameters
+491        ----------
+492        atol : float
+493            Absolute tolerance (for details see numpy documentation).
+494        """
+495        return np.isclose(0.0, self.value, 1e-14, atol) and all(np.allclose(0.0, delta, 1e-14, atol) for delta in self.deltas.values()) and all(np.allclose(0.0, delta.errsq(), 1e-14, atol) for delta in self.covobs.values())
 
    
 
 
@@ -3320,45 +3539,45 @@ Absolute tolerance (for details see numpy documentation).
    - 
    495    def plot_tauint(self, save=None):
-496        """Plot integrated autocorrelation time for each ensemble.
-497
-498        Parameters
-499        ----------
-500        save : str
-501            saves the figure to a file named 'save' if.
-502        """
-503        if not hasattr(self, 'e_dvalue'):
-504            raise Exception('Run the gamma method first.')
-505
-506        for e, e_name in enumerate(self.mc_names):
-507            fig = plt.figure()
-508            plt.xlabel(r'$W$')
-509            plt.ylabel(r'$\tau_\mathrm{int}$')
-510            length = int(len(self.e_n_tauint[e_name]))
-511            if self.tau_exp[e_name] > 0:
-512                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
-513                x_help = np.arange(2 * self.tau_exp[e_name])
-514                y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base
-515                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
-516                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
-517                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
-518                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
-519                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
-520                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
-521            else:
-522                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
-523                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
-524
-525            plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label)
-526            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
-527            plt.legend()
-528            plt.xlim(-0.5, xmax)
-529            ylim = plt.ylim()
-530            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
-531            plt.draw()
-532            if save:
-533                fig.savefig(save + "_" + str(e))
+            
    497    def plot_tauint(self, save=None):
+498        """Plot integrated autocorrelation time for each ensemble.
+499
+500        Parameters
+501        ----------
+502        save : str
+503            saves the figure to a file named 'save' if.
+504        """
+505        if not hasattr(self, 'e_dvalue'):
+506            raise Exception('Run the gamma method first.')
+507
+508        for e, e_name in enumerate(self.mc_names):
+509            fig = plt.figure()
+510            plt.xlabel(r'$W$')
+511            plt.ylabel(r'$\tau_\mathrm{int}$')
+512            length = int(len(self.e_n_tauint[e_name]))
+513            if self.tau_exp[e_name] > 0:
+514                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
+515                x_help = np.arange(2 * self.tau_exp[e_name])
+516                y_help = (x_help + 1) * np.abs(self.e_rho[e_name][self.e_windowsize[e_name] + 1]) * (1 - x_help / (2 * (2 * self.tau_exp[e_name] - 1))) + base
+517                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
+518                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
+519                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
+520                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
+521                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+522                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
+523            else:
+524                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
+525                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+526
+527            plt.errorbar(np.arange(length)[:int(xmax) + 1], self.e_n_tauint[e_name][:int(xmax) + 1], yerr=self.e_n_dtauint[e_name][:int(xmax) + 1], linewidth=1, capsize=2, label=label)
+528            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
+529            plt.legend()
+530            plt.xlim(-0.5, xmax)
+531            ylim = plt.ylim()
+532            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
+533            plt.draw()
+534            if save:
+535                fig.savefig(save + "_" + str(e))
 
    
 
 
@@ -3385,36 +3604,36 @@ saves the figure to a file named 'save' if.
    - 
    535    def plot_rho(self, save=None):
-536        """Plot normalized autocorrelation function time for each ensemble.
-537
-538        Parameters
-539        ----------
-540        save : str
-541            saves the figure to a file named 'save' if.
-542        """
-543        if not hasattr(self, 'e_dvalue'):
-544            raise Exception('Run the gamma method first.')
-545        for e, e_name in enumerate(self.mc_names):
-546            fig = plt.figure()
-547            plt.xlabel('W')
-548            plt.ylabel('rho')
-549            length = int(len(self.e_drho[e_name]))
-550            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
-551            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
-552            if self.tau_exp[e_name] > 0:
-553                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
-554                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
-555                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
-556                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
-557            else:
-558                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
-559                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
-560            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
-561            plt.xlim(-0.5, xmax)
-562            plt.draw()
-563            if save:
-564                fig.savefig(save + "_" + str(e))
+            
    537    def plot_rho(self, save=None):
+538        """Plot normalized autocorrelation function time for each ensemble.
+539
+540        Parameters
+541        ----------
+542        save : str
+543            saves the figure to a file named 'save' if.
+544        """
+545        if not hasattr(self, 'e_dvalue'):
+546            raise Exception('Run the gamma method first.')
+547        for e, e_name in enumerate(self.mc_names):
+548            fig = plt.figure()
+549            plt.xlabel('W')
+550            plt.ylabel('rho')
+551            length = int(len(self.e_drho[e_name]))
+552            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
+553            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
+554            if self.tau_exp[e_name] > 0:
+555                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
+556                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
+557                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+558                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
+559            else:
+560                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+561                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
+562            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
+563            plt.xlim(-0.5, xmax)
+564            plt.draw()
+565            if save:
+566                fig.savefig(save + "_" + str(e))
 
    
 
 
@@ -3441,27 +3660,27 @@ saves the figure to a file named 'save' if.
    - 
    566    def plot_rep_dist(self):
-567        """Plot replica distribution for each ensemble with more than one replicum."""
-568        if not hasattr(self, 'e_dvalue'):
-569            raise Exception('Run the gamma method first.')
-570        for e, e_name in enumerate(self.mc_names):
-571            if len(self.e_content[e_name]) == 1:
-572                print('No replica distribution for a single replicum (', e_name, ')')
-573                continue
-574            r_length = []
-575            sub_r_mean = 0
-576            for r, r_name in enumerate(self.e_content[e_name]):
-577                r_length.append(len(self.deltas[r_name]))
-578                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
-579            e_N = np.sum(r_length)
-580            sub_r_mean /= e_N
-581            arr = np.zeros(len(self.e_content[e_name]))
-582            for r, r_name in enumerate(self.e_content[e_name]):
-583                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
-584            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
-585            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
-586            plt.draw()
+            
    568    def plot_rep_dist(self):
+569        """Plot replica distribution for each ensemble with more than one replicum."""
+570        if not hasattr(self, 'e_dvalue'):
+571            raise Exception('Run the gamma method first.')
+572        for e, e_name in enumerate(self.mc_names):
+573            if len(self.e_content[e_name]) == 1:
+574                print('No replica distribution for a single replicum (', e_name, ')')
+575                continue
+576            r_length = []
+577            sub_r_mean = 0
+578            for r, r_name in enumerate(self.e_content[e_name]):
+579                r_length.append(len(self.deltas[r_name]))
+580                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
+581            e_N = np.sum(r_length)
+582            sub_r_mean /= e_N
+583            arr = np.zeros(len(self.e_content[e_name]))
+584            for r, r_name in enumerate(self.e_content[e_name]):
+585                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
+586            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
+587            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
+588            plt.draw()
 
    
 
 
@@ -3481,37 +3700,37 @@ saves the figure to a file named 'save' if.
    - 
    588    def plot_history(self, expand=True):
-589        """Plot derived Monte Carlo history for each ensemble
-590
-591        Parameters
-592        ----------
-593        expand : bool
-594            show expanded history for irregular Monte Carlo chains (default: True).
-595        """
-596        for e, e_name in enumerate(self.mc_names):
-597            plt.figure()
-598            r_length = []
-599            tmp = []
-600            tmp_expanded = []
-601            for r, r_name in enumerate(self.e_content[e_name]):
-602                tmp.append(self.deltas[r_name] + self.r_values[r_name])
-603                if expand:
-604                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name])
-605                    r_length.append(len(tmp_expanded[-1]))
-606                else:
-607                    r_length.append(len(tmp[-1]))
-608            e_N = np.sum(r_length)
-609            x = np.arange(e_N)
-610            y_test = np.concatenate(tmp, axis=0)
-611            if expand:
-612                y = np.concatenate(tmp_expanded, axis=0)
-613            else:
-614                y = y_test
-615            plt.errorbar(x, y, fmt='.', markersize=3)
-616            plt.xlim(-0.5, e_N - 0.5)
-617            plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})')
-618            plt.draw()
+            
    590    def plot_history(self, expand=True):
+591        """Plot derived Monte Carlo history for each ensemble
+592
+593        Parameters
+594        ----------
+595        expand : bool
+596            show expanded history for irregular Monte Carlo chains (default: True).
+597        """
+598        for e, e_name in enumerate(self.mc_names):
+599            plt.figure()
+600            r_length = []
+601            tmp = []
+602            tmp_expanded = []
+603            for r, r_name in enumerate(self.e_content[e_name]):
+604                tmp.append(self.deltas[r_name] + self.r_values[r_name])
+605                if expand:
+606                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name])
+607                    r_length.append(len(tmp_expanded[-1]))
+608                else:
+609                    r_length.append(len(tmp[-1]))
+610            e_N = np.sum(r_length)
+611            x = np.arange(e_N)
+612            y_test = np.concatenate(tmp, axis=0)
+613            if expand:
+614                y = np.concatenate(tmp_expanded, axis=0)
+615            else:
+616                y = y_test
+617            plt.errorbar(x, y, fmt='.', markersize=3)
+618            plt.xlim(-0.5, e_N - 0.5)
+619            plt.title(e_name + f'\nskew: {skew(y_test):.3f} (p={skewtest(y_test).pvalue:.3f}), kurtosis: {kurtosis(y_test):.3f} (p={kurtosistest(y_test).pvalue:.3f})')
+620            plt.draw()
 
    
 
 
@@ -3538,29 +3757,29 @@ show expanded history for irregular Monte Carlo chains (default: True).
    - 
    620    def plot_piechart(self, save=None):
-621        """Plot piechart which shows the fractional contribution of each
-622        ensemble to the error and returns a dictionary containing the fractions.
-623
-624        Parameters
-625        ----------
-626        save : str
-627            saves the figure to a file named 'save' if.
-628        """
-629        if not hasattr(self, 'e_dvalue'):
-630            raise Exception('Run the gamma method first.')
-631        if np.isclose(0.0, self._dvalue, atol=1e-15):
-632            raise Exception('Error is 0.0')
-633        labels = self.e_names
-634        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
-635        fig1, ax1 = plt.subplots()
-636        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
-637        ax1.axis('equal')
-638        plt.draw()
-639        if save:
-640            fig1.savefig(save)
-641
-642        return dict(zip(self.e_names, sizes))
+            
    622    def plot_piechart(self, save=None):
+623        """Plot piechart which shows the fractional contribution of each
+624        ensemble to the error and returns a dictionary containing the fractions.
+625
+626        Parameters
+627        ----------
+628        save : str
+629            saves the figure to a file named 'save' if.
+630        """
+631        if not hasattr(self, 'e_dvalue'):
+632            raise Exception('Run the gamma method first.')
+633        if np.isclose(0.0, self._dvalue, atol=1e-15):
+634            raise Exception('Error is 0.0')
+635        labels = self.e_names
+636        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
+637        fig1, ax1 = plt.subplots()
+638        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
+639        ax1.axis('equal')
+640        plt.draw()
+641        if save:
+642            fig1.savefig(save)
+643
+644        return dict(zip(self.e_names, sizes))
 
    
 
 
@@ -3588,34 +3807,34 @@ saves the figure to a file named 'save' if.
    - 
    644    def dump(self, filename, datatype="json.gz", description="", **kwargs):
-645        """Dump the Obs to a file 'name' of chosen format.
-646
-647        Parameters
-648        ----------
-649        filename : str
-650            name of the file to be saved.
-651        datatype : str
-652            Format of the exported file. Supported formats include
-653            "json.gz" and "pickle"
-654        description : str
-655            Description for output file, only relevant for json.gz format.
-656        path : str
-657            specifies a custom path for the file (default '.')
-658        """
-659        if 'path' in kwargs:
-660            file_name = kwargs.get('path') + '/' + filename
-661        else:
-662            file_name = filename
-663
-664        if datatype == "json.gz":
-665            from .input.json import dump_to_json
-666            dump_to_json([self], file_name, description=description)
-667        elif datatype == "pickle":
-668            with open(file_name + '.p', 'wb') as fb:
-669                pickle.dump(self, fb)
-670        else:
-671            raise Exception("Unknown datatype " + str(datatype))
+            
    646    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+647        """Dump the Obs to a file 'name' of chosen format.
+648
+649        Parameters
+650        ----------
+651        filename : str
+652            name of the file to be saved.
+653        datatype : str
+654            Format of the exported file. Supported formats include
+655            "json.gz" and "pickle"
+656        description : str
+657            Description for output file, only relevant for json.gz format.
+658        path : str
+659            specifies a custom path for the file (default '.')
+660        """
+661        if 'path' in kwargs:
+662            file_name = kwargs.get('path') + '/' + filename
+663        else:
+664            file_name = filename
+665
+666        if datatype == "json.gz":
+667            from .input.json import dump_to_json
+668            dump_to_json([self], file_name, description=description)
+669        elif datatype == "pickle":
+670            with open(file_name + '.p', 'wb') as fb:
+671                pickle.dump(self, fb)
+672        else:
+673            raise Exception("Unknown datatype " + str(datatype))
 
    
 
 
@@ -3649,31 +3868,31 @@ specifies a custom path for the file (default '.')
    - 
    673    def export_jackknife(self):
-674        """Export jackknife samples from the Obs
-675
-676        Returns
-677        -------
-678        numpy.ndarray
-679            Returns a numpy array of length N + 1 where N is the number of samples
-680            for the given ensemble and replicum. The zeroth entry of the array contains
-681            the mean value of the Obs, entries 1 to N contain the N jackknife samples
-682            derived from the Obs. The current implementation only works for observables
-683            defined on exactly one ensemble and replicum. The derived jackknife samples
-684            should agree with samples from a full jackknife analysis up to O(1/N).
-685        """
-686
-687        if len(self.names) != 1:
-688            raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
-689
-690        name = self.names[0]
-691        full_data = self.deltas[name] + self.r_values[name]
-692        n = full_data.size
-693        mean = self.value
-694        tmp_jacks = np.zeros(n + 1)
-695        tmp_jacks[0] = mean
-696        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
-697        return tmp_jacks
+            
    675    def export_jackknife(self):
+676        """Export jackknife samples from the Obs
+677
+678        Returns
+679        -------
+680        numpy.ndarray
+681            Returns a numpy array of length N + 1 where N is the number of samples
+682            for the given ensemble and replicum. The zeroth entry of the array contains
+683            the mean value of the Obs, entries 1 to N contain the N jackknife samples
+684            derived from the Obs. The current implementation only works for observables
+685            defined on exactly one ensemble and replicum. The derived jackknife samples
+686            should agree with samples from a full jackknife analysis up to O(1/N).
+687        """
+688
+689        if len(self.names) != 1:
+690            raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
+691
+692        name = self.names[0]
+693        full_data = self.deltas[name] + self.r_values[name]
+694        n = full_data.size
+695        mean = self.value
+696        tmp_jacks = np.zeros(n + 1)
+697        tmp_jacks[0] = mean
+698        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
+699        return tmp_jacks
 
    
 
 
@@ -3704,8 +3923,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    825    def sqrt(self):
-826        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
+            
    827    def sqrt(self):
+828        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
 
    
 
 
@@ -3723,8 +3942,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    828    def log(self):
-829        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
+            
    830    def log(self):
+831        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
 
    
 
 
@@ -3742,8 +3961,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    831    def exp(self):
-832        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
+            
    833    def exp(self):
+834        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
 
    
 
 
@@ -3761,8 +3980,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    834    def sin(self):
-835        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
+            
    836    def sin(self):
+837        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
 
    
 
 
@@ -3780,8 +3999,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    837    def cos(self):
-838        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
+            
    839    def cos(self):
+840        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
 
    
 
 
@@ -3799,8 +4018,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    840    def tan(self):
-841        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
+            
    842    def tan(self):
+843        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
 
    
 
 
@@ -3818,8 +4037,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    843    def arcsin(self):
-844        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
+            
    845    def arcsin(self):
+846        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
 
    
 
 
@@ -3837,8 +4056,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    846    def arccos(self):
-847        return derived_observable(lambda x: anp.arccos(x[0]), [self])
+            
    848    def arccos(self):
+849        return derived_observable(lambda x: anp.arccos(x[0]), [self])
 
    
 
 
@@ -3856,8 +4075,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    849    def arctan(self):
-850        return derived_observable(lambda x: anp.arctan(x[0]), [self])
+            
    851    def arctan(self):
+852        return derived_observable(lambda x: anp.arctan(x[0]), [self])
 
    
 
 
@@ -3875,8 +4094,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    852    def sinh(self):
-853        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
+            
    854    def sinh(self):
+855        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
 
    
 
 
@@ -3894,8 +4113,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    855    def cosh(self):
-856        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
+            
    857    def cosh(self):
+858        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
 
    
 
 
@@ -3913,8 +4132,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    858    def tanh(self):
-859        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
+            
    860    def tanh(self):
+861        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
 
    
 
 
@@ -3932,8 +4151,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    861    def arcsinh(self):
-862        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
+            
    863    def arcsinh(self):
+864        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
 
    
 
 
@@ -3951,8 +4170,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    864    def arccosh(self):
-865        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
+            
    866    def arccosh(self):
+867        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
 
    
 
 
@@ -3970,8 +4189,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    867    def arctanh(self):
-868        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
+            
    869    def arctanh(self):
+870        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
 
    
 
 
@@ -3990,115 +4209,115 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    871class CObs:
-872    """Class for a complex valued observable."""
-873    __slots__ = ['_real', '_imag', 'tag']
-874
-875    def __init__(self, real, imag=0.0):
-876        self._real = real
-877        self._imag = imag
-878        self.tag = None
-879
-880    @property
-881    def real(self):
-882        return self._real
-883
-884    @property
-885    def imag(self):
-886        return self._imag
-887
-888    def gamma_method(self, **kwargs):
-889        """Executes the gamma_method for the real and the imaginary part."""
-890        if isinstance(self.real, Obs):
-891            self.real.gamma_method(**kwargs)
-892        if isinstance(self.imag, Obs):
-893            self.imag.gamma_method(**kwargs)
-894
-895    def is_zero(self):
-896        """Checks whether both real and imaginary part are zero within machine precision."""
-897        return self.real == 0.0 and self.imag == 0.0
-898
-899    def conjugate(self):
-900        return CObs(self.real, -self.imag)
-901
-902    def __add__(self, other):
-903        if isinstance(other, np.ndarray):
-904            return other + self
-905        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-906            return CObs(self.real + other.real,
-907                        self.imag + other.imag)
-908        else:
-909            return CObs(self.real + other, self.imag)
-910
-911    def __radd__(self, y):
-912        return self + y
-913
-914    def __sub__(self, other):
-915        if isinstance(other, np.ndarray):
-916            return -1 * (other - self)
-917        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-918            return CObs(self.real - other.real, self.imag - other.imag)
-919        else:
-920            return CObs(self.real - other, self.imag)
-921
-922    def __rsub__(self, other):
-923        return -1 * (self - other)
-924
-925    def __mul__(self, other):
-926        if isinstance(other, np.ndarray):
-927            return other * self
-928        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-929            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
-930                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
-931                                               [self.real, other.real, self.imag, other.imag],
-932                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
-933                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
-934                                               [self.real, other.real, self.imag, other.imag],
-935                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
-936            elif getattr(other, 'imag', 0) != 0:
-937                return CObs(self.real * other.real - self.imag * other.imag,
-938                            self.imag * other.real + self.real * other.imag)
-939            else:
-940                return CObs(self.real * other.real, self.imag * other.real)
-941        else:
-942            return CObs(self.real * other, self.imag * other)
-943
-944    def __rmul__(self, other):
-945        return self * other
-946
-947    def __truediv__(self, other):
-948        if isinstance(other, np.ndarray):
-949            return 1 / (other / self)
-950        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-951            r = other.real ** 2 + other.imag ** 2
-952            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
-953        else:
-954            return CObs(self.real / other, self.imag / other)
-955
-956    def __rtruediv__(self, other):
-957        r = self.real ** 2 + self.imag ** 2
-958        if hasattr(other, 'real') and hasattr(other, 'imag'):
-959            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
-960        else:
-961            return CObs(self.real * other / r, -self.imag * other / r)
-962
-963    def __abs__(self):
-964        return np.sqrt(self.real**2 + self.imag**2)
-965
-966    def __pos__(self):
-967        return self
-968
-969    def __neg__(self):
-970        return -1 * self
-971
-972    def __eq__(self, other):
-973        return self.real == other.real and self.imag == other.imag
-974
-975    def __str__(self):
-976        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
-977
-978    def __repr__(self):
-979        return 'CObs[' + str(self) + ']'
+            
    873class CObs:
+874    """Class for a complex valued observable."""
+875    __slots__ = ['_real', '_imag', 'tag']
+876
+877    def __init__(self, real, imag=0.0):
+878        self._real = real
+879        self._imag = imag
+880        self.tag = None
+881
+882    @property
+883    def real(self):
+884        return self._real
+885
+886    @property
+887    def imag(self):
+888        return self._imag
+889
+890    def gamma_method(self, **kwargs):
+891        """Executes the gamma_method for the real and the imaginary part."""
+892        if isinstance(self.real, Obs):
+893            self.real.gamma_method(**kwargs)
+894        if isinstance(self.imag, Obs):
+895            self.imag.gamma_method(**kwargs)
+896
+897    def is_zero(self):
+898        """Checks whether both real and imaginary part are zero within machine precision."""
+899        return self.real == 0.0 and self.imag == 0.0
+900
+901    def conjugate(self):
+902        return CObs(self.real, -self.imag)
+903
+904    def __add__(self, other):
+905        if isinstance(other, np.ndarray):
+906            return other + self
+907        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+908            return CObs(self.real + other.real,
+909                        self.imag + other.imag)
+910        else:
+911            return CObs(self.real + other, self.imag)
+912
+913    def __radd__(self, y):
+914        return self + y
+915
+916    def __sub__(self, other):
+917        if isinstance(other, np.ndarray):
+918            return -1 * (other - self)
+919        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+920            return CObs(self.real - other.real, self.imag - other.imag)
+921        else:
+922            return CObs(self.real - other, self.imag)
+923
+924    def __rsub__(self, other):
+925        return -1 * (self - other)
+926
+927    def __mul__(self, other):
+928        if isinstance(other, np.ndarray):
+929            return other * self
+930        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+931            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
+932                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
+933                                               [self.real, other.real, self.imag, other.imag],
+934                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
+935                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
+936                                               [self.real, other.real, self.imag, other.imag],
+937                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
+938            elif getattr(other, 'imag', 0) != 0:
+939                return CObs(self.real * other.real - self.imag * other.imag,
+940                            self.imag * other.real + self.real * other.imag)
+941            else:
+942                return CObs(self.real * other.real, self.imag * other.real)
+943        else:
+944            return CObs(self.real * other, self.imag * other)
+945
+946    def __rmul__(self, other):
+947        return self * other
+948
+949    def __truediv__(self, other):
+950        if isinstance(other, np.ndarray):
+951            return 1 / (other / self)
+952        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+953            r = other.real ** 2 + other.imag ** 2
+954            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
+955        else:
+956            return CObs(self.real / other, self.imag / other)
+957
+958    def __rtruediv__(self, other):
+959        r = self.real ** 2 + self.imag ** 2
+960        if hasattr(other, 'real') and hasattr(other, 'imag'):
+961            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
+962        else:
+963            return CObs(self.real * other / r, -self.imag * other / r)
+964
+965    def __abs__(self):
+966        return np.sqrt(self.real**2 + self.imag**2)
+967
+968    def __pos__(self):
+969        return self
+970
+971    def __neg__(self):
+972        return -1 * self
+973
+974    def __eq__(self, other):
+975        return self.real == other.real and self.imag == other.imag
+976
+977    def __str__(self):
+978        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
+979
+980    def __repr__(self):
+981        return 'CObs[' + str(self) + ']'
 
    
 
 
@@ -4116,10 +4335,10 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    875    def __init__(self, real, imag=0.0):
-876        self._real = real
-877        self._imag = imag
-878        self.tag = None
+            
    877    def __init__(self, real, imag=0.0):
+878        self._real = real
+879        self._imag = imag
+880        self.tag = None
 
    
 
 
@@ -4137,12 +4356,12 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    888    def gamma_method(self, **kwargs):
-889        """Executes the gamma_method for the real and the imaginary part."""
-890        if isinstance(self.real, Obs):
-891            self.real.gamma_method(**kwargs)
-892        if isinstance(self.imag, Obs):
-893            self.imag.gamma_method(**kwargs)
+            
    890    def gamma_method(self, **kwargs):
+891        """Executes the gamma_method for the real and the imaginary part."""
+892        if isinstance(self.real, Obs):
+893            self.real.gamma_method(**kwargs)
+894        if isinstance(self.imag, Obs):
+895            self.imag.gamma_method(**kwargs)
 
    
 
 
@@ -4162,9 +4381,9 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    895    def is_zero(self):
-896        """Checks whether both real and imaginary part are zero within machine precision."""
-897        return self.real == 0.0 and self.imag == 0.0
+            
    897    def is_zero(self):
+898        """Checks whether both real and imaginary part are zero within machine precision."""
+899        return self.real == 0.0 and self.imag == 0.0
 
    
 
 
@@ -4184,8 +4403,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    899    def conjugate(self):
-900        return CObs(self.real, -self.imag)
+            
    901    def conjugate(self):
+902        return CObs(self.real, -self.imag)
 
    
 
 
@@ -4204,184 +4423,184 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    1133def derived_observable(func, data, array_mode=False, **kwargs):
-1134    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
-1135
-1136    Parameters
-1137    ----------
-1138    func : object
-1139        arbitrary function of the form func(data, **kwargs). For the
-1140        automatic differentiation to work, all numpy functions have to have
-1141        the autograd wrapper (use 'import autograd.numpy as anp').
-1142    data : list
-1143        list of Obs, e.g. [obs1, obs2, obs3].
-1144    num_grad : bool
-1145        if True, numerical derivatives are used instead of autograd
-1146        (default False). To control the numerical differentiation the
-1147        kwargs of numdifftools.step_generators.MaxStepGenerator
-1148        can be used.
-1149    man_grad : list
-1150        manually supply a list or an array which contains the jacobian
-1151        of func. Use cautiously, supplying the wrong derivative will
-1152        not be intercepted.
-1153
-1154    Notes
-1155    -----
-1156    For simple mathematical operations it can be practical to use anonymous
-1157    functions. For the ratio of two observables one can e.g. use
-1158
-1159    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
-1160    """
-1161
-1162    data = np.asarray(data)
-1163    raveled_data = data.ravel()
-1164
-1165    # Workaround for matrix operations containing non Obs data
-1166    if not all(isinstance(x, Obs) for x in raveled_data):
-1167        for i in range(len(raveled_data)):
-1168            if isinstance(raveled_data[i], (int, float)):
-1169                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
-1170
-1171    allcov = {}
-1172    for o in raveled_data:
-1173        for name in o.cov_names:
-1174            if name in allcov:
-1175                if not np.allclose(allcov[name], o.covobs[name].cov):
-1176                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
-1177            else:
-1178                allcov[name] = o.covobs[name].cov
-1179
-1180    n_obs = len(raveled_data)
-1181    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
-1182    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
-1183    new_sample_names = sorted(set(new_names) - set(new_cov_names))
-1184
-1185    is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names}
-1186    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
-1187
-1188    if data.ndim == 1:
-1189        values = np.array([o.value for o in data])
-1190    else:
-1191        values = np.vectorize(lambda x: x.value)(data)
-1192
-1193    new_values = func(values, **kwargs)
+            
    1135def derived_observable(func, data, array_mode=False, **kwargs):
+1136    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
+1137
+1138    Parameters
+1139    ----------
+1140    func : object
+1141        arbitrary function of the form func(data, **kwargs). For the
+1142        automatic differentiation to work, all numpy functions have to have
+1143        the autograd wrapper (use 'import autograd.numpy as anp').
+1144    data : list
+1145        list of Obs, e.g. [obs1, obs2, obs3].
+1146    num_grad : bool
+1147        if True, numerical derivatives are used instead of autograd
+1148        (default False). To control the numerical differentiation the
+1149        kwargs of numdifftools.step_generators.MaxStepGenerator
+1150        can be used.
+1151    man_grad : list
+1152        manually supply a list or an array which contains the jacobian
+1153        of func. Use cautiously, supplying the wrong derivative will
+1154        not be intercepted.
+1155
+1156    Notes
+1157    -----
+1158    For simple mathematical operations it can be practical to use anonymous
+1159    functions. For the ratio of two observables one can e.g. use
+1160
+1161    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
+1162    """
+1163
+1164    data = np.asarray(data)
+1165    raveled_data = data.ravel()
+1166
+1167    # Workaround for matrix operations containing non Obs data
+1168    if not all(isinstance(x, Obs) for x in raveled_data):
+1169        for i in range(len(raveled_data)):
+1170            if isinstance(raveled_data[i], (int, float)):
+1171                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
+1172
+1173    allcov = {}
+1174    for o in raveled_data:
+1175        for name in o.cov_names:
+1176            if name in allcov:
+1177                if not np.allclose(allcov[name], o.covobs[name].cov):
+1178                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
+1179            else:
+1180                allcov[name] = o.covobs[name].cov
+1181
+1182    n_obs = len(raveled_data)
+1183    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
+1184    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
+1185    new_sample_names = sorted(set(new_names) - set(new_cov_names))
+1186
+1187    is_merged = {name: (len(list(filter(lambda o: o.is_merged.get(name, False) is True, raveled_data))) > 0) for name in new_sample_names}
+1188    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1189
+1190    if data.ndim == 1:
+1191        values = np.array([o.value for o in data])
+1192    else:
+1193        values = np.vectorize(lambda x: x.value)(data)
 1194
-1195    multi = int(isinstance(new_values, np.ndarray))
+1195    new_values = func(values, **kwargs)
 1196
-1197    new_r_values = {}
-1198    new_idl_d = {}
-1199    for name in new_sample_names:
-1200        idl = []
-1201        tmp_values = np.zeros(n_obs)
-1202        for i, item in enumerate(raveled_data):
-1203            tmp_values[i] = item.r_values.get(name, item.value)
-1204            tmp_idl = item.idl.get(name)
-1205            if tmp_idl is not None:
-1206                idl.append(tmp_idl)
-1207        if multi > 0:
-1208            tmp_values = np.array(tmp_values).reshape(data.shape)
-1209        new_r_values[name] = func(tmp_values, **kwargs)
-1210        new_idl_d[name] = _merge_idx(idl)
-1211        if not is_merged[name]:
-1212            is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]])))
-1213
-1214    if 'man_grad' in kwargs:
-1215        deriv = np.asarray(kwargs.get('man_grad'))
-1216        if new_values.shape + data.shape != deriv.shape:
-1217            raise Exception('Manual derivative does not have correct shape.')
-1218    elif kwargs.get('num_grad') is True:
-1219        if multi > 0:
-1220            raise Exception('Multi mode currently not supported for numerical derivative')
-1221        options = {
-1222            'base_step': 0.1,
-1223            'step_ratio': 2.5}
-1224        for key in options.keys():
-1225            kwarg = kwargs.get(key)
-1226            if kwarg is not None:
-1227                options[key] = kwarg
-1228        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
-1229        if tmp_df.size == 1:
-1230            deriv = np.array([tmp_df.real])
-1231        else:
-1232            deriv = tmp_df.real
-1233    else:
-1234        deriv = jacobian(func)(values, **kwargs)
-1235
-1236    final_result = np.zeros(new_values.shape, dtype=object)
+1197    multi = int(isinstance(new_values, np.ndarray))
+1198
+1199    new_r_values = {}
+1200    new_idl_d = {}
+1201    for name in new_sample_names:
+1202        idl = []
+1203        tmp_values = np.zeros(n_obs)
+1204        for i, item in enumerate(raveled_data):
+1205            tmp_values[i] = item.r_values.get(name, item.value)
+1206            tmp_idl = item.idl.get(name)
+1207            if tmp_idl is not None:
+1208                idl.append(tmp_idl)
+1209        if multi > 0:
+1210            tmp_values = np.array(tmp_values).reshape(data.shape)
+1211        new_r_values[name] = func(tmp_values, **kwargs)
+1212        new_idl_d[name] = _merge_idx(idl)
+1213        if not is_merged[name]:
+1214            is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]])))
+1215
+1216    if 'man_grad' in kwargs:
+1217        deriv = np.asarray(kwargs.get('man_grad'))
+1218        if new_values.shape + data.shape != deriv.shape:
+1219            raise Exception('Manual derivative does not have correct shape.')
+1220    elif kwargs.get('num_grad') is True:
+1221        if multi > 0:
+1222            raise Exception('Multi mode currently not supported for numerical derivative')
+1223        options = {
+1224            'base_step': 0.1,
+1225            'step_ratio': 2.5}
+1226        for key in options.keys():
+1227            kwarg = kwargs.get(key)
+1228            if kwarg is not None:
+1229                options[key] = kwarg
+1230        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
+1231        if tmp_df.size == 1:
+1232            deriv = np.array([tmp_df.real])
+1233        else:
+1234            deriv = tmp_df.real
+1235    else:
+1236        deriv = jacobian(func)(values, **kwargs)
 1237
-1238    if array_mode is True:
+1238    final_result = np.zeros(new_values.shape, dtype=object)
 1239
-1240        class _Zero_grad():
-1241            def __init__(self, N):
-1242                self.grad = np.zeros((N, 1))
-1243
-1244        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
-1245        d_extracted = {}
-1246        g_extracted = {}
-1247        for name in new_sample_names:
-1248            d_extracted[name] = []
-1249            ens_length = len(new_idl_d[name])
-1250            for i_dat, dat in enumerate(data):
-1251                d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
-1252        for name in new_cov_names:
-1253            g_extracted[name] = []
-1254            zero_grad = _Zero_grad(new_covobs_lengths[name])
-1255            for i_dat, dat in enumerate(data):
-1256                g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1)))
-1257
-1258    for i_val, new_val in np.ndenumerate(new_values):
-1259        new_deltas = {}
-1260        new_grad = {}
-1261        if array_mode is True:
-1262            for name in new_sample_names:
-1263                ens_length = d_extracted[name][0].shape[-1]
-1264                new_deltas[name] = np.zeros(ens_length)
-1265                for i_dat, dat in enumerate(d_extracted[name]):
-1266                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1267            for name in new_cov_names:
-1268                new_grad[name] = 0
-1269                for i_dat, dat in enumerate(g_extracted[name]):
-1270                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1271        else:
-1272            for j_obs, obs in np.ndenumerate(data):
-1273                for name in obs.names:
-1274                    if name in obs.cov_names:
-1275                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
-1276                    else:
-1277                        new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name])
-1278
-1279        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1240    if array_mode is True:
+1241
+1242        class _Zero_grad():
+1243            def __init__(self, N):
+1244                self.grad = np.zeros((N, 1))
+1245
+1246        new_covobs_lengths = dict(set([y for x in [[(n, o.covobs[n].N) for n in o.cov_names] for o in raveled_data] for y in x]))
+1247        d_extracted = {}
+1248        g_extracted = {}
+1249        for name in new_sample_names:
+1250            d_extracted[name] = []
+1251            ens_length = len(new_idl_d[name])
+1252            for i_dat, dat in enumerate(data):
+1253                d_extracted[name].append(np.array([_expand_deltas_for_merge(o.deltas.get(name, np.zeros(ens_length)), o.idl.get(name, new_idl_d[name]), o.shape.get(name, ens_length), new_idl_d[name]) for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (ens_length, )))
+1254        for name in new_cov_names:
+1255            g_extracted[name] = []
+1256            zero_grad = _Zero_grad(new_covobs_lengths[name])
+1257            for i_dat, dat in enumerate(data):
+1258                g_extracted[name].append(np.array([o.covobs.get(name, zero_grad).grad for o in dat.reshape(np.prod(dat.shape))]).reshape(dat.shape + (new_covobs_lengths[name], 1)))
+1259
+1260    for i_val, new_val in np.ndenumerate(new_values):
+1261        new_deltas = {}
+1262        new_grad = {}
+1263        if array_mode is True:
+1264            for name in new_sample_names:
+1265                ens_length = d_extracted[name][0].shape[-1]
+1266                new_deltas[name] = np.zeros(ens_length)
+1267                for i_dat, dat in enumerate(d_extracted[name]):
+1268                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1269            for name in new_cov_names:
+1270                new_grad[name] = 0
+1271                for i_dat, dat in enumerate(g_extracted[name]):
+1272                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1273        else:
+1274            for j_obs, obs in np.ndenumerate(data):
+1275                for name in obs.names:
+1276                    if name in obs.cov_names:
+1277                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
+1278                    else:
+1279                        new_deltas[name] = new_deltas.get(name, 0) + deriv[i_val + j_obs] * _expand_deltas_for_merge(obs.deltas[name], obs.idl[name], obs.shape[name], new_idl_d[name])
 1280
-1281        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
-1282            raise Exception('The same name has been used for deltas and covobs!')
-1283        new_samples = []
-1284        new_means = []
-1285        new_idl = []
-1286        new_names_obs = []
-1287        for name in new_names:
-1288            if name not in new_covobs:
-1289                if is_merged[name]:
-1290                    filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name])
-1291                else:
-1292                    filtered_deltas = new_deltas[name]
-1293                    filtered_idl_d = new_idl_d[name]
-1294
-1295                new_samples.append(filtered_deltas)
-1296                new_idl.append(filtered_idl_d)
-1297                new_means.append(new_r_values[name][i_val])
-1298                new_names_obs.append(name)
-1299        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
-1300        for name in new_covobs:
-1301            final_result[i_val].names.append(name)
-1302        final_result[i_val]._covobs = new_covobs
-1303        final_result[i_val]._value = new_val
-1304        final_result[i_val].is_merged = is_merged
-1305        final_result[i_val].reweighted = reweighted
-1306
-1307    if multi == 0:
-1308        final_result = final_result.item()
-1309
-1310    return final_result
+1281        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1282
+1283        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
+1284            raise Exception('The same name has been used for deltas and covobs!')
+1285        new_samples = []
+1286        new_means = []
+1287        new_idl = []
+1288        new_names_obs = []
+1289        for name in new_names:
+1290            if name not in new_covobs:
+1291                if is_merged[name]:
+1292                    filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name])
+1293                else:
+1294                    filtered_deltas = new_deltas[name]
+1295                    filtered_idl_d = new_idl_d[name]
+1296
+1297                new_samples.append(filtered_deltas)
+1298                new_idl.append(filtered_idl_d)
+1299                new_means.append(new_r_values[name][i_val])
+1300                new_names_obs.append(name)
+1301        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
+1302        for name in new_covobs:
+1303            final_result[i_val].names.append(name)
+1304        final_result[i_val]._covobs = new_covobs
+1305        final_result[i_val]._value = new_val
+1306        final_result[i_val].is_merged = is_merged
+1307        final_result[i_val].reweighted = reweighted
+1308
+1309    if multi == 0:
+1310        final_result = final_result.item()
+1311
+1312    return final_result
 
    
 
 
@@ -4428,47 +4647,47 @@ functions. For the ratio of two observables one can e.g. use
    - 
    1347def reweight(weight, obs, **kwargs):
-1348    """Reweight a list of observables.
-1349
-1350    Parameters
-1351    ----------
-1352    weight : Obs
-1353        Reweighting factor. An Observable that has to be defined on a superset of the
-1354        configurations in obs[i].idl for all i.
-1355    obs : list
-1356        list of Obs, e.g. [obs1, obs2, obs3].
-1357    all_configs : bool
-1358        if True, the reweighted observables are normalized by the average of
-1359        the reweighting factor on all configurations in weight.idl and not
-1360        on the configurations in obs[i].idl. Default False.
-1361    """
-1362    result = []
-1363    for i in range(len(obs)):
-1364        if len(obs[i].cov_names):
-1365            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
-1366        if not set(obs[i].names).issubset(weight.names):
-1367            raise Exception('Error: Ensembles do not fit')
-1368        for name in obs[i].names:
-1369            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
-1370                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
-1371        new_samples = []
-1372        w_deltas = {}
-1373        for name in sorted(obs[i].names):
-1374            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
-1375            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
-1376        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1377
-1378        if kwargs.get('all_configs'):
-1379            new_weight = weight
-1380        else:
-1381            new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1382
-1383        result.append(tmp_obs / new_weight)
-1384        result[-1].reweighted = True
-1385        result[-1].is_merged = obs[i].is_merged
-1386
-1387    return result
+            
    1349def reweight(weight, obs, **kwargs):
+1350    """Reweight a list of observables.
+1351
+1352    Parameters
+1353    ----------
+1354    weight : Obs
+1355        Reweighting factor. An Observable that has to be defined on a superset of the
+1356        configurations in obs[i].idl for all i.
+1357    obs : list
+1358        list of Obs, e.g. [obs1, obs2, obs3].
+1359    all_configs : bool
+1360        if True, the reweighted observables are normalized by the average of
+1361        the reweighting factor on all configurations in weight.idl and not
+1362        on the configurations in obs[i].idl. Default False.
+1363    """
+1364    result = []
+1365    for i in range(len(obs)):
+1366        if len(obs[i].cov_names):
+1367            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
+1368        if not set(obs[i].names).issubset(weight.names):
+1369            raise Exception('Error: Ensembles do not fit')
+1370        for name in obs[i].names:
+1371            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
+1372                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
+1373        new_samples = []
+1374        w_deltas = {}
+1375        for name in sorted(obs[i].names):
+1376            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
+1377            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
+1378        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1379
+1380        if kwargs.get('all_configs'):
+1381            new_weight = weight
+1382        else:
+1383            new_weight = Obs([w_deltas[name] + weight.r_values[name] for name in sorted(obs[i].names)], sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1384
+1385        result.append(tmp_obs / new_weight)
+1386        result[-1].reweighted = True
+1387        result[-1].is_merged = obs[i].is_merged
+1388
+1389    return result
 
    
 
 
@@ -4502,48 +4721,48 @@ on the configurations in obs[i].idl. Default False.
    - 
    1390def correlate(obs_a, obs_b):
-1391    """Correlate two observables.
-1392
-1393    Parameters
-1394    ----------
-1395    obs_a : Obs
-1396        First observable
-1397    obs_b : Obs
-1398        Second observable
-1399
-1400    Notes
-1401    -----
-1402    Keep in mind to only correlate primary observables which have not been reweighted
-1403    yet. The reweighting has to be applied after correlating the observables.
-1404    Currently only works if ensembles are identical (this is not strictly necessary).
-1405    """
-1406
-1407    if sorted(obs_a.names) != sorted(obs_b.names):
-1408        raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
-1409    if len(obs_a.cov_names) or len(obs_b.cov_names):
-1410        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
-1411    for name in obs_a.names:
-1412        if obs_a.shape[name] != obs_b.shape[name]:
-1413            raise Exception('Shapes of ensemble', name, 'do not fit')
-1414        if obs_a.idl[name] != obs_b.idl[name]:
-1415            raise Exception('idl of ensemble', name, 'do not fit')
-1416
-1417    if obs_a.reweighted is True:
-1418        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
-1419    if obs_b.reweighted is True:
-1420        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
-1421
-1422    new_samples = []
-1423    new_idl = []
-1424    for name in sorted(obs_a.names):
-1425        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
-1426        new_idl.append(obs_a.idl[name])
-1427
-1428    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
-1429    o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names}
-1430    o.reweighted = obs_a.reweighted or obs_b.reweighted
-1431    return o
+            
    1392def correlate(obs_a, obs_b):
+1393    """Correlate two observables.
+1394
+1395    Parameters
+1396    ----------
+1397    obs_a : Obs
+1398        First observable
+1399    obs_b : Obs
+1400        Second observable
+1401
+1402    Notes
+1403    -----
+1404    Keep in mind to only correlate primary observables which have not been reweighted
+1405    yet. The reweighting has to be applied after correlating the observables.
+1406    Currently only works if ensembles are identical (this is not strictly necessary).
+1407    """
+1408
+1409    if sorted(obs_a.names) != sorted(obs_b.names):
+1410        raise Exception(f"Ensembles do not fit {set(sorted(obs_a.names)) ^ set(sorted(obs_b.names))}")
+1411    if len(obs_a.cov_names) or len(obs_b.cov_names):
+1412        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
+1413    for name in obs_a.names:
+1414        if obs_a.shape[name] != obs_b.shape[name]:
+1415            raise Exception('Shapes of ensemble', name, 'do not fit')
+1416        if obs_a.idl[name] != obs_b.idl[name]:
+1417            raise Exception('idl of ensemble', name, 'do not fit')
+1418
+1419    if obs_a.reweighted is True:
+1420        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
+1421    if obs_b.reweighted is True:
+1422        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
+1423
+1424    new_samples = []
+1425    new_idl = []
+1426    for name in sorted(obs_a.names):
+1427        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
+1428        new_idl.append(obs_a.idl[name])
+1429
+1430    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
+1431    o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names}
+1432    o.reweighted = obs_a.reweighted or obs_b.reweighted
+1433    return o
 
    
 
 
@@ -4578,74 +4797,74 @@ Currently only works if ensembles are identical (this is not strictly necessary)
    - 
    1434def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
-1435    r'''Calculates the error covariance matrix of a set of observables.
-1436
-1437    WARNING: This function should be used with care, especially for observables with support on multiple
-1438             ensembles with differing autocorrelations. See the notes below for details.
-1439
-1440    The gamma method has to be applied first to all observables.
+            
    1436def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+1437    r'''Calculates the error covariance matrix of a set of observables.
+1438
+1439    WARNING: This function should be used with care, especially for observables with support on multiple
+1440             ensembles with differing autocorrelations. See the notes below for details.
 1441
-1442    Parameters
-1443    ----------
-1444    obs : list or numpy.ndarray
-1445        List or one dimensional array of Obs
-1446    visualize : bool
-1447        If True plots the corresponding normalized correlation matrix (default False).
-1448    correlation : bool
-1449        If True the correlation matrix instead of the error covariance matrix is returned (default False).
-1450    smooth : None or int
-1451        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
-1452        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
-1453        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
-1454        small ones.
-1455
-1456    Notes
-1457    -----
-1458    The error covariance is defined such that it agrees with the squared standard error for two identical observables
-1459    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
-1460    in the absence of autocorrelation.
-1461    The 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
-1462    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
-1463    For 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.
-1464    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
-1465    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
-1466    '''
-1467
-1468    length = len(obs)
+1442    The gamma method has to be applied first to all observables.
+1443
+1444    Parameters
+1445    ----------
+1446    obs : list or numpy.ndarray
+1447        List or one dimensional array of Obs
+1448    visualize : bool
+1449        If True plots the corresponding normalized correlation matrix (default False).
+1450    correlation : bool
+1451        If True the correlation matrix instead of the error covariance matrix is returned (default False).
+1452    smooth : None or int
+1453        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
+1454        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
+1455        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
+1456        small ones.
+1457
+1458    Notes
+1459    -----
+1460    The error covariance is defined such that it agrees with the squared standard error for two identical observables
+1461    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
+1462    in the absence of autocorrelation.
+1463    The 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
+1464    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
+1465    For 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.
+1466    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
+1467    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
+1468    '''
 1469
-1470    max_samples = np.max([o.N for o in obs])
-1471    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
-1472        warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning)
-1473
-1474    cov = np.zeros((length, length))
-1475    for i in range(length):
-1476        for j in range(i, length):
-1477            cov[i, j] = _covariance_element(obs[i], obs[j])
-1478    cov = cov + cov.T - np.diag(np.diag(cov))
-1479
-1480    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
+1470    length = len(obs)
+1471
+1472    max_samples = np.max([o.N for o in obs])
+1473    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
+1474        warnings.warn(f"The dimension of the covariance matrix ({length}) is larger or equal to the number of samples ({max_samples}). This will result in a rank deficient matrix.", RuntimeWarning)
+1475
+1476    cov = np.zeros((length, length))
+1477    for i in range(length):
+1478        for j in range(i, length):
+1479            cov[i, j] = _covariance_element(obs[i], obs[j])
+1480    cov = cov + cov.T - np.diag(np.diag(cov))
 1481
-1482    if isinstance(smooth, int):
-1483        corr = _smooth_eigenvalues(corr, smooth)
-1484
-1485    if visualize:
-1486        plt.matshow(corr, vmin=-1, vmax=1)
-1487        plt.set_cmap('RdBu')
-1488        plt.colorbar()
-1489        plt.draw()
-1490
-1491    if correlation is True:
-1492        return corr
-1493
-1494    errors = [o.dvalue for o in obs]
-1495    cov = np.diag(errors) @ corr @ np.diag(errors)
-1496
-1497    eigenvalues = np.linalg.eigh(cov)[0]
-1498    if not np.all(eigenvalues >= 0):
-1499        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
-1500
-1501    return cov
+1482    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
+1483
+1484    if isinstance(smooth, int):
+1485        corr = _smooth_eigenvalues(corr, smooth)
+1486
+1487    if visualize:
+1488        plt.matshow(corr, vmin=-1, vmax=1)
+1489        plt.set_cmap('RdBu')
+1490        plt.colorbar()
+1491        plt.draw()
+1492
+1493    if correlation is True:
+1494        return corr
+1495
+1496    errors = [o.dvalue for o in obs]
+1497    cov = np.diag(errors) @ corr @ np.diag(errors)
+1498
+1499    eigenvalues = np.linalg.eigh(cov)[0]
+1500    if not np.all(eigenvalues >= 0):
+1501        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
+1502
+1503    return cov
 
    
 
 
@@ -4697,24 +4916,24 @@ This construction ensures that the estimated covariance matrix is positive semi-
    - 
    1581def import_jackknife(jacks, name, idl=None):
-1582    """Imports jackknife samples and returns an Obs
-1583
-1584    Parameters
-1585    ----------
-1586    jacks : numpy.ndarray
-1587        numpy array containing the mean value as zeroth entry and
-1588        the N jackknife samples as first to Nth entry.
-1589    name : str
-1590        name of the ensemble the samples are defined on.
-1591    """
-1592    length = len(jacks) - 1
-1593    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
-1594    samples = jacks[1:] @ prj
-1595    mean = np.mean(samples)
-1596    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
-1597    new_obs._value = jacks[0]
-1598    return new_obs
+            
    1583def import_jackknife(jacks, name, idl=None):
+1584    """Imports jackknife samples and returns an Obs
+1585
+1586    Parameters
+1587    ----------
+1588    jacks : numpy.ndarray
+1589        numpy array containing the mean value as zeroth entry and
+1590        the N jackknife samples as first to Nth entry.
+1591    name : str
+1592        name of the ensemble the samples are defined on.
+1593    """
+1594    length = len(jacks) - 1
+1595    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
+1596    samples = jacks[1:] @ prj
+1597    mean = np.mean(samples)
+1598    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
+1599    new_obs._value = jacks[0]
+1600    return new_obs
 
    
 
 
@@ -4744,35 +4963,35 @@ name of the ensemble the samples are defined on.
    - 
    1601def merge_obs(list_of_obs):
-1602    """Combine all observables in list_of_obs into one new observable
-1603
-1604    Parameters
-1605    ----------
-1606    list_of_obs : list
-1607        list of the Obs object to be combined
-1608
-1609    Notes
-1610    -----
-1611    It is not possible to combine obs which are based on the same replicum
-1612    """
-1613    replist = [item for obs in list_of_obs for item in obs.names]
-1614    if (len(replist) == len(set(replist))) is False:
-1615        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
-1616    if any([len(o.cov_names) for o in list_of_obs]):
-1617        raise Exception('Not possible to merge data that contains covobs!')
-1618    new_dict = {}
-1619    idl_dict = {}
-1620    for o in list_of_obs:
-1621        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
-1622                        for key in set(o.deltas) | set(o.r_values)})
-1623        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
-1624
-1625    names = sorted(new_dict.keys())
-1626    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
-1627    o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names}
-1628    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
-1629    return o
+            
    1603def merge_obs(list_of_obs):
+1604    """Combine all observables in list_of_obs into one new observable
+1605
+1606    Parameters
+1607    ----------
+1608    list_of_obs : list
+1609        list of the Obs object to be combined
+1610
+1611    Notes
+1612    -----
+1613    It is not possible to combine obs which are based on the same replicum
+1614    """
+1615    replist = [item for obs in list_of_obs for item in obs.names]
+1616    if (len(replist) == len(set(replist))) is False:
+1617        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
+1618    if any([len(o.cov_names) for o in list_of_obs]):
+1619        raise Exception('Not possible to merge data that contains covobs!')
+1620    new_dict = {}
+1621    idl_dict = {}
+1622    for o in list_of_obs:
+1623        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
+1624                        for key in set(o.deltas) | set(o.r_values)})
+1625        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
+1626
+1627    names = sorted(new_dict.keys())
+1628    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
+1629    o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names}
+1630    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
+1631    return o
 
    
 
 
@@ -4803,47 +5022,47 @@ list of the Obs object to be combined
    - 
    1632def cov_Obs(means, cov, name, grad=None):
-1633    """Create an Obs based on mean(s) and a covariance matrix
-1634
-1635    Parameters
-1636    ----------
-1637    mean : list of floats or float
-1638        N mean value(s) of the new Obs
-1639    cov : list or array
-1640        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
-1641    name : str
-1642        identifier for the covariance matrix
-1643    grad : list or array
-1644        Gradient of the Covobs wrt. the means belonging to cov.
-1645    """
-1646
-1647    def covobs_to_obs(co):
-1648        """Make an Obs out of a Covobs
-1649
-1650        Parameters
-1651        ----------
-1652        co : Covobs
-1653            Covobs to be embedded into the Obs
-1654        """
-1655        o = Obs([], [], means=[])
-1656        o._value = co.value
-1657        o.names.append(co.name)
-1658        o._covobs[co.name] = co
-1659        o._dvalue = np.sqrt(co.errsq())
-1660        return o
-1661
-1662    ol = []
-1663    if isinstance(means, (float, int)):
-1664        means = [means]
-1665
-1666    for i in range(len(means)):
-1667        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
-1668    if ol[0].covobs[name].N != len(means):
-1669        raise Exception('You have to provide %d mean values!' % (ol[0].N))
-1670    if len(ol) == 1:
-1671        return ol[0]
-1672    return ol
+            
    1634def cov_Obs(means, cov, name, grad=None):
+1635    """Create an Obs based on mean(s) and a covariance matrix
+1636
+1637    Parameters
+1638    ----------
+1639    mean : list of floats or float
+1640        N mean value(s) of the new Obs
+1641    cov : list or array
+1642        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
+1643    name : str
+1644        identifier for the covariance matrix
+1645    grad : list or array
+1646        Gradient of the Covobs wrt. the means belonging to cov.
+1647    """
+1648
+1649    def covobs_to_obs(co):
+1650        """Make an Obs out of a Covobs
+1651
+1652        Parameters
+1653        ----------
+1654        co : Covobs
+1655            Covobs to be embedded into the Obs
+1656        """
+1657        o = Obs([], [], means=[])
+1658        o._value = co.value
+1659        o.names.append(co.name)
+1660        o._covobs[co.name] = co
+1661        o._dvalue = np.sqrt(co.errsq())
+1662        return o
+1663
+1664    ol = []
+1665    if isinstance(means, (float, int)):
+1666        means = [means]
+1667
+1668    for i in range(len(means)):
+1669        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
+1670    if ol[0].covobs[name].N != len(means):
+1671        raise Exception('You have to provide %d mean values!' % (ol[0].N))
+1672    if len(ol) == 1:
+1673        return ol[0]
+1674    return ol
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index 1811c937..24bf5557 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. 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this.config},t.Configuration.prototype.reset=function(){this.config={}},lunr.SortedSet=function(){this.length=0,this.elements=[]},lunr.SortedSet.load=function(e){var t=new this;return t.elements=e,t.length=e.length,t},lunr.SortedSet.prototype.add=function(){var e,t;for(e=0;e1;){if(r===e)return o;e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o]}return r===e?o:-1},lunr.SortedSet.prototype.locationFor=function(e){for(var t=0,n=this.elements.length,i=n-t,o=t+Math.floor(i/2),r=this.elements[o];i>1;)e>r&&(t=o),r>e&&(n=o),i=n-t,o=t+Math.floor(i/2),r=this.elements[o];return r>e?o:e>r?o+1:void 0},lunr.SortedSet.prototype.intersect=function(e){for(var t=new lunr.SortedSet,n=0,i=0,o=this.length,r=e.length,s=this.elements,u=e.elements;;){if(n>o-1||i>r-1)break;s[n]!==u[i]?s[n]u[i]&&i++:(t.add(s[n]),n++,i++)}return t},lunr.SortedSet.prototype.clone=function(){var e=new lunr.SortedSet;return e.elements=this.toArray(),e.length=e.elements.length,e},lunr.SortedSet.prototype.union=function(e){var t,n,i;this.length>=e.length?(t=this,n=e):(t=e,n=this),i=t.clone();for(var o=0,r=n.toArray();oWhat is pyerrors?\n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. [arXiv:2209.14371 [hep-lat]].
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\tfname,\tnoempty=False,\tfull_output=False,\tgz=True,\tseparator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "kind": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact linear error propagation as suggested in arXiv:1809.01289 (partly based on the autograd package).
      • \n
    • treatment of slow modes in the simulation as suggested in arXiv:1009.5228.
      • \n
    • coherent error propagation for data from different Markov chains.
      • \n
    • non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in arXiv:1809.01289.
      • \n
    • real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).
      • \n
    \n\n
    More detailed examples can found in the GitHub repository \"badge\".
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, pyerrors: a python framework for error analysis of Monte Carlo data. [arXiv:2209.14371 [hep-lat]].
      • \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.
      • \n
    \n\n
    and
    \n\n
      \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.
      • \n
    \n\n
    where applicable.
    \n\n
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    \n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    \n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    \n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    \n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_rho.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    \n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    \n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    \n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    \n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    \n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    \n
    print(my_corr[3])\n> 0.3227(33)\n
    \n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    \n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    \n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    \n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    \n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    \n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    \n
    o.covobs[k].grad\n
    \n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    \n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    \n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    \n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    \n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only difference being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    \n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(data_input, padding=[0, 0], prange=None)"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j):", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "
    Checks whether a correlator matrices is symmetric on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    \n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue'):", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt):", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0):", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner):", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1):", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, log, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric'):", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0):", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False):", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange):", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\tself,\tx_range=None,\tcomp=None,\ty_range=None,\tlogscale=False,\tplateau=None,\tfit_res=None,\tylabel=None,\tsave=None,\tauto_gamma=False,\thide_sigma=None,\treferences=None,\ttitle=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True):", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs):", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "
    \n", "signature": "(self, print_range=None):", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None):", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(mean, cov, name, pos=None, grad=None)"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k):", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o):", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag):", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    • chisquare_by_dof (float):\nreduced chisquare.
      • \n
    • p_value (float):\np-value of the fit
      • \n
    • t2_p_value (float):\nHotelling t-squared p-value for correlated fits.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      \n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n
      \n\n
      For multiple x values func can be of the form
      \n\n
      \n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    • num_grad (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs):", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs):", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p):", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res):", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta):", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None):", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs):", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='',\torigin='',\tsymbol=[],\tenstag=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None):", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\tfname,\tnoempty=False,\tfull_output=False,\tgz=True,\tseparator_insertion=True):", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\tobsl,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None):", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\tobsl,\tfname,\tname,\tspec='dobs v1.0',\torigin='',\tsymbol=[],\twho=None,\tenstags=None,\tgz=True):", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    \n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n
    \n\n
    Second mode:
    \n\n
    \n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "kind": "function", "doc": "
    \n", "signature": "()"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None):", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV']):", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1):", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True):", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False):", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True):", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS'):", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "
    Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.
    \n\n
    Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, Zeuthen_flow=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0):", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs):", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "
    Read data from files in the specified directory with the specified prefix and quark combination extension, and return a Corr object containing the data.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nThe directory to search for the files in.
      • \n
    • prefix (str):\nThe prefix to match the files against.
      • \n
    • qc (str):\nThe quark combination extension to match the files against.
      • \n
    • corr (str):\nThe correlator to extract data for.
      • \n
    • sep (str, optional):\nThe separator to use when parsing the replika names.
      • \n
    • **kwargs: Additional keyword arguments. The following keyword arguments are recognized:
      \n\n
        \n
      • names (List[str]): A list of names to use for the replicas.
        • \n
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Corr: A complex valued Corr object containing the data read from the files. In case of boudary to bulk correlators.
      • \n
    • or
      • \n
    • CObs: A complex valued CObs object containing the data read from the files. In case of boudary to boundary correlators.
      • \n
    \n\n
    Raises
    \n\n
      \n
    • FileNotFoundError: If no files matching the specified prefix and quark combination extension are found in the specified directory.
      • \n
    • IOError: If there is an error reading a file.
      • \n
    • struct.error: If there is an error unpacking binary data.
      • \n
    \n", "signature": "(path, prefix, qc, corr, sep='r', **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "
    \n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "
    Write DataFrame including Obs or Corr valued columns to sqlite database.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be written to the database.
      • \n
    • table_name (str):\nName of the table in the database.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • if exists (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.
      • \n
    • gz (bool):\nIf True the json strings are gzipped.
      • \n
    \n", "signature": "(df, table_name, db, if_exists='fail', gz=True, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "
    Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.
    \n\n
    Parameters
    \n\n
      \n
    • sql (str):\nSQL query to be executed.
      • \n
    • db (str):\nPath to the sqlite database.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    \n", "signature": "(sql, db, auto_gamma=False, **kwargs):", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "
    Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.
    \n\n
    Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.
    \n\n
    Parameters
    \n\n
      \n
    • df (pandas.DataFrame):\nDataframe to be dumped to a file.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • gz (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.
      • \n
    \n", "signature": "(df, fname, gz=True):", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "
    Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • auto_gamma (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    \n", "signature": "(fname, auto_gamma=False, gz=True):", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to the sfcf files.
      • \n
    • prefix (str):\nPrefix of the sfcf files.
      • \n
    • name (str):\nName of the correlation function to read.
      • \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • corr_type (str):\nType of correlation function to read. Can be\n
        \n
      • 'bi' for boundary-inner
        • \n
      • 'bb' for boundary-boundary
        • \n
      • 'bib' for boundary-inner-boundary
        • \n
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\tpath,\tprefix,\tname,\tquarks='.*',\tcorr_type='bi',\tnoffset=0,\twf=0,\twf2=0,\tversion='1.0c',\tcfg_separator='n',\t**kwargs):", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che):", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands):", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands):", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x):", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs):", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs):", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path):", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000):", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000):", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(samples, names, idl=None, **kwargs)"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True):", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, weight):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1):", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True):", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None):", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs):", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "
    \n", "signature": "(real, imag=0.0)"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs):", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "
    \n", "signature": "(self):", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs):", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs):", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b):", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs):", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None):", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs):", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None):", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:
      \n\n
      \n
      import autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      \n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs):", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "
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