diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html index 890a731d..1b40d9e8 100644 --- a/docs/pyerrors/obs.html +++ b/docs/pyerrors/obs.html @@ -131,6 +131,9 @@
  • details
    • +
  • + reweight +
  • is_zero_within_error
    • @@ -739,1220 +742,1235 @@ 426 my_string_list.append(my_string) 427 print('\n'.join(my_string_list)) 428 - 429 def is_zero_within_error(self, sigma=1): - 430 """Checks whether the observable is zero within 'sigma' standard errors. + 429 def reweight(self, rw): + 430 """Reweight the obs with given rewighting factors. 431 432 Parameters 433 ---------- - 434 sigma : int - 435 Number of standard errors used for the check. - 436 - 437 Works only properly when the gamma method was run. - 438 """ - 439 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue - 440 - 441 def is_zero(self, atol=1e-10): - 442 """Checks whether the observable is zero within a given tolerance. + 434 weight : Obs + 435 Reweighting factor. An Observable that has to be defined on a superset of the + 436 configurations in obs[i].idl for all i. + 437 all_configs : bool + 438 if True, the reweighted observables are normalized by the average of + 439 the reweighting factor on all configurations in weight.idl and not + 440 on the configurations in obs[i].idl. Default False. + 441 """ + 442 return reweight(rw, [self])[0] 443 - 444 Parameters - 445 ---------- - 446 atol : float - 447 Absolute tolerance (for details see numpy documentation). - 448 """ - 449 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()) - 450 - 451 def plot_tauint(self, save=None): - 452 """Plot integrated autocorrelation time for each ensemble. - 453 - 454 Parameters - 455 ---------- - 456 save : str - 457 saves the figure to a file named 'save' if. - 458 """ - 459 if not hasattr(self, 'e_dvalue'): - 460 raise Exception('Run the gamma method first.') - 461 - 462 for e, e_name in enumerate(self.mc_names): - 463 fig = plt.figure() - 464 plt.xlabel(r'$W$') - 465 plt.ylabel(r'$\tau_\mathrm{int}$') - 466 length = int(len(self.e_n_tauint[e_name])) - 467 if self.tau_exp[e_name] > 0: - 468 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] - 469 x_help = np.arange(2 * self.tau_exp[e_name]) - 470 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 - 471 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) - 472 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') - 473 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], - 474 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) - 475 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 - 476 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) - 477 else: - 478 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) - 479 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) - 480 - 481 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) - 482 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') - 483 plt.legend() - 484 plt.xlim(-0.5, xmax) - 485 ylim = plt.ylim() - 486 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) - 487 plt.draw() - 488 if save: - 489 fig.savefig(save + "_" + str(e)) - 490 - 491 def plot_rho(self, save=None): - 492 """Plot normalized autocorrelation function time for each ensemble. - 493 - 494 Parameters - 495 ---------- - 496 save : str - 497 saves the figure to a file named 'save' if. - 498 """ - 499 if not hasattr(self, 'e_dvalue'): - 500 raise Exception('Run the gamma method first.') - 501 for e, e_name in enumerate(self.mc_names): - 502 fig = plt.figure() - 503 plt.xlabel('W') - 504 plt.ylabel('rho') - 505 length = int(len(self.e_drho[e_name])) - 506 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) - 507 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') - 508 if self.tau_exp[e_name] > 0: - 509 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], - 510 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) - 511 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 - 512 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) - 513 else: - 514 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) - 515 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) - 516 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) - 517 plt.xlim(-0.5, xmax) - 518 plt.draw() - 519 if save: - 520 fig.savefig(save + "_" + str(e)) - 521 - 522 def plot_rep_dist(self): - 523 """Plot replica distribution for each ensemble with more than one replicum.""" - 524 if not hasattr(self, 'e_dvalue'): - 525 raise Exception('Run the gamma method first.') - 526 for e, e_name in enumerate(self.mc_names): - 527 if len(self.e_content[e_name]) == 1: - 528 print('No replica distribution for a single replicum (', e_name, ')') - 529 continue - 530 r_length = [] - 531 sub_r_mean = 0 - 532 for r, r_name in enumerate(self.e_content[e_name]): - 533 r_length.append(len(self.deltas[r_name])) - 534 sub_r_mean += self.shape[r_name] * self.r_values[r_name] - 535 e_N = np.sum(r_length) - 536 sub_r_mean /= e_N - 537 arr = np.zeros(len(self.e_content[e_name])) - 538 for r, r_name in enumerate(self.e_content[e_name]): - 539 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) - 540 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) - 541 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') - 542 plt.draw() - 543 - 544 def plot_history(self, expand=True): - 545 """Plot derived Monte Carlo history for each ensemble - 546 - 547 Parameters - 548 ---------- - 549 expand : bool - 550 show expanded history for irregular Monte Carlo chains (default: True). - 551 """ - 552 for e, e_name in enumerate(self.mc_names): - 553 plt.figure() - 554 r_length = [] - 555 tmp = [] - 556 tmp_expanded = [] - 557 for r, r_name in enumerate(self.e_content[e_name]): - 558 tmp.append(self.deltas[r_name] + self.r_values[r_name]) - 559 if expand: - 560 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) - 561 r_length.append(len(tmp_expanded[-1])) - 562 else: - 563 r_length.append(len(tmp[-1])) - 564 e_N = np.sum(r_length) - 565 x = np.arange(e_N) - 566 y_test = np.concatenate(tmp, axis=0) - 567 if expand: - 568 y = np.concatenate(tmp_expanded, axis=0) - 569 else: - 570 y = y_test - 571 plt.errorbar(x, y, fmt='.', markersize=3) - 572 plt.xlim(-0.5, e_N - 0.5) - 573 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})') - 574 plt.draw() - 575 - 576 def plot_piechart(self, save=None): - 577 """Plot piechart which shows the fractional contribution of each - 578 ensemble to the error and returns a dictionary containing the fractions. - 579 - 580 Parameters - 581 ---------- - 582 save : str - 583 saves the figure to a file named 'save' if. - 584 """ - 585 if not hasattr(self, 'e_dvalue'): - 586 raise Exception('Run the gamma method first.') - 587 if np.isclose(0.0, self._dvalue, atol=1e-15): - 588 raise Exception('Error is 0.0') - 589 labels = self.e_names - 590 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 - 591 fig1, ax1 = plt.subplots() - 592 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) - 593 ax1.axis('equal') - 594 plt.draw() - 595 if save: - 596 fig1.savefig(save) - 597 - 598 return dict(zip(self.e_names, sizes)) - 599 - 600 def dump(self, filename, datatype="json.gz", description="", **kwargs): - 601 """Dump the Obs to a file 'name' of chosen format. - 602 - 603 Parameters - 604 ---------- - 605 filename : str - 606 name of the file to be saved. - 607 datatype : str - 608 Format of the exported file. Supported formats include - 609 "json.gz" and "pickle" - 610 description : str - 611 Description for output file, only relevant for json.gz format. - 612 path : str - 613 specifies a custom path for the file (default '.') - 614 """ - 615 if 'path' in kwargs: - 616 file_name = kwargs.get('path') + '/' + filename - 617 else: - 618 file_name = filename - 619 - 620 if datatype == "json.gz": - 621 from .input.json import dump_to_json - 622 dump_to_json([self], file_name, description=description) - 623 elif datatype == "pickle": - 624 with open(file_name + '.p', 'wb') as fb: - 625 pickle.dump(self, fb) - 626 else: - 627 raise Exception("Unknown datatype " + str(datatype)) - 628 - 629 def export_jackknife(self): - 630 """Export jackknife samples from the Obs - 631 - 632 Returns - 633 ------- - 634 numpy.ndarray - 635 Returns a numpy array of length N + 1 where N is the number of samples - 636 for the given ensemble and replicum. The zeroth entry of the array contains - 637 the mean value of the Obs, entries 1 to N contain the N jackknife samples - 638 derived from the Obs. The current implementation only works for observables - 639 defined on exactly one ensemble and replicum. The derived jackknife samples - 640 should agree with samples from a full jackknife analysis up to O(1/N). - 641 """ - 642 - 643 if len(self.names) != 1: - 644 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") - 645 - 646 name = self.names[0] - 647 full_data = self.deltas[name] + self.r_values[name] - 648 n = full_data.size - 649 mean = self.value - 650 tmp_jacks = np.zeros(n + 1) - 651 tmp_jacks[0] = mean - 652 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) - 653 return tmp_jacks - 654 - 655 def __float__(self): - 656 return float(self.value) + 444 def is_zero_within_error(self, sigma=1): + 445 """Checks whether the observable is zero within 'sigma' standard errors. + 446 + 447 Parameters + 448 ---------- + 449 sigma : int + 450 Number of standard errors used for the check. + 451 + 452 Works only properly when the gamma method was run. + 453 """ + 454 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue + 455 + 456 def is_zero(self, atol=1e-10): + 457 """Checks whether the observable is zero within a given tolerance. + 458 + 459 Parameters + 460 ---------- + 461 atol : float + 462 Absolute tolerance (for details see numpy documentation). + 463 """ + 464 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()) + 465 + 466 def plot_tauint(self, save=None): + 467 """Plot integrated autocorrelation time for each ensemble. + 468 + 469 Parameters + 470 ---------- + 471 save : str + 472 saves the figure to a file named 'save' if. + 473 """ + 474 if not hasattr(self, 'e_dvalue'): + 475 raise Exception('Run the gamma method first.') + 476 + 477 for e, e_name in enumerate(self.mc_names): + 478 fig = plt.figure() + 479 plt.xlabel(r'$W$') + 480 plt.ylabel(r'$\tau_\mathrm{int}$') + 481 length = int(len(self.e_n_tauint[e_name])) + 482 if self.tau_exp[e_name] > 0: + 483 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] + 484 x_help = np.arange(2 * self.tau_exp[e_name]) + 485 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 + 486 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) + 487 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') + 488 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], + 489 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) + 490 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 + 491 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) + 492 else: + 493 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) + 494 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) + 495 + 496 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) + 497 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') + 498 plt.legend() + 499 plt.xlim(-0.5, xmax) + 500 ylim = plt.ylim() + 501 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) + 502 plt.draw() + 503 if save: + 504 fig.savefig(save + "_" + str(e)) + 505 + 506 def plot_rho(self, save=None): + 507 """Plot normalized autocorrelation function time for each ensemble. + 508 + 509 Parameters + 510 ---------- + 511 save : str + 512 saves the figure to a file named 'save' if. + 513 """ + 514 if not hasattr(self, 'e_dvalue'): + 515 raise Exception('Run the gamma method first.') + 516 for e, e_name in enumerate(self.mc_names): + 517 fig = plt.figure() + 518 plt.xlabel('W') + 519 plt.ylabel('rho') + 520 length = int(len(self.e_drho[e_name])) + 521 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) + 522 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') + 523 if self.tau_exp[e_name] > 0: + 524 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], + 525 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) + 526 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 + 527 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) + 528 else: + 529 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) + 530 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) + 531 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) + 532 plt.xlim(-0.5, xmax) + 533 plt.draw() + 534 if save: + 535 fig.savefig(save + "_" + str(e)) + 536 + 537 def plot_rep_dist(self): + 538 """Plot replica distribution for each ensemble with more than one replicum.""" + 539 if not hasattr(self, 'e_dvalue'): + 540 raise Exception('Run the gamma method first.') + 541 for e, e_name in enumerate(self.mc_names): + 542 if len(self.e_content[e_name]) == 1: + 543 print('No replica distribution for a single replicum (', e_name, ')') + 544 continue + 545 r_length = [] + 546 sub_r_mean = 0 + 547 for r, r_name in enumerate(self.e_content[e_name]): + 548 r_length.append(len(self.deltas[r_name])) + 549 sub_r_mean += self.shape[r_name] * self.r_values[r_name] + 550 e_N = np.sum(r_length) + 551 sub_r_mean /= e_N + 552 arr = np.zeros(len(self.e_content[e_name])) + 553 for r, r_name in enumerate(self.e_content[e_name]): + 554 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) + 555 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) + 556 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') + 557 plt.draw() + 558 + 559 def plot_history(self, expand=True): + 560 """Plot derived Monte Carlo history for each ensemble + 561 + 562 Parameters + 563 ---------- + 564 expand : bool + 565 show expanded history for irregular Monte Carlo chains (default: True). + 566 """ + 567 for e, e_name in enumerate(self.mc_names): + 568 plt.figure() + 569 r_length = [] + 570 tmp = [] + 571 tmp_expanded = [] + 572 for r, r_name in enumerate(self.e_content[e_name]): + 573 tmp.append(self.deltas[r_name] + self.r_values[r_name]) + 574 if expand: + 575 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) + 576 r_length.append(len(tmp_expanded[-1])) + 577 else: + 578 r_length.append(len(tmp[-1])) + 579 e_N = np.sum(r_length) + 580 x = np.arange(e_N) + 581 y_test = np.concatenate(tmp, axis=0) + 582 if expand: + 583 y = np.concatenate(tmp_expanded, axis=0) + 584 else: + 585 y = y_test + 586 plt.errorbar(x, y, fmt='.', markersize=3) + 587 plt.xlim(-0.5, e_N - 0.5) + 588 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})') + 589 plt.draw() + 590 + 591 def plot_piechart(self, save=None): + 592 """Plot piechart which shows the fractional contribution of each + 593 ensemble to the error and returns a dictionary containing the fractions. + 594 + 595 Parameters + 596 ---------- + 597 save : str + 598 saves the figure to a file named 'save' if. + 599 """ + 600 if not hasattr(self, 'e_dvalue'): + 601 raise Exception('Run the gamma method first.') + 602 if np.isclose(0.0, self._dvalue, atol=1e-15): + 603 raise Exception('Error is 0.0') + 604 labels = self.e_names + 605 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 + 606 fig1, ax1 = plt.subplots() + 607 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) + 608 ax1.axis('equal') + 609 plt.draw() + 610 if save: + 611 fig1.savefig(save) + 612 + 613 return dict(zip(self.e_names, sizes)) + 614 + 615 def dump(self, filename, datatype="json.gz", description="", **kwargs): + 616 """Dump the Obs to a file 'name' of chosen format. + 617 + 618 Parameters + 619 ---------- + 620 filename : str + 621 name of the file to be saved. + 622 datatype : str + 623 Format of the exported file. Supported formats include + 624 "json.gz" and "pickle" + 625 description : str + 626 Description for output file, only relevant for json.gz format. + 627 path : str + 628 specifies a custom path for the file (default '.') + 629 """ + 630 if 'path' in kwargs: + 631 file_name = kwargs.get('path') + '/' + filename + 632 else: + 633 file_name = filename + 634 + 635 if datatype == "json.gz": + 636 from .input.json import dump_to_json + 637 dump_to_json([self], file_name, description=description) + 638 elif datatype == "pickle": + 639 with open(file_name + '.p', 'wb') as fb: + 640 pickle.dump(self, fb) + 641 else: + 642 raise Exception("Unknown datatype " + str(datatype)) + 643 + 644 def export_jackknife(self): + 645 """Export jackknife samples from the Obs + 646 + 647 Returns + 648 ------- + 649 numpy.ndarray + 650 Returns a numpy array of length N + 1 where N is the number of samples + 651 for the given ensemble and replicum. The zeroth entry of the array contains + 652 the mean value of the Obs, entries 1 to N contain the N jackknife samples + 653 derived from the Obs. The current implementation only works for observables + 654 defined on exactly one ensemble and replicum. The derived jackknife samples + 655 should agree with samples from a full jackknife analysis up to O(1/N). + 656 """ 657 - 658 def __repr__(self): - 659 return 'Obs[' + str(self) + ']' + 658 if len(self.names) != 1: + 659 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") 660 - 661 def __str__(self): - 662 if self._dvalue == 0.0: - 663 return str(self.value) - 664 fexp = np.floor(np.log10(self._dvalue)) - 665 if fexp < 0.0: - 666 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') - 667 elif fexp == 0.0: - 668 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) - 669 else: - 670 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) - 671 - 672 # Overload comparisons - 673 def __lt__(self, other): - 674 return self.value < other + 661 name = self.names[0] + 662 full_data = self.deltas[name] + self.r_values[name] + 663 n = full_data.size + 664 mean = self.value + 665 tmp_jacks = np.zeros(n + 1) + 666 tmp_jacks[0] = mean + 667 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) + 668 return tmp_jacks + 669 + 670 def __float__(self): + 671 return float(self.value) + 672 + 673 def __repr__(self): + 674 return 'Obs[' + str(self) + ']' 675 - 676 def __le__(self, other): - 677 return self.value <= other - 678 - 679 def __gt__(self, other): - 680 return self.value > other - 681 - 682 def __ge__(self, other): - 683 return self.value >= other - 684 - 685 def __eq__(self, other): - 686 return (self - other).is_zero() - 687 - 688 def __ne__(self, other): - 689 return not (self - other).is_zero() + 676 def __str__(self): + 677 if self._dvalue == 0.0: + 678 return str(self.value) + 679 fexp = np.floor(np.log10(self._dvalue)) + 680 if fexp < 0.0: + 681 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') + 682 elif fexp == 0.0: + 683 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) + 684 else: + 685 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) + 686 + 687 # Overload comparisons + 688 def __lt__(self, other): + 689 return self.value < other 690 - 691 # Overload math operations - 692 def __add__(self, y): - 693 if isinstance(y, Obs): - 694 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) - 695 else: - 696 if isinstance(y, np.ndarray): - 697 return np.array([self + o for o in y]) - 698 elif y.__class__.__name__ in ['Corr', 'CObs']: - 699 return NotImplemented - 700 else: - 701 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) + 691 def __le__(self, other): + 692 return self.value <= other + 693 + 694 def __gt__(self, other): + 695 return self.value > other + 696 + 697 def __ge__(self, other): + 698 return self.value >= other + 699 + 700 def __eq__(self, other): + 701 return (self - other).is_zero() 702 - 703 def __radd__(self, y): - 704 return self + y + 703 def __ne__(self, other): + 704 return not (self - other).is_zero() 705 - 706 def __mul__(self, y): - 707 if isinstance(y, Obs): - 708 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) - 709 else: - 710 if isinstance(y, np.ndarray): - 711 return np.array([self * o for o in y]) - 712 elif isinstance(y, complex): - 713 return CObs(self * y.real, self * y.imag) - 714 elif y.__class__.__name__ in ['Corr', 'CObs']: - 715 return NotImplemented - 716 else: - 717 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) - 718 - 719 def __rmul__(self, y): - 720 return self * y - 721 - 722 def __sub__(self, y): - 723 if isinstance(y, Obs): - 724 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) - 725 else: - 726 if isinstance(y, np.ndarray): - 727 return np.array([self - o for o in y]) - 728 elif y.__class__.__name__ in ['Corr', 'CObs']: - 729 return NotImplemented - 730 else: - 731 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) - 732 - 733 def __rsub__(self, y): - 734 return -1 * (self - y) - 735 - 736 def __pos__(self): - 737 return self - 738 - 739 def __neg__(self): - 740 return -1 * self - 741 - 742 def __truediv__(self, y): - 743 if isinstance(y, Obs): - 744 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) - 745 else: - 746 if isinstance(y, np.ndarray): - 747 return np.array([self / o for o in y]) - 748 elif y.__class__.__name__ in ['Corr', 'CObs']: - 749 return NotImplemented - 750 else: - 751 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) - 752 - 753 def __rtruediv__(self, y): - 754 if isinstance(y, Obs): - 755 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) - 756 else: - 757 if isinstance(y, np.ndarray): - 758 return np.array([o / self for o in y]) - 759 elif y.__class__.__name__ in ['Corr', 'CObs']: - 760 return NotImplemented - 761 else: - 762 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) - 763 - 764 def __pow__(self, y): - 765 if isinstance(y, Obs): - 766 return derived_observable(lambda x: x[0] ** x[1], [self, y]) - 767 else: - 768 return derived_observable(lambda x: x[0] ** y, [self]) - 769 - 770 def __rpow__(self, y): - 771 if isinstance(y, Obs): - 772 return derived_observable(lambda x: x[0] ** x[1], [y, self]) - 773 else: - 774 return derived_observable(lambda x: y ** x[0], [self]) - 775 - 776 def __abs__(self): - 777 return derived_observable(lambda x: anp.abs(x[0]), [self]) + 706 # Overload math operations + 707 def __add__(self, y): + 708 if isinstance(y, Obs): + 709 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) + 710 else: + 711 if isinstance(y, np.ndarray): + 712 return np.array([self + o for o in y]) + 713 elif y.__class__.__name__ in ['Corr', 'CObs']: + 714 return NotImplemented + 715 else: + 716 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) + 717 + 718 def __radd__(self, y): + 719 return self + y + 720 + 721 def __mul__(self, y): + 722 if isinstance(y, Obs): + 723 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) + 724 else: + 725 if isinstance(y, np.ndarray): + 726 return np.array([self * o for o in y]) + 727 elif isinstance(y, complex): + 728 return CObs(self * y.real, self * y.imag) + 729 elif y.__class__.__name__ in ['Corr', 'CObs']: + 730 return NotImplemented + 731 else: + 732 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) + 733 + 734 def __rmul__(self, y): + 735 return self * y + 736 + 737 def __sub__(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 __rsub__(self, y): + 749 return -1 * (self - y) + 750 + 751 def __pos__(self): + 752 return self + 753 + 754 def __neg__(self): + 755 return -1 * self + 756 + 757 def __truediv__(self, y): + 758 if isinstance(y, Obs): + 759 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) + 760 else: + 761 if isinstance(y, np.ndarray): + 762 return np.array([self / o for o in y]) + 763 elif y.__class__.__name__ in ['Corr', 'CObs']: + 764 return NotImplemented + 765 else: + 766 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) + 767 + 768 def __rtruediv__(self, y): + 769 if isinstance(y, Obs): + 770 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) + 771 else: + 772 if isinstance(y, np.ndarray): + 773 return np.array([o / self for o in y]) + 774 elif y.__class__.__name__ in ['Corr', 'CObs']: + 775 return NotImplemented + 776 else: + 777 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) 778 - 779 # Overload numpy functions - 780 def sqrt(self): - 781 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) - 782 - 783 def log(self): - 784 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) - 785 - 786 def exp(self): - 787 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) - 788 - 789 def sin(self): - 790 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) - 791 - 792 def cos(self): - 793 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) - 794 - 795 def tan(self): - 796 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) + 779 def __pow__(self, y): + 780 if isinstance(y, Obs): + 781 return derived_observable(lambda x: x[0] ** x[1], [self, y]) + 782 else: + 783 return derived_observable(lambda x: x[0] ** y, [self]) + 784 + 785 def __rpow__(self, y): + 786 if isinstance(y, Obs): + 787 return derived_observable(lambda x: x[0] ** x[1], [y, self]) + 788 else: + 789 return derived_observable(lambda x: y ** x[0], [self]) + 790 + 791 def __abs__(self): + 792 return derived_observable(lambda x: anp.abs(x[0]), [self]) + 793 + 794 # Overload numpy functions + 795 def sqrt(self): + 796 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) 797 - 798 def arcsin(self): - 799 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) + 798 def log(self): + 799 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) 800 - 801 def arccos(self): - 802 return derived_observable(lambda x: anp.arccos(x[0]), [self]) + 801 def exp(self): + 802 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) 803 - 804 def arctan(self): - 805 return derived_observable(lambda x: anp.arctan(x[0]), [self]) + 804 def sin(self): + 805 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) 806 - 807 def sinh(self): - 808 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) + 807 def cos(self): + 808 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) 809 - 810 def cosh(self): - 811 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) + 810 def tan(self): + 811 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) 812 - 813 def tanh(self): - 814 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) + 813 def arcsin(self): + 814 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) 815 - 816 def arcsinh(self): - 817 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) + 816 def arccos(self): + 817 return derived_observable(lambda x: anp.arccos(x[0]), [self]) 818 - 819 def arccosh(self): - 820 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) + 819 def arctan(self): + 820 return derived_observable(lambda x: anp.arctan(x[0]), [self]) 821 - 822 def arctanh(self): - 823 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) + 822 def sinh(self): + 823 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) 824 - 825 - 826class CObs: - 827 """Class for a complex valued observable.""" - 828 __slots__ = ['_real', '_imag', 'tag'] - 829 - 830 def __init__(self, real, imag=0.0): - 831 self._real = real - 832 self._imag = imag - 833 self.tag = None - 834 - 835 @property - 836 def real(self): - 837 return self._real - 838 - 839 @property - 840 def imag(self): - 841 return self._imag - 842 - 843 def gamma_method(self, **kwargs): - 844 """Executes the gamma_method for the real and the imaginary part.""" - 845 if isinstance(self.real, Obs): - 846 self.real.gamma_method(**kwargs) - 847 if isinstance(self.imag, Obs): - 848 self.imag.gamma_method(**kwargs) + 825 def cosh(self): + 826 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) + 827 + 828 def tanh(self): + 829 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) + 830 + 831 def arcsinh(self): + 832 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) + 833 + 834 def arccosh(self): + 835 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) + 836 + 837 def arctanh(self): + 838 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) + 839 + 840 + 841class CObs: + 842 """Class for a complex valued observable.""" + 843 __slots__ = ['_real', '_imag', 'tag'] + 844 + 845 def __init__(self, real, imag=0.0): + 846 self._real = real + 847 self._imag = imag + 848 self.tag = None 849 - 850 def is_zero(self): - 851 """Checks whether both real and imaginary part are zero within machine precision.""" - 852 return self.real == 0.0 and self.imag == 0.0 + 850 @property + 851 def real(self): + 852 return self._real 853 - 854 def conjugate(self): - 855 return CObs(self.real, -self.imag) - 856 - 857 def __add__(self, other): - 858 if isinstance(other, np.ndarray): - 859 return other + self - 860 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 861 return CObs(self.real + other.real, - 862 self.imag + other.imag) - 863 else: - 864 return CObs(self.real + other, self.imag) - 865 - 866 def __radd__(self, y): - 867 return self + y + 854 @property + 855 def imag(self): + 856 return self._imag + 857 + 858 def gamma_method(self, **kwargs): + 859 """Executes the gamma_method for the real and the imaginary part.""" + 860 if isinstance(self.real, Obs): + 861 self.real.gamma_method(**kwargs) + 862 if isinstance(self.imag, Obs): + 863 self.imag.gamma_method(**kwargs) + 864 + 865 def is_zero(self): + 866 """Checks whether both real and imaginary part are zero within machine precision.""" + 867 return self.real == 0.0 and self.imag == 0.0 868 - 869 def __sub__(self, other): - 870 if isinstance(other, np.ndarray): - 871 return -1 * (other - self) - 872 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 873 return CObs(self.real - other.real, self.imag - other.imag) - 874 else: - 875 return CObs(self.real - other, self.imag) - 876 - 877 def __rsub__(self, other): - 878 return -1 * (self - other) - 879 - 880 def __mul__(self, other): - 881 if isinstance(other, np.ndarray): - 882 return other * self - 883 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 884 if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]): - 885 return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3], - 886 [self.real, other.real, self.imag, other.imag], - 887 man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]), - 888 derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3], - 889 [self.real, other.real, self.imag, other.imag], - 890 man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value])) - 891 elif getattr(other, 'imag', 0) != 0: - 892 return CObs(self.real * other.real - self.imag * other.imag, - 893 self.imag * other.real + self.real * other.imag) - 894 else: - 895 return CObs(self.real * other.real, self.imag * other.real) - 896 else: - 897 return CObs(self.real * other, self.imag * other) - 898 - 899 def __rmul__(self, other): - 900 return self * other - 901 - 902 def __truediv__(self, other): - 903 if isinstance(other, np.ndarray): - 904 return 1 / (other / self) - 905 elif hasattr(other, 'real') and hasattr(other, 'imag'): - 906 r = other.real ** 2 + other.imag ** 2 - 907 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r) - 908 else: - 909 return CObs(self.real / other, self.imag / other) - 910 - 911 def __rtruediv__(self, other): - 912 r = self.real ** 2 + self.imag ** 2 - 913 if hasattr(other, 'real') and hasattr(other, 'imag'): - 914 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r) - 915 else: - 916 return CObs(self.real * other / r, -self.imag * other / r) - 917 - 918 def __abs__(self): - 919 return np.sqrt(self.real**2 + self.imag**2) - 920 - 921 def __pos__(self): - 922 return self - 923 - 924 def __neg__(self): - 925 return -1 * self - 926 - 927 def __eq__(self, other): - 928 return self.real == other.real and self.imag == other.imag - 929 - 930 def __str__(self): - 931 return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)' + 869 def conjugate(self): + 870 return CObs(self.real, -self.imag) + 871 + 872 def __add__(self, other): + 873 if isinstance(other, np.ndarray): + 874 return other + self + 875 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 876 return CObs(self.real + other.real, + 877 self.imag + other.imag) + 878 else: + 879 return CObs(self.real + other, self.imag) + 880 + 881 def __radd__(self, y): + 882 return self + y + 883 + 884 def __sub__(self, other): + 885 if isinstance(other, np.ndarray): + 886 return -1 * (other - self) + 887 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 888 return CObs(self.real - other.real, self.imag - other.imag) + 889 else: + 890 return CObs(self.real - other, self.imag) + 891 + 892 def __rsub__(self, other): + 893 return -1 * (self - other) + 894 + 895 def __mul__(self, other): + 896 if isinstance(other, np.ndarray): + 897 return other * self + 898 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 899 if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]): + 900 return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3], + 901 [self.real, other.real, self.imag, other.imag], + 902 man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]), + 903 derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3], + 904 [self.real, other.real, self.imag, other.imag], + 905 man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value])) + 906 elif getattr(other, 'imag', 0) != 0: + 907 return CObs(self.real * other.real - self.imag * other.imag, + 908 self.imag * other.real + self.real * other.imag) + 909 else: + 910 return CObs(self.real * other.real, self.imag * other.real) + 911 else: + 912 return CObs(self.real * other, self.imag * other) + 913 + 914 def __rmul__(self, other): + 915 return self * other + 916 + 917 def __truediv__(self, other): + 918 if isinstance(other, np.ndarray): + 919 return 1 / (other / self) + 920 elif hasattr(other, 'real') and hasattr(other, 'imag'): + 921 r = other.real ** 2 + other.imag ** 2 + 922 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r) + 923 else: + 924 return CObs(self.real / other, self.imag / other) + 925 + 926 def __rtruediv__(self, other): + 927 r = self.real ** 2 + self.imag ** 2 + 928 if hasattr(other, 'real') and hasattr(other, 'imag'): + 929 return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r) + 930 else: + 931 return CObs(self.real * other / r, -self.imag * other / r) 932 - 933 def __repr__(self): - 934 return 'CObs[' + str(self) + ']' + 933 def __abs__(self): + 934 return np.sqrt(self.real**2 + self.imag**2) 935 - 936 - 937def _expand_deltas(deltas, idx, shape): - 938 """Expand deltas defined on idx to a regular, contiguous range, where holes are filled by 0. - 939 If idx is of type range, the deltas are not changed - 940 - 941 Parameters - 942 ---------- - 943 deltas : list - 944 List of fluctuations - 945 idx : list - 946 List or range of configs on which the deltas are defined, has to be sorted in ascending order. - 947 shape : int - 948 Number of configs in idx. - 949 """ - 950 if isinstance(idx, range): - 951 return deltas - 952 else: - 953 ret = np.zeros(idx[-1] - idx[0] + 1) - 954 for i in range(shape): - 955 ret[idx[i] - idx[0]] = deltas[i] - 956 return ret - 957 - 958 - 959def _merge_idx(idl): - 960 """Returns the union of all lists in idl as sorted list - 961 - 962 Parameters - 963 ---------- - 964 idl : list - 965 List of lists or ranges. - 966 """ - 967 - 968 # Use groupby to efficiently check whether all elements of idl are identical - 969 try: - 970 g = groupby(idl) - 971 if next(g, True) and not next(g, False): - 972 return idl[0] - 973 except Exception: - 974 pass - 975 - 976 if np.all([type(idx) is range for idx in idl]): - 977 if len(set([idx[0] for idx in idl])) == 1: - 978 idstart = min([idx.start for idx in idl]) - 979 idstop = max([idx.stop for idx in idl]) - 980 idstep = min([idx.step for idx in idl]) - 981 return range(idstart, idstop, idstep) + 936 def __pos__(self): + 937 return self + 938 + 939 def __neg__(self): + 940 return -1 * self + 941 + 942 def __eq__(self, other): + 943 return self.real == other.real and self.imag == other.imag + 944 + 945 def __str__(self): + 946 return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)' + 947 + 948 def __repr__(self): + 949 return 'CObs[' + str(self) + ']' + 950 + 951 + 952def _expand_deltas(deltas, idx, shape): + 953 """Expand deltas defined on idx to a regular, contiguous range, where holes are filled by 0. + 954 If idx is of type range, the deltas are not changed + 955 + 956 Parameters + 957 ---------- + 958 deltas : list + 959 List of fluctuations + 960 idx : list + 961 List or range of configs on which the deltas are defined, has to be sorted in ascending order. + 962 shape : int + 963 Number of configs in idx. + 964 """ + 965 if isinstance(idx, range): + 966 return deltas + 967 else: + 968 ret = np.zeros(idx[-1] - idx[0] + 1) + 969 for i in range(shape): + 970 ret[idx[i] - idx[0]] = deltas[i] + 971 return ret + 972 + 973 + 974def _merge_idx(idl): + 975 """Returns the union of all lists in idl as sorted list + 976 + 977 Parameters + 978 ---------- + 979 idl : list + 980 List of lists or ranges. + 981 """ 982 - 983 return sorted(set().union(*idl)) - 984 - 985 - 986def _intersection_idx(idl): - 987 """Returns the intersection of all lists in idl as sorted list - 988 - 989 Parameters - 990 ---------- - 991 idl : list - 992 List of lists or ranges. - 993 """ - 994 - 995 def _lcm(*args): - 996 """Returns the lowest common multiple of args. + 983 # Use groupby to efficiently check whether all elements of idl are identical + 984 try: + 985 g = groupby(idl) + 986 if next(g, True) and not next(g, False): + 987 return idl[0] + 988 except Exception: + 989 pass + 990 + 991 if np.all([type(idx) is range for idx in idl]): + 992 if len(set([idx[0] for idx in idl])) == 1: + 993 idstart = min([idx.start for idx in idl]) + 994 idstop = max([idx.stop for idx in idl]) + 995 idstep = min([idx.step for idx in idl]) + 996 return range(idstart, idstop, idstep) 997 - 998 From python 3.9 onwards the math library contains an lcm function.""" - 999 return reduce(lambda a, b: a * b // gcd(a, b), args) + 998 return sorted(set().union(*idl)) + 999 1000 -1001 # Use groupby to efficiently check whether all elements of idl are identical -1002 try: -1003 g = groupby(idl) -1004 if next(g, True) and not next(g, False): -1005 return idl[0] -1006 except Exception: -1007 pass -1008 -1009 if np.all([type(idx) is range for idx in idl]): -1010 if len(set([idx[0] for idx in idl])) == 1: -1011 idstart = max([idx.start for idx in idl]) -1012 idstop = min([idx.stop for idx in idl]) -1013 idstep = _lcm(*[idx.step for idx in idl]) -1014 return range(idstart, idstop, idstep) +1001def _intersection_idx(idl): +1002 """Returns the intersection of all lists in idl as sorted list +1003 +1004 Parameters +1005 ---------- +1006 idl : list +1007 List of lists or ranges. +1008 """ +1009 +1010 def _lcm(*args): +1011 """Returns the lowest common multiple of args. +1012 +1013 From python 3.9 onwards the math library contains an lcm function.""" +1014 return reduce(lambda a, b: a * b // gcd(a, b), args) 1015 -1016 return sorted(set.intersection(*[set(o) for o in idl])) -1017 -1018 -1019def _expand_deltas_for_merge(deltas, idx, shape, new_idx): -1020 """Expand deltas defined on idx to the list of configs that is defined by new_idx. -1021 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest -1022 common divisor of the step sizes is used as new step size. +1016 # Use groupby to efficiently check whether all elements of idl are identical +1017 try: +1018 g = groupby(idl) +1019 if next(g, True) and not next(g, False): +1020 return idl[0] +1021 except Exception: +1022 pass 1023 -1024 Parameters -1025 ---------- -1026 deltas : list -1027 List of fluctuations -1028 idx : list -1029 List or range of configs on which the deltas are defined. -1030 Has to be a subset of new_idx and has to be sorted in ascending order. -1031 shape : list -1032 Number of configs in idx. -1033 new_idx : list -1034 List of configs that defines the new range, has to be sorted in ascending order. -1035 """ -1036 -1037 if type(idx) is range and type(new_idx) is range: -1038 if idx == new_idx: -1039 return deltas -1040 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) -1041 for i in range(shape): -1042 ret[idx[i] - new_idx[0]] = deltas[i] -1043 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) -1044 -1045 -1046def _collapse_deltas_for_merge(deltas, idx, shape, new_idx): -1047 """Collapse deltas defined on idx to the list of configs that is defined by new_idx. -1048 If idx and new_idx are of type range, the smallest -1049 common divisor of the step sizes is used as new step size. -1050 -1051 Parameters -1052 ---------- -1053 deltas : list -1054 List of fluctuations -1055 idx : list -1056 List or range of configs on which the deltas are defined. -1057 Has to be a subset of new_idx and has to be sorted in ascending order. -1058 shape : list -1059 Number of configs in idx. -1060 new_idx : list -1061 List of configs that defines the new range, has to be sorted in ascending order. -1062 """ -1063 -1064 if type(idx) is range and type(new_idx) is range: -1065 if idx == new_idx: -1066 return deltas -1067 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) -1068 for i in range(shape): -1069 if idx[i] in new_idx: -1070 ret[idx[i] - new_idx[0]] = deltas[i] -1071 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) -1072 -1073 -1074def _filter_zeroes(deltas, idx, eps=Obs.filter_eps): -1075 """Filter out all configurations with vanishing fluctuation such that they do not -1076 contribute to the error estimate anymore. Returns the new deltas and -1077 idx according to the filtering. -1078 A fluctuation is considered to be vanishing, if it is smaller than eps times -1079 the mean of the absolute values of all deltas in one list. -1080 -1081 Parameters -1082 ---------- -1083 deltas : list -1084 List of fluctuations -1085 idx : list -1086 List or ranges of configs on which the deltas are defined. -1087 eps : float -1088 Prefactor that enters the filter criterion. -1089 """ -1090 new_deltas = [] -1091 new_idx = [] -1092 maxd = np.mean(np.fabs(deltas)) -1093 for i in range(len(deltas)): -1094 if abs(deltas[i]) > eps * maxd: -1095 new_deltas.append(deltas[i]) -1096 new_idx.append(idx[i]) -1097 if new_idx: -1098 return np.array(new_deltas), new_idx -1099 else: -1100 return deltas, idx -1101 -1102 -1103def derived_observable(func, data, array_mode=False, **kwargs): -1104 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. -1105 -1106 Parameters -1107 ---------- -1108 func : object -1109 arbitrary function of the form func(data, **kwargs). For the -1110 automatic differentiation to work, all numpy functions have to have -1111 the autograd wrapper (use 'import autograd.numpy as anp'). -1112 data : list -1113 list of Obs, e.g. [obs1, obs2, obs3]. -1114 num_grad : bool -1115 if True, numerical derivatives are used instead of autograd -1116 (default False). To control the numerical differentiation the -1117 kwargs of numdifftools.step_generators.MaxStepGenerator -1118 can be used. -1119 man_grad : list -1120 manually supply a list or an array which contains the jacobian -1121 of func. Use cautiously, supplying the wrong derivative will -1122 not be intercepted. -1123 -1124 Notes -1125 ----- -1126 For simple mathematical operations it can be practical to use anonymous -1127 functions. For the ratio of two observables one can e.g. use -1128 -1129 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) -1130 """ -1131 -1132 data = np.asarray(data) -1133 raveled_data = data.ravel() -1134 -1135 # Workaround for matrix operations containing non Obs data -1136 if not all(isinstance(x, Obs) for x in raveled_data): -1137 for i in range(len(raveled_data)): -1138 if isinstance(raveled_data[i], (int, float)): -1139 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") -1140 -1141 allcov = {} -1142 for o in raveled_data: -1143 for name in o.cov_names: -1144 if name in allcov: -1145 if not np.allclose(allcov[name], o.covobs[name].cov): -1146 raise Exception('Inconsistent covariance matrices for %s!' % (name)) -1147 else: -1148 allcov[name] = o.covobs[name].cov +1024 if np.all([type(idx) is range for idx in idl]): +1025 if len(set([idx[0] for idx in idl])) == 1: +1026 idstart = max([idx.start for idx in idl]) +1027 idstop = min([idx.stop for idx in idl]) +1028 idstep = _lcm(*[idx.step for idx in idl]) +1029 return range(idstart, idstop, idstep) +1030 +1031 return sorted(set.intersection(*[set(o) for o in idl])) +1032 +1033 +1034def _expand_deltas_for_merge(deltas, idx, shape, new_idx): +1035 """Expand deltas defined on idx to the list of configs that is defined by new_idx. +1036 New, empty entries are filled by 0. If idx and new_idx are of type range, the smallest +1037 common divisor of the step sizes is used as new step size. +1038 +1039 Parameters +1040 ---------- +1041 deltas : list +1042 List of fluctuations +1043 idx : list +1044 List or range of configs on which the deltas are defined. +1045 Has to be a subset of new_idx and has to be sorted in ascending order. +1046 shape : list +1047 Number of configs in idx. +1048 new_idx : list +1049 List of configs that defines the new range, has to be sorted in ascending order. +1050 """ +1051 +1052 if type(idx) is range and type(new_idx) is range: +1053 if idx == new_idx: +1054 return deltas +1055 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) +1056 for i in range(shape): +1057 ret[idx[i] - new_idx[0]] = deltas[i] +1058 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) +1059 +1060 +1061def _collapse_deltas_for_merge(deltas, idx, shape, new_idx): +1062 """Collapse deltas defined on idx to the list of configs that is defined by new_idx. +1063 If idx and new_idx are of type range, the smallest +1064 common divisor of the step sizes is used as new step size. +1065 +1066 Parameters +1067 ---------- +1068 deltas : list +1069 List of fluctuations +1070 idx : list +1071 List or range of configs on which the deltas are defined. +1072 Has to be a subset of new_idx and has to be sorted in ascending order. +1073 shape : list +1074 Number of configs in idx. +1075 new_idx : list +1076 List of configs that defines the new range, has to be sorted in ascending order. +1077 """ +1078 +1079 if type(idx) is range and type(new_idx) is range: +1080 if idx == new_idx: +1081 return deltas +1082 ret = np.zeros(new_idx[-1] - new_idx[0] + 1) +1083 for i in range(shape): +1084 if idx[i] in new_idx: +1085 ret[idx[i] - new_idx[0]] = deltas[i] +1086 return np.array([ret[new_idx[i] - new_idx[0]] for i in range(len(new_idx))]) +1087 +1088 +1089def _filter_zeroes(deltas, idx, eps=Obs.filter_eps): +1090 """Filter out all configurations with vanishing fluctuation such that they do not +1091 contribute to the error estimate anymore. Returns the new deltas and +1092 idx according to the filtering. +1093 A fluctuation is considered to be vanishing, if it is smaller than eps times +1094 the mean of the absolute values of all deltas in one list. +1095 +1096 Parameters +1097 ---------- +1098 deltas : list +1099 List of fluctuations +1100 idx : list +1101 List or ranges of configs on which the deltas are defined. +1102 eps : float +1103 Prefactor that enters the filter criterion. +1104 """ +1105 new_deltas = [] +1106 new_idx = [] +1107 maxd = np.mean(np.fabs(deltas)) +1108 for i in range(len(deltas)): +1109 if abs(deltas[i]) > eps * maxd: +1110 new_deltas.append(deltas[i]) +1111 new_idx.append(idx[i]) +1112 if new_idx: +1113 return np.array(new_deltas), new_idx +1114 else: +1115 return deltas, idx +1116 +1117 +1118def derived_observable(func, data, array_mode=False, **kwargs): +1119 """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation. +1120 +1121 Parameters +1122 ---------- +1123 func : object +1124 arbitrary function of the form func(data, **kwargs). For the +1125 automatic differentiation to work, all numpy functions have to have +1126 the autograd wrapper (use 'import autograd.numpy as anp'). +1127 data : list +1128 list of Obs, e.g. [obs1, obs2, obs3]. +1129 num_grad : bool +1130 if True, numerical derivatives are used instead of autograd +1131 (default False). To control the numerical differentiation the +1132 kwargs of numdifftools.step_generators.MaxStepGenerator +1133 can be used. +1134 man_grad : list +1135 manually supply a list or an array which contains the jacobian +1136 of func. Use cautiously, supplying the wrong derivative will +1137 not be intercepted. +1138 +1139 Notes +1140 ----- +1141 For simple mathematical operations it can be practical to use anonymous +1142 functions. For the ratio of two observables one can e.g. use +1143 +1144 new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2]) +1145 """ +1146 +1147 data = np.asarray(data) +1148 raveled_data = data.ravel() 1149 -1150 n_obs = len(raveled_data) -1151 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) -1152 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) -1153 new_sample_names = sorted(set(new_names) - set(new_cov_names)) -1154 -1155 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} -1156 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 -1157 -1158 if data.ndim == 1: -1159 values = np.array([o.value for o in data]) -1160 else: -1161 values = np.vectorize(lambda x: x.value)(data) -1162 -1163 new_values = func(values, **kwargs) +1150 # Workaround for matrix operations containing non Obs data +1151 if not all(isinstance(x, Obs) for x in raveled_data): +1152 for i in range(len(raveled_data)): +1153 if isinstance(raveled_data[i], (int, float)): +1154 raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###") +1155 +1156 allcov = {} +1157 for o in raveled_data: +1158 for name in o.cov_names: +1159 if name in allcov: +1160 if not np.allclose(allcov[name], o.covobs[name].cov): +1161 raise Exception('Inconsistent covariance matrices for %s!' % (name)) +1162 else: +1163 allcov[name] = o.covobs[name].cov 1164 -1165 multi = int(isinstance(new_values, np.ndarray)) -1166 -1167 new_r_values = {} -1168 new_idl_d = {} -1169 for name in new_sample_names: -1170 idl = [] -1171 tmp_values = np.zeros(n_obs) -1172 for i, item in enumerate(raveled_data): -1173 tmp_values[i] = item.r_values.get(name, item.value) -1174 tmp_idl = item.idl.get(name) -1175 if tmp_idl is not None: -1176 idl.append(tmp_idl) -1177 if multi > 0: -1178 tmp_values = np.array(tmp_values).reshape(data.shape) -1179 new_r_values[name] = func(tmp_values, **kwargs) -1180 new_idl_d[name] = _merge_idx(idl) -1181 if not is_merged[name]: -1182 is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]]))) -1183 -1184 if 'man_grad' in kwargs: -1185 deriv = np.asarray(kwargs.get('man_grad')) -1186 if new_values.shape + data.shape != deriv.shape: -1187 raise Exception('Manual derivative does not have correct shape.') -1188 elif kwargs.get('num_grad') is True: -1189 if multi > 0: -1190 raise Exception('Multi mode currently not supported for numerical derivative') -1191 options = { -1192 'base_step': 0.1, -1193 'step_ratio': 2.5} -1194 for key in options.keys(): -1195 kwarg = kwargs.get(key) -1196 if kwarg is not None: -1197 options[key] = kwarg -1198 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) -1199 if tmp_df.size == 1: -1200 deriv = np.array([tmp_df.real]) -1201 else: -1202 deriv = tmp_df.real -1203 else: -1204 deriv = jacobian(func)(values, **kwargs) -1205 -1206 final_result = np.zeros(new_values.shape, dtype=object) -1207 -1208 if array_mode is True: -1209 -1210 class _Zero_grad(): -1211 def __init__(self, N): -1212 self.grad = np.zeros((N, 1)) -1213 -1214 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])) -1215 d_extracted = {} -1216 g_extracted = {} -1217 for name in new_sample_names: -1218 d_extracted[name] = [] -1219 ens_length = len(new_idl_d[name]) -1220 for i_dat, dat in enumerate(data): -1221 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, ))) -1222 for name in new_cov_names: -1223 g_extracted[name] = [] -1224 zero_grad = _Zero_grad(new_covobs_lengths[name]) -1225 for i_dat, dat in enumerate(data): -1226 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))) -1227 -1228 for i_val, new_val in np.ndenumerate(new_values): -1229 new_deltas = {} -1230 new_grad = {} -1231 if array_mode is True: -1232 for name in new_sample_names: -1233 ens_length = d_extracted[name][0].shape[-1] -1234 new_deltas[name] = np.zeros(ens_length) -1235 for i_dat, dat in enumerate(d_extracted[name]): -1236 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1237 for name in new_cov_names: -1238 new_grad[name] = 0 -1239 for i_dat, dat in enumerate(g_extracted[name]): -1240 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) -1241 else: -1242 for j_obs, obs in np.ndenumerate(data): -1243 for name in obs.names: -1244 if name in obs.cov_names: -1245 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad -1246 else: -1247 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]) -1248 -1249 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} -1250 -1251 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): -1252 raise Exception('The same name has been used for deltas and covobs!') -1253 new_samples = [] -1254 new_means = [] -1255 new_idl = [] -1256 new_names_obs = [] -1257 for name in new_names: -1258 if name not in new_covobs: -1259 if is_merged[name]: -1260 filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name]) -1261 else: -1262 filtered_deltas = new_deltas[name] -1263 filtered_idl_d = new_idl_d[name] -1264 -1265 new_samples.append(filtered_deltas) -1266 new_idl.append(filtered_idl_d) -1267 new_means.append(new_r_values[name][i_val]) -1268 new_names_obs.append(name) -1269 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) -1270 for name in new_covobs: -1271 final_result[i_val].names.append(name) -1272 final_result[i_val]._covobs = new_covobs -1273 final_result[i_val]._value = new_val -1274 final_result[i_val].is_merged = is_merged -1275 final_result[i_val].reweighted = reweighted -1276 -1277 if multi == 0: -1278 final_result = final_result.item() +1165 n_obs = len(raveled_data) +1166 new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x])) +1167 new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x])) +1168 new_sample_names = sorted(set(new_names) - set(new_cov_names)) +1169 +1170 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} +1171 reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0 +1172 +1173 if data.ndim == 1: +1174 values = np.array([o.value for o in data]) +1175 else: +1176 values = np.vectorize(lambda x: x.value)(data) +1177 +1178 new_values = func(values, **kwargs) +1179 +1180 multi = int(isinstance(new_values, np.ndarray)) +1181 +1182 new_r_values = {} +1183 new_idl_d = {} +1184 for name in new_sample_names: +1185 idl = [] +1186 tmp_values = np.zeros(n_obs) +1187 for i, item in enumerate(raveled_data): +1188 tmp_values[i] = item.r_values.get(name, item.value) +1189 tmp_idl = item.idl.get(name) +1190 if tmp_idl is not None: +1191 idl.append(tmp_idl) +1192 if multi > 0: +1193 tmp_values = np.array(tmp_values).reshape(data.shape) +1194 new_r_values[name] = func(tmp_values, **kwargs) +1195 new_idl_d[name] = _merge_idx(idl) +1196 if not is_merged[name]: +1197 is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]]))) +1198 +1199 if 'man_grad' in kwargs: +1200 deriv = np.asarray(kwargs.get('man_grad')) +1201 if new_values.shape + data.shape != deriv.shape: +1202 raise Exception('Manual derivative does not have correct shape.') +1203 elif kwargs.get('num_grad') is True: +1204 if multi > 0: +1205 raise Exception('Multi mode currently not supported for numerical derivative') +1206 options = { +1207 'base_step': 0.1, +1208 'step_ratio': 2.5} +1209 for key in options.keys(): +1210 kwarg = kwargs.get(key) +1211 if kwarg is not None: +1212 options[key] = kwarg +1213 tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs) +1214 if tmp_df.size == 1: +1215 deriv = np.array([tmp_df.real]) +1216 else: +1217 deriv = tmp_df.real +1218 else: +1219 deriv = jacobian(func)(values, **kwargs) +1220 +1221 final_result = np.zeros(new_values.shape, dtype=object) +1222 +1223 if array_mode is True: +1224 +1225 class _Zero_grad(): +1226 def __init__(self, N): +1227 self.grad = np.zeros((N, 1)) +1228 +1229 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])) +1230 d_extracted = {} +1231 g_extracted = {} +1232 for name in new_sample_names: +1233 d_extracted[name] = [] +1234 ens_length = len(new_idl_d[name]) +1235 for i_dat, dat in enumerate(data): +1236 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, ))) +1237 for name in new_cov_names: +1238 g_extracted[name] = [] +1239 zero_grad = _Zero_grad(new_covobs_lengths[name]) +1240 for i_dat, dat in enumerate(data): +1241 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))) +1242 +1243 for i_val, new_val in np.ndenumerate(new_values): +1244 new_deltas = {} +1245 new_grad = {} +1246 if array_mode is True: +1247 for name in new_sample_names: +1248 ens_length = d_extracted[name][0].shape[-1] +1249 new_deltas[name] = np.zeros(ens_length) +1250 for i_dat, dat in enumerate(d_extracted[name]): +1251 new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1252 for name in new_cov_names: +1253 new_grad[name] = 0 +1254 for i_dat, dat in enumerate(g_extracted[name]): +1255 new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat) +1256 else: +1257 for j_obs, obs in np.ndenumerate(data): +1258 for name in obs.names: +1259 if name in obs.cov_names: +1260 new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad +1261 else: +1262 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]) +1263 +1264 new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad} +1265 +1266 if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()): +1267 raise Exception('The same name has been used for deltas and covobs!') +1268 new_samples = [] +1269 new_means = [] +1270 new_idl = [] +1271 new_names_obs = [] +1272 for name in new_names: +1273 if name not in new_covobs: +1274 if is_merged[name]: +1275 filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name]) +1276 else: +1277 filtered_deltas = new_deltas[name] +1278 filtered_idl_d = new_idl_d[name] 1279 -1280 return final_result -1281 -1282 -1283def _reduce_deltas(deltas, idx_old, idx_new): -1284 """Extract deltas defined on idx_old on all configs of idx_new. -1285 -1286 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they -1287 are ordered in an ascending order. -1288 -1289 Parameters -1290 ---------- -1291 deltas : list -1292 List of fluctuations -1293 idx_old : list -1294 List or range of configs on which the deltas are defined -1295 idx_new : list -1296 List of configs for which we want to extract the deltas. -1297 Has to be a subset of idx_old. -1298 """ -1299 if not len(deltas) == len(idx_old): -1300 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) -1301 if type(idx_old) is range and type(idx_new) is range: -1302 if idx_old == idx_new: -1303 return deltas -1304 shape = len(idx_new) -1305 ret = np.zeros(shape) -1306 oldpos = 0 -1307 for i in range(shape): -1308 pos = -1 -1309 for j in range(oldpos, len(idx_old)): -1310 if idx_old[j] == idx_new[i]: -1311 pos = j -1312 break -1313 if pos < 0: -1314 raise Exception('Error in _reduce_deltas: Config %d not in idx_old' % (idx_new[i])) -1315 ret[i] = deltas[pos] -1316 oldpos = pos -1317 return np.array(ret) -1318 -1319 -1320def reweight(weight, obs, **kwargs): -1321 """Reweight a list of observables. -1322 -1323 Parameters -1324 ---------- -1325 weight : Obs -1326 Reweighting factor. An Observable that has to be defined on a superset of the -1327 configurations in obs[i].idl for all i. -1328 obs : list -1329 list of Obs, e.g. [obs1, obs2, obs3]. -1330 all_configs : bool -1331 if True, the reweighted observables are normalized by the average of -1332 the reweighting factor on all configurations in weight.idl and not -1333 on the configurations in obs[i].idl. -1334 """ -1335 result = [] -1336 for i in range(len(obs)): -1337 if len(obs[i].cov_names): -1338 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') -1339 if not set(obs[i].names).issubset(weight.names): -1340 raise Exception('Error: Ensembles do not fit') -1341 for name in obs[i].names: -1342 if not set(obs[i].idl[name]).issubset(weight.idl[name]): -1343 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) -1344 new_samples = [] -1345 w_deltas = {} -1346 for name in sorted(obs[i].names): -1347 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) -1348 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) -1349 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) -1350 -1351 if kwargs.get('all_configs'): -1352 new_weight = weight -1353 else: -1354 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)]) -1355 -1356 result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs)) -1357 result[-1].reweighted = True -1358 result[-1].is_merged = obs[i].is_merged -1359 -1360 return result -1361 -1362 -1363def correlate(obs_a, obs_b): -1364 """Correlate two observables. +1280 new_samples.append(filtered_deltas) +1281 new_idl.append(filtered_idl_d) +1282 new_means.append(new_r_values[name][i_val]) +1283 new_names_obs.append(name) +1284 final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl) +1285 for name in new_covobs: +1286 final_result[i_val].names.append(name) +1287 final_result[i_val]._covobs = new_covobs +1288 final_result[i_val]._value = new_val +1289 final_result[i_val].is_merged = is_merged +1290 final_result[i_val].reweighted = reweighted +1291 +1292 if multi == 0: +1293 final_result = final_result.item() +1294 +1295 return final_result +1296 +1297 +1298def _reduce_deltas(deltas, idx_old, idx_new): +1299 """Extract deltas defined on idx_old on all configs of idx_new. +1300 +1301 Assumes, that idx_old and idx_new are correctly defined idl, i.e., they +1302 are ordered in an ascending order. +1303 +1304 Parameters +1305 ---------- +1306 deltas : list +1307 List of fluctuations +1308 idx_old : list +1309 List or range of configs on which the deltas are defined +1310 idx_new : list +1311 List of configs for which we want to extract the deltas. +1312 Has to be a subset of idx_old. +1313 """ +1314 if not len(deltas) == len(idx_old): +1315 raise Exception('Length of deltas and idx_old have to be the same: %d != %d' % (len(deltas), len(idx_old))) +1316 if type(idx_old) is range and type(idx_new) is range: +1317 if idx_old == idx_new: +1318 return deltas +1319 shape = len(idx_new) +1320 ret = np.zeros(shape) +1321 oldpos = 0 +1322 for i in range(shape): +1323 pos = -1 +1324 for j in range(oldpos, len(idx_old)): +1325 if idx_old[j] == idx_new[i]: +1326 pos = j +1327 break +1328 if pos < 0: +1329 raise Exception('Error in _reduce_deltas: Config %d not in idx_old' % (idx_new[i])) +1330 ret[i] = deltas[pos] +1331 oldpos = pos +1332 return np.array(ret) +1333 +1334 +1335def reweight(weight, obs, **kwargs): +1336 """Reweight a list of observables. +1337 +1338 Parameters +1339 ---------- +1340 weight : Obs +1341 Reweighting factor. An Observable that has to be defined on a superset of the +1342 configurations in obs[i].idl for all i. +1343 obs : list +1344 list of Obs, e.g. [obs1, obs2, obs3]. +1345 all_configs : bool +1346 if True, the reweighted observables are normalized by the average of +1347 the reweighting factor on all configurations in weight.idl and not +1348 on the configurations in obs[i].idl. Default False. +1349 """ +1350 result = [] +1351 for i in range(len(obs)): +1352 if len(obs[i].cov_names): +1353 raise Exception('Error: Not possible to reweight an Obs that contains covobs!') +1354 if not set(obs[i].names).issubset(weight.names): +1355 raise Exception('Error: Ensembles do not fit') +1356 for name in obs[i].names: +1357 if not set(obs[i].idl[name]).issubset(weight.idl[name]): +1358 raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name)) +1359 new_samples = [] +1360 w_deltas = {} +1361 for name in sorted(obs[i].names): +1362 w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name]) +1363 new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name])) +1364 tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)]) 1365 -1366 Parameters -1367 ---------- -1368 obs_a : Obs -1369 First observable -1370 obs_b : Obs -1371 Second observable -1372 -1373 Notes -1374 ----- -1375 Keep in mind to only correlate primary observables which have not been reweighted -1376 yet. The reweighting has to be applied after correlating the observables. -1377 Currently only works if ensembles are identical (this is not strictly necessary). -1378 """ -1379 -1380 if sorted(obs_a.names) != sorted(obs_b.names): -1381 raise Exception('Ensembles do not fit') -1382 if len(obs_a.cov_names) or len(obs_b.cov_names): -1383 raise Exception('Error: Not possible to correlate Obs that contain covobs!') -1384 for name in obs_a.names: -1385 if obs_a.shape[name] != obs_b.shape[name]: -1386 raise Exception('Shapes of ensemble', name, 'do not fit') -1387 if obs_a.idl[name] != obs_b.idl[name]: -1388 raise Exception('idl of ensemble', name, 'do not fit') -1389 -1390 if obs_a.reweighted is True: -1391 warnings.warn("The first observable is already reweighted.", RuntimeWarning) -1392 if obs_b.reweighted is True: -1393 warnings.warn("The second observable is already reweighted.", RuntimeWarning) +1366 if kwargs.get('all_configs'): +1367 new_weight = weight +1368 else: +1369 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)]) +1370 +1371 result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs)) +1372 result[-1].reweighted = True +1373 result[-1].is_merged = obs[i].is_merged +1374 +1375 return result +1376 +1377 +1378def correlate(obs_a, obs_b): +1379 """Correlate two observables. +1380 +1381 Parameters +1382 ---------- +1383 obs_a : Obs +1384 First observable +1385 obs_b : Obs +1386 Second observable +1387 +1388 Notes +1389 ----- +1390 Keep in mind to only correlate primary observables which have not been reweighted +1391 yet. The reweighting has to be applied after correlating the observables. +1392 Currently only works if ensembles are identical (this is not strictly necessary). +1393 """ 1394 -1395 new_samples = [] -1396 new_idl = [] -1397 for name in sorted(obs_a.names): -1398 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) -1399 new_idl.append(obs_a.idl[name]) -1400 -1401 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) -1402 o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names} -1403 o.reweighted = obs_a.reweighted or obs_b.reweighted -1404 return o -1405 -1406 -1407def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): -1408 r'''Calculates the error covariance matrix of a set of observables. +1395 if sorted(obs_a.names) != sorted(obs_b.names): +1396 raise Exception('Ensembles do not fit') +1397 if len(obs_a.cov_names) or len(obs_b.cov_names): +1398 raise Exception('Error: Not possible to correlate Obs that contain covobs!') +1399 for name in obs_a.names: +1400 if obs_a.shape[name] != obs_b.shape[name]: +1401 raise Exception('Shapes of ensemble', name, 'do not fit') +1402 if obs_a.idl[name] != obs_b.idl[name]: +1403 raise Exception('idl of ensemble', name, 'do not fit') +1404 +1405 if obs_a.reweighted is True: +1406 warnings.warn("The first observable is already reweighted.", RuntimeWarning) +1407 if obs_b.reweighted is True: +1408 warnings.warn("The second observable is already reweighted.", RuntimeWarning) 1409 -1410 The gamma method has to be applied first to all observables. -1411 -1412 Parameters -1413 ---------- -1414 obs : list or numpy.ndarray -1415 List or one dimensional array of Obs -1416 visualize : bool -1417 If True plots the corresponding normalized correlation matrix (default False). -1418 correlation : bool -1419 If True the correlation matrix instead of the error covariance matrix is returned (default False). -1420 smooth : None or int -1421 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue -1422 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the -1423 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely -1424 small ones. -1425 -1426 Notes -1427 ----- -1428 The error covariance is defined such that it agrees with the squared standard error for two identical observables -1429 $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$ -1430 in the absence of autocorrelation. -1431 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 -1432 $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. -1433 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. -1434 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ -1435 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). -1436 ''' -1437 -1438 length = len(obs) -1439 -1440 max_samples = np.max([o.N for o in obs]) -1441 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: -1442 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) -1443 -1444 cov = np.zeros((length, length)) -1445 for i in range(length): -1446 for j in range(i, length): -1447 cov[i, j] = _covariance_element(obs[i], obs[j]) -1448 cov = cov + cov.T - np.diag(np.diag(cov)) -1449 -1450 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) -1451 -1452 if isinstance(smooth, int): -1453 corr = _smooth_eigenvalues(corr, smooth) +1410 new_samples = [] +1411 new_idl = [] +1412 for name in sorted(obs_a.names): +1413 new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name])) +1414 new_idl.append(obs_a.idl[name]) +1415 +1416 o = Obs(new_samples, sorted(obs_a.names), idl=new_idl) +1417 o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names} +1418 o.reweighted = obs_a.reweighted or obs_b.reweighted +1419 return o +1420 +1421 +1422def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs): +1423 r'''Calculates the error covariance matrix of a set of observables. +1424 +1425 The gamma method has to be applied first to all observables. +1426 +1427 Parameters +1428 ---------- +1429 obs : list or numpy.ndarray +1430 List or one dimensional array of Obs +1431 visualize : bool +1432 If True plots the corresponding normalized correlation matrix (default False). +1433 correlation : bool +1434 If True the correlation matrix instead of the error covariance matrix is returned (default False). +1435 smooth : None or int +1436 If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue +1437 smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the +1438 largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely +1439 small ones. +1440 +1441 Notes +1442 ----- +1443 The error covariance is defined such that it agrees with the squared standard error for two identical observables +1444 $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$ +1445 in the absence of autocorrelation. +1446 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 +1447 $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags. +1448 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. +1449 $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$ +1450 This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors). +1451 ''' +1452 +1453 length = len(obs) 1454 -1455 if visualize: -1456 plt.matshow(corr, vmin=-1, vmax=1) -1457 plt.set_cmap('RdBu') -1458 plt.colorbar() -1459 plt.draw() -1460 -1461 if correlation is True: -1462 return corr -1463 -1464 errors = [o.dvalue for o in obs] -1465 cov = np.diag(errors) @ corr @ np.diag(errors) +1455 max_samples = np.max([o.N for o in obs]) +1456 if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]: +1457 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) +1458 +1459 cov = np.zeros((length, length)) +1460 for i in range(length): +1461 for j in range(i, length): +1462 cov[i, j] = _covariance_element(obs[i], obs[j]) +1463 cov = cov + cov.T - np.diag(np.diag(cov)) +1464 +1465 corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov))) 1466 -1467 eigenvalues = np.linalg.eigh(cov)[0] -1468 if not np.all(eigenvalues >= 0): -1469 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) -1470 -1471 return cov -1472 -1473 -1474def _smooth_eigenvalues(corr, E): -1475 """Eigenvalue smoothing as described in hep-lat/9412087 -1476 -1477 corr : np.ndarray -1478 correlation matrix -1479 E : integer -1480 Number of eigenvalues to be left substantially unchanged -1481 """ -1482 if not (2 < E < corr.shape[0] - 1): -1483 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") -1484 vals, vec = np.linalg.eigh(corr) -1485 lambda_min = np.mean(vals[:-E]) -1486 vals[vals < lambda_min] = lambda_min -1487 vals /= np.mean(vals) -1488 return vec @ np.diag(vals) @ vec.T -1489 -1490 -1491def _covariance_element(obs1, obs2): -1492 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" -1493 -1494 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): -1495 deltas1 = _collapse_deltas_for_merge(deltas1, idx1, len(idx1), new_idx) -1496 deltas2 = _collapse_deltas_for_merge(deltas2, idx2, len(idx2), new_idx) -1497 return np.sum(deltas1 * deltas2) -1498 -1499 if set(obs1.names).isdisjoint(set(obs2.names)): -1500 return 0.0 -1501 -1502 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): -1503 raise Exception('The gamma method has to be applied to both Obs first.') +1467 if isinstance(smooth, int): +1468 corr = _smooth_eigenvalues(corr, smooth) +1469 +1470 if visualize: +1471 plt.matshow(corr, vmin=-1, vmax=1) +1472 plt.set_cmap('RdBu') +1473 plt.colorbar() +1474 plt.draw() +1475 +1476 if correlation is True: +1477 return corr +1478 +1479 errors = [o.dvalue for o in obs] +1480 cov = np.diag(errors) @ corr @ np.diag(errors) +1481 +1482 eigenvalues = np.linalg.eigh(cov)[0] +1483 if not np.all(eigenvalues >= 0): +1484 warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning) +1485 +1486 return cov +1487 +1488 +1489def _smooth_eigenvalues(corr, E): +1490 """Eigenvalue smoothing as described in hep-lat/9412087 +1491 +1492 corr : np.ndarray +1493 correlation matrix +1494 E : integer +1495 Number of eigenvalues to be left substantially unchanged +1496 """ +1497 if not (2 < E < corr.shape[0] - 1): +1498 raise Exception(f"'E' has to be between 2 and the dimension of the correlation matrix minus 1 ({corr.shape[0] - 1}).") +1499 vals, vec = np.linalg.eigh(corr) +1500 lambda_min = np.mean(vals[:-E]) +1501 vals[vals < lambda_min] = lambda_min +1502 vals /= np.mean(vals) +1503 return vec @ np.diag(vals) @ vec.T 1504 -1505 dvalue = 0.0 -1506 -1507 for e_name in obs1.mc_names: +1505 +1506def _covariance_element(obs1, obs2): +1507 """Estimates the covariance of two Obs objects, neglecting autocorrelations.""" 1508 -1509 if e_name not in obs2.mc_names: -1510 continue -1511 -1512 idl_d = {} -1513 for r_name in obs1.e_content[e_name]: -1514 if r_name not in obs2.e_content[e_name]: -1515 continue -1516 idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]]) -1517 -1518 gamma = 0.0 +1509 def calc_gamma(deltas1, deltas2, idx1, idx2, new_idx): +1510 deltas1 = _collapse_deltas_for_merge(deltas1, idx1, len(idx1), new_idx) +1511 deltas2 = _collapse_deltas_for_merge(deltas2, idx2, len(idx2), new_idx) +1512 return np.sum(deltas1 * deltas2) +1513 +1514 if set(obs1.names).isdisjoint(set(obs2.names)): +1515 return 0.0 +1516 +1517 if not hasattr(obs1, 'e_dvalue') or not hasattr(obs2, 'e_dvalue'): +1518 raise Exception('The gamma method has to be applied to both Obs first.') 1519 -1520 for r_name in obs1.e_content[e_name]: -1521 if r_name not in obs2.e_content[e_name]: -1522 continue -1523 if len(idl_d[r_name]) == 0: -1524 continue -1525 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) +1520 dvalue = 0.0 +1521 +1522 for e_name in obs1.mc_names: +1523 +1524 if e_name not in obs2.mc_names: +1525 continue 1526 -1527 if gamma == 0.0: -1528 continue -1529 -1530 gamma_div = 0.0 -1531 for r_name in obs1.e_content[e_name]: -1532 if r_name not in obs2.e_content[e_name]: -1533 continue -1534 if len(idl_d[r_name]) == 0: -1535 continue -1536 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])) -1537 gamma /= gamma_div -1538 -1539 dvalue += gamma -1540 -1541 for e_name in obs1.cov_names: -1542 -1543 if e_name not in obs2.cov_names: -1544 continue -1545 -1546 dvalue += float(np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad))) -1547 -1548 return dvalue -1549 -1550 -1551def import_jackknife(jacks, name, idl=None): -1552 """Imports jackknife samples and returns an Obs +1527 idl_d = {} +1528 for r_name in obs1.e_content[e_name]: +1529 if r_name not in obs2.e_content[e_name]: +1530 continue +1531 idl_d[r_name] = _intersection_idx([obs1.idl[r_name], obs2.idl[r_name]]) +1532 +1533 gamma = 0.0 +1534 +1535 for r_name in obs1.e_content[e_name]: +1536 if r_name not in obs2.e_content[e_name]: +1537 continue +1538 if len(idl_d[r_name]) == 0: +1539 continue +1540 gamma += calc_gamma(obs1.deltas[r_name], obs2.deltas[r_name], obs1.idl[r_name], obs2.idl[r_name], idl_d[r_name]) +1541 +1542 if gamma == 0.0: +1543 continue +1544 +1545 gamma_div = 0.0 +1546 for r_name in obs1.e_content[e_name]: +1547 if r_name not in obs2.e_content[e_name]: +1548 continue +1549 if len(idl_d[r_name]) == 0: +1550 continue +1551 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])) +1552 gamma /= gamma_div 1553 -1554 Parameters -1555 ---------- -1556 jacks : numpy.ndarray -1557 numpy array containing the mean value as zeroth entry and -1558 the N jackknife samples as first to Nth entry. -1559 name : str -1560 name of the ensemble the samples are defined on. -1561 """ -1562 length = len(jacks) - 1 -1563 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) -1564 samples = jacks[1:] @ prj -1565 mean = np.mean(samples) -1566 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) -1567 new_obs._value = jacks[0] -1568 return new_obs -1569 -1570 -1571def merge_obs(list_of_obs): -1572 """Combine all observables in list_of_obs into one new observable -1573 -1574 Parameters -1575 ---------- -1576 list_of_obs : list -1577 list of the Obs object to be combined -1578 -1579 Notes -1580 ----- -1581 It is not possible to combine obs which are based on the same replicum -1582 """ -1583 replist = [item for obs in list_of_obs for item in obs.names] -1584 if (len(replist) == len(set(replist))) is False: -1585 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) -1586 if any([len(o.cov_names) for o in list_of_obs]): -1587 raise Exception('Not possible to merge data that contains covobs!') -1588 new_dict = {} -1589 idl_dict = {} -1590 for o in list_of_obs: -1591 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) -1592 for key in set(o.deltas) | set(o.r_values)}) -1593 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) -1594 -1595 names = sorted(new_dict.keys()) -1596 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) -1597 o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names} -1598 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) -1599 return o -1600 -1601 -1602def cov_Obs(means, cov, name, grad=None): -1603 """Create an Obs based on mean(s) and a covariance matrix -1604 -1605 Parameters -1606 ---------- -1607 mean : list of floats or float -1608 N mean value(s) of the new Obs -1609 cov : list or array -1610 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance -1611 name : str -1612 identifier for the covariance matrix -1613 grad : list or array -1614 Gradient of the Covobs wrt. the means belonging to cov. -1615 """ +1554 dvalue += gamma +1555 +1556 for e_name in obs1.cov_names: +1557 +1558 if e_name not in obs2.cov_names: +1559 continue +1560 +1561 dvalue += float(np.dot(np.transpose(obs1.covobs[e_name].grad), np.dot(obs1.covobs[e_name].cov, obs2.covobs[e_name].grad))) +1562 +1563 return dvalue +1564 +1565 +1566def import_jackknife(jacks, name, idl=None): +1567 """Imports jackknife samples and returns an Obs +1568 +1569 Parameters +1570 ---------- +1571 jacks : numpy.ndarray +1572 numpy array containing the mean value as zeroth entry and +1573 the N jackknife samples as first to Nth entry. +1574 name : str +1575 name of the ensemble the samples are defined on. +1576 """ +1577 length = len(jacks) - 1 +1578 prj = (np.ones((length, length)) - (length - 1) * np.identity(length)) +1579 samples = jacks[1:] @ prj +1580 mean = np.mean(samples) +1581 new_obs = Obs([samples - mean], [name], idl=idl, means=[mean]) +1582 new_obs._value = jacks[0] +1583 return new_obs +1584 +1585 +1586def merge_obs(list_of_obs): +1587 """Combine all observables in list_of_obs into one new observable +1588 +1589 Parameters +1590 ---------- +1591 list_of_obs : list +1592 list of the Obs object to be combined +1593 +1594 Notes +1595 ----- +1596 It is not possible to combine obs which are based on the same replicum +1597 """ +1598 replist = [item for obs in list_of_obs for item in obs.names] +1599 if (len(replist) == len(set(replist))) is False: +1600 raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist))) +1601 if any([len(o.cov_names) for o in list_of_obs]): +1602 raise Exception('Not possible to merge data that contains covobs!') +1603 new_dict = {} +1604 idl_dict = {} +1605 for o in list_of_obs: +1606 new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0) +1607 for key in set(o.deltas) | set(o.r_values)}) +1608 idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)}) +1609 +1610 names = sorted(new_dict.keys()) +1611 o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names]) +1612 o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names} +1613 o.reweighted = np.max([oi.reweighted for oi in list_of_obs]) +1614 return o +1615 1616 -1617 def covobs_to_obs(co): -1618 """Make an Obs out of a Covobs +1617def cov_Obs(means, cov, name, grad=None): +1618 """Create an Obs based on mean(s) and a covariance matrix 1619 -1620 Parameters -1621 ---------- -1622 co : Covobs -1623 Covobs to be embedded into the Obs -1624 """ -1625 o = Obs([], [], means=[]) -1626 o._value = co.value -1627 o.names.append(co.name) -1628 o._covobs[co.name] = co -1629 o._dvalue = np.sqrt(co.errsq()) -1630 return o +1620 Parameters +1621 ---------- +1622 mean : list of floats or float +1623 N mean value(s) of the new Obs +1624 cov : list or array +1625 2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance +1626 name : str +1627 identifier for the covariance matrix +1628 grad : list or array +1629 Gradient of the Covobs wrt. the means belonging to cov. +1630 """ 1631 -1632 ol = [] -1633 if isinstance(means, (float, int)): -1634 means = [means] -1635 -1636 for i in range(len(means)): -1637 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) -1638 if ol[0].covobs[name].N != len(means): -1639 raise Exception('You have to provide %d mean values!' % (ol[0].N)) -1640 if len(ol) == 1: -1641 return ol[0] -1642 return ol +1632 def covobs_to_obs(co): +1633 """Make an Obs out of a Covobs +1634 +1635 Parameters +1636 ---------- +1637 co : Covobs +1638 Covobs to be embedded into the Obs +1639 """ +1640 o = Obs([], [], means=[]) +1641 o._value = co.value +1642 o.names.append(co.name) +1643 o._covobs[co.name] = co +1644 o._dvalue = np.sqrt(co.errsq()) +1645 return o +1646 +1647 ol = [] +1648 if isinstance(means, (float, int)): +1649 means = [means] +1650 +1651 for i in range(len(means)): +1652 ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad))) +1653 if ol[0].covobs[name].N != len(means): +1654 raise Exception('You have to provide %d mean values!' % (ol[0].N)) +1655 if len(ol) == 1: +1656 return ol[0] +1657 return ol @@ -2382,401 +2400,416 @@ 427 my_string_list.append(my_string) 428 print('\n'.join(my_string_list)) 429 -430 def is_zero_within_error(self, sigma=1): -431 """Checks whether the observable is zero within 'sigma' standard errors. +430 def reweight(self, rw): +431 """Reweight the obs with given rewighting factors. 432 433 Parameters 434 ---------- -435 sigma : int -436 Number of standard errors used for the check. -437 -438 Works only properly when the gamma method was run. -439 """ -440 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue -441 -442 def is_zero(self, atol=1e-10): -443 """Checks whether the observable is zero within a given tolerance. +435 weight : Obs +436 Reweighting factor. An Observable that has to be defined on a superset of the +437 configurations in obs[i].idl for all i. +438 all_configs : bool +439 if True, the reweighted observables are normalized by the average of +440 the reweighting factor on all configurations in weight.idl and not +441 on the configurations in obs[i].idl. Default False. +442 """ +443 return reweight(rw, [self])[0] 444 -445 Parameters -446 ---------- -447 atol : float -448 Absolute tolerance (for details see numpy documentation). -449 """ -450 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()) -451 -452 def plot_tauint(self, save=None): -453 """Plot integrated autocorrelation time for each ensemble. -454 -455 Parameters -456 ---------- -457 save : str -458 saves the figure to a file named 'save' if. -459 """ -460 if not hasattr(self, 'e_dvalue'): -461 raise Exception('Run the gamma method first.') -462 -463 for e, e_name in enumerate(self.mc_names): -464 fig = plt.figure() -465 plt.xlabel(r'$W$') -466 plt.ylabel(r'$\tau_\mathrm{int}$') -467 length = int(len(self.e_n_tauint[e_name])) -468 if self.tau_exp[e_name] > 0: -469 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] -470 x_help = np.arange(2 * self.tau_exp[e_name]) -471 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 -472 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) -473 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') -474 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], -475 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) -476 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 -477 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) -478 else: -479 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) -480 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) -481 -482 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) -483 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') -484 plt.legend() -485 plt.xlim(-0.5, xmax) -486 ylim = plt.ylim() -487 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) -488 plt.draw() -489 if save: -490 fig.savefig(save + "_" + str(e)) -491 -492 def plot_rho(self, save=None): -493 """Plot normalized autocorrelation function time for each ensemble. -494 -495 Parameters -496 ---------- -497 save : str -498 saves the figure to a file named 'save' if. -499 """ -500 if not hasattr(self, 'e_dvalue'): -501 raise Exception('Run the gamma method first.') -502 for e, e_name in enumerate(self.mc_names): -503 fig = plt.figure() -504 plt.xlabel('W') -505 plt.ylabel('rho') -506 length = int(len(self.e_drho[e_name])) -507 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) -508 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') -509 if self.tau_exp[e_name] > 0: -510 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], -511 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) -512 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 -513 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) -514 else: -515 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) -516 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) -517 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) -518 plt.xlim(-0.5, xmax) -519 plt.draw() -520 if save: -521 fig.savefig(save + "_" + str(e)) -522 -523 def plot_rep_dist(self): -524 """Plot replica distribution for each ensemble with more than one replicum.""" -525 if not hasattr(self, 'e_dvalue'): -526 raise Exception('Run the gamma method first.') -527 for e, e_name in enumerate(self.mc_names): -528 if len(self.e_content[e_name]) == 1: -529 print('No replica distribution for a single replicum (', e_name, ')') -530 continue -531 r_length = [] -532 sub_r_mean = 0 -533 for r, r_name in enumerate(self.e_content[e_name]): -534 r_length.append(len(self.deltas[r_name])) -535 sub_r_mean += self.shape[r_name] * self.r_values[r_name] -536 e_N = np.sum(r_length) -537 sub_r_mean /= e_N -538 arr = np.zeros(len(self.e_content[e_name])) -539 for r, r_name in enumerate(self.e_content[e_name]): -540 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) -541 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) -542 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') -543 plt.draw() -544 -545 def plot_history(self, expand=True): -546 """Plot derived Monte Carlo history for each ensemble -547 -548 Parameters -549 ---------- -550 expand : bool -551 show expanded history for irregular Monte Carlo chains (default: True). -552 """ -553 for e, e_name in enumerate(self.mc_names): -554 plt.figure() -555 r_length = [] -556 tmp = [] -557 tmp_expanded = [] -558 for r, r_name in enumerate(self.e_content[e_name]): -559 tmp.append(self.deltas[r_name] + self.r_values[r_name]) -560 if expand: -561 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) -562 r_length.append(len(tmp_expanded[-1])) -563 else: -564 r_length.append(len(tmp[-1])) -565 e_N = np.sum(r_length) -566 x = np.arange(e_N) -567 y_test = np.concatenate(tmp, axis=0) -568 if expand: -569 y = np.concatenate(tmp_expanded, axis=0) -570 else: -571 y = y_test -572 plt.errorbar(x, y, fmt='.', markersize=3) -573 plt.xlim(-0.5, e_N - 0.5) -574 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})') -575 plt.draw() -576 -577 def plot_piechart(self, save=None): -578 """Plot piechart which shows the fractional contribution of each -579 ensemble to the error and returns a dictionary containing the fractions. -580 -581 Parameters -582 ---------- -583 save : str -584 saves the figure to a file named 'save' if. -585 """ -586 if not hasattr(self, 'e_dvalue'): -587 raise Exception('Run the gamma method first.') -588 if np.isclose(0.0, self._dvalue, atol=1e-15): -589 raise Exception('Error is 0.0') -590 labels = self.e_names -591 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 -592 fig1, ax1 = plt.subplots() -593 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) -594 ax1.axis('equal') -595 plt.draw() -596 if save: -597 fig1.savefig(save) -598 -599 return dict(zip(self.e_names, sizes)) -600 -601 def dump(self, filename, datatype="json.gz", description="", **kwargs): -602 """Dump the Obs to a file 'name' of chosen format. -603 -604 Parameters -605 ---------- -606 filename : str -607 name of the file to be saved. -608 datatype : str -609 Format of the exported file. Supported formats include -610 "json.gz" and "pickle" -611 description : str -612 Description for output file, only relevant for json.gz format. -613 path : str -614 specifies a custom path for the file (default '.') -615 """ -616 if 'path' in kwargs: -617 file_name = kwargs.get('path') + '/' + filename -618 else: -619 file_name = filename -620 -621 if datatype == "json.gz": -622 from .input.json import dump_to_json -623 dump_to_json([self], file_name, description=description) -624 elif datatype == "pickle": -625 with open(file_name + '.p', 'wb') as fb: -626 pickle.dump(self, fb) -627 else: -628 raise Exception("Unknown datatype " + str(datatype)) -629 -630 def export_jackknife(self): -631 """Export jackknife samples from the Obs -632 -633 Returns -634 ------- -635 numpy.ndarray -636 Returns a numpy array of length N + 1 where N is the number of samples -637 for the given ensemble and replicum. The zeroth entry of the array contains -638 the mean value of the Obs, entries 1 to N contain the N jackknife samples -639 derived from the Obs. The current implementation only works for observables -640 defined on exactly one ensemble and replicum. The derived jackknife samples -641 should agree with samples from a full jackknife analysis up to O(1/N). -642 """ -643 -644 if len(self.names) != 1: -645 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") -646 -647 name = self.names[0] -648 full_data = self.deltas[name] + self.r_values[name] -649 n = full_data.size -650 mean = self.value -651 tmp_jacks = np.zeros(n + 1) -652 tmp_jacks[0] = mean -653 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) -654 return tmp_jacks -655 -656 def __float__(self): -657 return float(self.value) +445 def is_zero_within_error(self, sigma=1): +446 """Checks whether the observable is zero within 'sigma' standard errors. +447 +448 Parameters +449 ---------- +450 sigma : int +451 Number of standard errors used for the check. +452 +453 Works only properly when the gamma method was run. +454 """ +455 return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue +456 +457 def is_zero(self, atol=1e-10): +458 """Checks whether the observable is zero within a given tolerance. +459 +460 Parameters +461 ---------- +462 atol : float +463 Absolute tolerance (for details see numpy documentation). +464 """ +465 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()) +466 +467 def plot_tauint(self, save=None): +468 """Plot integrated autocorrelation time for each ensemble. +469 +470 Parameters +471 ---------- +472 save : str +473 saves the figure to a file named 'save' if. +474 """ +475 if not hasattr(self, 'e_dvalue'): +476 raise Exception('Run the gamma method first.') +477 +478 for e, e_name in enumerate(self.mc_names): +479 fig = plt.figure() +480 plt.xlabel(r'$W$') +481 plt.ylabel(r'$\tau_\mathrm{int}$') +482 length = int(len(self.e_n_tauint[e_name])) +483 if self.tau_exp[e_name] > 0: +484 base = self.e_n_tauint[e_name][self.e_windowsize[e_name]] +485 x_help = np.arange(2 * self.tau_exp[e_name]) +486 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 +487 x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]) +488 plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',') +489 plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]], +490 yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor']) +491 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 +492 label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2)) +493 else: +494 label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)) +495 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) +496 +497 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) +498 plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--') +499 plt.legend() +500 plt.xlim(-0.5, xmax) +501 ylim = plt.ylim() +502 plt.ylim(bottom=0.0, top=max(1.0, ylim[1])) +503 plt.draw() +504 if save: +505 fig.savefig(save + "_" + str(e)) +506 +507 def plot_rho(self, save=None): +508 """Plot normalized autocorrelation function time for each ensemble. +509 +510 Parameters +511 ---------- +512 save : str +513 saves the figure to a file named 'save' if. +514 """ +515 if not hasattr(self, 'e_dvalue'): +516 raise Exception('Run the gamma method first.') +517 for e, e_name in enumerate(self.mc_names): +518 fig = plt.figure() +519 plt.xlabel('W') +520 plt.ylabel('rho') +521 length = int(len(self.e_drho[e_name])) +522 plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2) +523 plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',') +524 if self.tau_exp[e_name] > 0: +525 plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]], +526 [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1) +527 xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5 +528 plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2))) +529 else: +530 xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5) +531 plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))) +532 plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1) +533 plt.xlim(-0.5, xmax) +534 plt.draw() +535 if save: +536 fig.savefig(save + "_" + str(e)) +537 +538 def plot_rep_dist(self): +539 """Plot replica distribution for each ensemble with more than one replicum.""" +540 if not hasattr(self, 'e_dvalue'): +541 raise Exception('Run the gamma method first.') +542 for e, e_name in enumerate(self.mc_names): +543 if len(self.e_content[e_name]) == 1: +544 print('No replica distribution for a single replicum (', e_name, ')') +545 continue +546 r_length = [] +547 sub_r_mean = 0 +548 for r, r_name in enumerate(self.e_content[e_name]): +549 r_length.append(len(self.deltas[r_name])) +550 sub_r_mean += self.shape[r_name] * self.r_values[r_name] +551 e_N = np.sum(r_length) +552 sub_r_mean /= e_N +553 arr = np.zeros(len(self.e_content[e_name])) +554 for r, r_name in enumerate(self.e_content[e_name]): +555 arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1)) +556 plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name])) +557 plt.title('Replica distribution' + e_name + ' (mean=0, var=1)') +558 plt.draw() +559 +560 def plot_history(self, expand=True): +561 """Plot derived Monte Carlo history for each ensemble +562 +563 Parameters +564 ---------- +565 expand : bool +566 show expanded history for irregular Monte Carlo chains (default: True). +567 """ +568 for e, e_name in enumerate(self.mc_names): +569 plt.figure() +570 r_length = [] +571 tmp = [] +572 tmp_expanded = [] +573 for r, r_name in enumerate(self.e_content[e_name]): +574 tmp.append(self.deltas[r_name] + self.r_values[r_name]) +575 if expand: +576 tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name]) +577 r_length.append(len(tmp_expanded[-1])) +578 else: +579 r_length.append(len(tmp[-1])) +580 e_N = np.sum(r_length) +581 x = np.arange(e_N) +582 y_test = np.concatenate(tmp, axis=0) +583 if expand: +584 y = np.concatenate(tmp_expanded, axis=0) +585 else: +586 y = y_test +587 plt.errorbar(x, y, fmt='.', markersize=3) +588 plt.xlim(-0.5, e_N - 0.5) +589 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})') +590 plt.draw() +591 +592 def plot_piechart(self, save=None): +593 """Plot piechart which shows the fractional contribution of each +594 ensemble to the error and returns a dictionary containing the fractions. +595 +596 Parameters +597 ---------- +598 save : str +599 saves the figure to a file named 'save' if. +600 """ +601 if not hasattr(self, 'e_dvalue'): +602 raise Exception('Run the gamma method first.') +603 if np.isclose(0.0, self._dvalue, atol=1e-15): +604 raise Exception('Error is 0.0') +605 labels = self.e_names +606 sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2 +607 fig1, ax1 = plt.subplots() +608 ax1.pie(sizes, labels=labels, startangle=90, normalize=True) +609 ax1.axis('equal') +610 plt.draw() +611 if save: +612 fig1.savefig(save) +613 +614 return dict(zip(self.e_names, sizes)) +615 +616 def dump(self, filename, datatype="json.gz", description="", **kwargs): +617 """Dump the Obs to a file 'name' of chosen format. +618 +619 Parameters +620 ---------- +621 filename : str +622 name of the file to be saved. +623 datatype : str +624 Format of the exported file. Supported formats include +625 "json.gz" and "pickle" +626 description : str +627 Description for output file, only relevant for json.gz format. +628 path : str +629 specifies a custom path for the file (default '.') +630 """ +631 if 'path' in kwargs: +632 file_name = kwargs.get('path') + '/' + filename +633 else: +634 file_name = filename +635 +636 if datatype == "json.gz": +637 from .input.json import dump_to_json +638 dump_to_json([self], file_name, description=description) +639 elif datatype == "pickle": +640 with open(file_name + '.p', 'wb') as fb: +641 pickle.dump(self, fb) +642 else: +643 raise Exception("Unknown datatype " + str(datatype)) +644 +645 def export_jackknife(self): +646 """Export jackknife samples from the Obs +647 +648 Returns +649 ------- +650 numpy.ndarray +651 Returns a numpy array of length N + 1 where N is the number of samples +652 for the given ensemble and replicum. The zeroth entry of the array contains +653 the mean value of the Obs, entries 1 to N contain the N jackknife samples +654 derived from the Obs. The current implementation only works for observables +655 defined on exactly one ensemble and replicum. The derived jackknife samples +656 should agree with samples from a full jackknife analysis up to O(1/N). +657 """ 658 -659 def __repr__(self): -660 return 'Obs[' + str(self) + ']' +659 if len(self.names) != 1: +660 raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.") 661 -662 def __str__(self): -663 if self._dvalue == 0.0: -664 return str(self.value) -665 fexp = np.floor(np.log10(self._dvalue)) -666 if fexp < 0.0: -667 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') -668 elif fexp == 0.0: -669 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) -670 else: -671 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) -672 -673 # Overload comparisons -674 def __lt__(self, other): -675 return self.value < other +662 name = self.names[0] +663 full_data = self.deltas[name] + self.r_values[name] +664 n = full_data.size +665 mean = self.value +666 tmp_jacks = np.zeros(n + 1) +667 tmp_jacks[0] = mean +668 tmp_jacks[1:] = (n * mean - full_data) / (n - 1) +669 return tmp_jacks +670 +671 def __float__(self): +672 return float(self.value) +673 +674 def __repr__(self): +675 return 'Obs[' + str(self) + ']' 676 -677 def __le__(self, other): -678 return self.value <= other -679 -680 def __gt__(self, other): -681 return self.value > other -682 -683 def __ge__(self, other): -684 return self.value >= other -685 -686 def __eq__(self, other): -687 return (self - other).is_zero() -688 -689 def __ne__(self, other): -690 return not (self - other).is_zero() +677 def __str__(self): +678 if self._dvalue == 0.0: +679 return str(self.value) +680 fexp = np.floor(np.log10(self._dvalue)) +681 if fexp < 0.0: +682 return '{:{form}}({:2.0f})'.format(self.value, self._dvalue * 10 ** (-fexp + 1), form='.' + str(-int(fexp) + 1) + 'f') +683 elif fexp == 0.0: +684 return '{:.1f}({:1.1f})'.format(self.value, self._dvalue) +685 else: +686 return '{:.0f}({:2.0f})'.format(self.value, self._dvalue) +687 +688 # Overload comparisons +689 def __lt__(self, other): +690 return self.value < other 691 -692 # Overload math operations -693 def __add__(self, y): -694 if isinstance(y, Obs): -695 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) -696 else: -697 if isinstance(y, np.ndarray): -698 return np.array([self + o for o in y]) -699 elif y.__class__.__name__ in ['Corr', 'CObs']: -700 return NotImplemented -701 else: -702 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) +692 def __le__(self, other): +693 return self.value <= other +694 +695 def __gt__(self, other): +696 return self.value > other +697 +698 def __ge__(self, other): +699 return self.value >= other +700 +701 def __eq__(self, other): +702 return (self - other).is_zero() 703 -704 def __radd__(self, y): -705 return self + y +704 def __ne__(self, other): +705 return not (self - other).is_zero() 706 -707 def __mul__(self, y): -708 if isinstance(y, Obs): -709 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) -710 else: -711 if isinstance(y, np.ndarray): -712 return np.array([self * o for o in y]) -713 elif isinstance(y, complex): -714 return CObs(self * y.real, self * y.imag) -715 elif y.__class__.__name__ in ['Corr', 'CObs']: -716 return NotImplemented -717 else: -718 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) -719 -720 def __rmul__(self, y): -721 return self * y -722 -723 def __sub__(self, y): -724 if isinstance(y, Obs): -725 return derived_observable(lambda x, **kwargs: x[0] - x[1], [self, y], man_grad=[1, -1]) -726 else: -727 if isinstance(y, np.ndarray): -728 return np.array([self - o for o in y]) -729 elif y.__class__.__name__ in ['Corr', 'CObs']: -730 return NotImplemented -731 else: -732 return derived_observable(lambda x, **kwargs: x[0] - y, [self], man_grad=[1]) -733 -734 def __rsub__(self, y): -735 return -1 * (self - y) -736 -737 def __pos__(self): -738 return self -739 -740 def __neg__(self): -741 return -1 * self -742 -743 def __truediv__(self, y): -744 if isinstance(y, Obs): -745 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) -746 else: -747 if isinstance(y, np.ndarray): -748 return np.array([self / o for o in y]) -749 elif y.__class__.__name__ in ['Corr', 'CObs']: -750 return NotImplemented -751 else: -752 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) -753 -754 def __rtruediv__(self, y): -755 if isinstance(y, Obs): -756 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) -757 else: -758 if isinstance(y, np.ndarray): -759 return np.array([o / self for o in y]) -760 elif y.__class__.__name__ in ['Corr', 'CObs']: -761 return NotImplemented -762 else: -763 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) -764 -765 def __pow__(self, y): -766 if isinstance(y, Obs): -767 return derived_observable(lambda x: x[0] ** x[1], [self, y]) -768 else: -769 return derived_observable(lambda x: x[0] ** y, [self]) -770 -771 def __rpow__(self, y): -772 if isinstance(y, Obs): -773 return derived_observable(lambda x: x[0] ** x[1], [y, self]) -774 else: -775 return derived_observable(lambda x: y ** x[0], [self]) -776 -777 def __abs__(self): -778 return derived_observable(lambda x: anp.abs(x[0]), [self]) +707 # Overload math operations +708 def __add__(self, y): +709 if isinstance(y, Obs): +710 return derived_observable(lambda x, **kwargs: x[0] + x[1], [self, y], man_grad=[1, 1]) +711 else: +712 if isinstance(y, np.ndarray): +713 return np.array([self + o for o in y]) +714 elif y.__class__.__name__ in ['Corr', 'CObs']: +715 return NotImplemented +716 else: +717 return derived_observable(lambda x, **kwargs: x[0] + y, [self], man_grad=[1]) +718 +719 def __radd__(self, y): +720 return self + y +721 +722 def __mul__(self, y): +723 if isinstance(y, Obs): +724 return derived_observable(lambda x, **kwargs: x[0] * x[1], [self, y], man_grad=[y.value, self.value]) +725 else: +726 if isinstance(y, np.ndarray): +727 return np.array([self * o for o in y]) +728 elif isinstance(y, complex): +729 return CObs(self * y.real, self * y.imag) +730 elif y.__class__.__name__ in ['Corr', 'CObs']: +731 return NotImplemented +732 else: +733 return derived_observable(lambda x, **kwargs: x[0] * y, [self], man_grad=[y]) +734 +735 def __rmul__(self, y): +736 return self * y +737 +738 def __sub__(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 __rsub__(self, y): +750 return -1 * (self - y) +751 +752 def __pos__(self): +753 return self +754 +755 def __neg__(self): +756 return -1 * self +757 +758 def __truediv__(self, y): +759 if isinstance(y, Obs): +760 return derived_observable(lambda x, **kwargs: x[0] / x[1], [self, y], man_grad=[1 / y.value, - self.value / y.value ** 2]) +761 else: +762 if isinstance(y, np.ndarray): +763 return np.array([self / o for o in y]) +764 elif y.__class__.__name__ in ['Corr', 'CObs']: +765 return NotImplemented +766 else: +767 return derived_observable(lambda x, **kwargs: x[0] / y, [self], man_grad=[1 / y]) +768 +769 def __rtruediv__(self, y): +770 if isinstance(y, Obs): +771 return derived_observable(lambda x, **kwargs: x[0] / x[1], [y, self], man_grad=[1 / self.value, - y.value / self.value ** 2]) +772 else: +773 if isinstance(y, np.ndarray): +774 return np.array([o / self for o in y]) +775 elif y.__class__.__name__ in ['Corr', 'CObs']: +776 return NotImplemented +777 else: +778 return derived_observable(lambda x, **kwargs: y / x[0], [self], man_grad=[-y / self.value ** 2]) 779 -780 # Overload numpy functions -781 def sqrt(self): -782 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) -783 -784 def log(self): -785 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) -786 -787 def exp(self): -788 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) -789 -790 def sin(self): -791 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) -792 -793 def cos(self): -794 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) -795 -796 def tan(self): -797 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) +780 def __pow__(self, y): +781 if isinstance(y, Obs): +782 return derived_observable(lambda x: x[0] ** x[1], [self, y]) +783 else: +784 return derived_observable(lambda x: x[0] ** y, [self]) +785 +786 def __rpow__(self, y): +787 if isinstance(y, Obs): +788 return derived_observable(lambda x: x[0] ** x[1], [y, self]) +789 else: +790 return derived_observable(lambda x: y ** x[0], [self]) +791 +792 def __abs__(self): +793 return derived_observable(lambda x: anp.abs(x[0]), [self]) +794 +795 # Overload numpy functions +796 def sqrt(self): +797 return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)]) 798 -799 def arcsin(self): -800 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) +799 def log(self): +800 return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value]) 801 -802 def arccos(self): -803 return derived_observable(lambda x: anp.arccos(x[0]), [self]) +802 def exp(self): +803 return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)]) 804 -805 def arctan(self): -806 return derived_observable(lambda x: anp.arctan(x[0]), [self]) +805 def sin(self): +806 return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)]) 807 -808 def sinh(self): -809 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) +808 def cos(self): +809 return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)]) 810 -811 def cosh(self): -812 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) +811 def tan(self): +812 return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2]) 813 -814 def tanh(self): -815 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) +814 def arcsin(self): +815 return derived_observable(lambda x: anp.arcsin(x[0]), [self]) 816 -817 def arcsinh(self): -818 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) +817 def arccos(self): +818 return derived_observable(lambda x: anp.arccos(x[0]), [self]) 819 -820 def arccosh(self): -821 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) +820 def arctan(self): +821 return derived_observable(lambda x: anp.arctan(x[0]), [self]) 822 -823 def arctanh(self): -824 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) +823 def sinh(self): +824 return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)]) +825 +826 def cosh(self): +827 return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)]) +828 +829 def tanh(self): +830 return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2]) +831 +832 def arcsinh(self): +833 return derived_observable(lambda x: anp.arcsinh(x[0]), [self]) +834 +835 def arccosh(self): +836 return derived_observable(lambda x: anp.arccosh(x[0]), [self]) +837 +838 def arctanh(self): +839 return derived_observable(lambda x: anp.arctanh(x[0]), [self]) @@ -3470,6 +3503,51 @@ print details about the ensembles and replica if true. + +
    + +
    + + def + reweight(self, rw) + + + +
    + + 
    430    def reweight(self, rw):
+431        """Reweight the obs with given rewighting factors.
+432
+433        Parameters
+434        ----------
+435        weight : Obs
+436            Reweighting factor. An Observable that has to be defined on a superset of the
+437            configurations in obs[i].idl for all i.
+438        all_configs : bool
+439            if True, the reweighted observables are normalized by the average of
+440            the reweighting factor on all configurations in weight.idl and not
+441            on the configurations in obs[i].idl. Default False.
+442        """
+443        return reweight(rw, [self])[0]
+
    + + +

    Reweight the obs with given rewighting factors.

    + +
    Parameters
    + + +
    + +
    @@ -3482,17 +3560,17 @@ print details about the ensembles and replica if true.
    - 
    430    def is_zero_within_error(self, sigma=1):
-431        """Checks whether the observable is zero within 'sigma' standard errors.
-432
-433        Parameters
-434        ----------
-435        sigma : int
-436            Number of standard errors used for the check.
-437
-438        Works only properly when the gamma method was run.
-439        """
-440        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
+            
    445    def is_zero_within_error(self, sigma=1):
+446        """Checks whether the observable is zero within 'sigma' standard errors.
+447
+448        Parameters
+449        ----------
+450        sigma : int
+451            Number of standard errors used for the check.
+452
+453        Works only properly when the gamma method was run.
+454        """
+455        return self.is_zero() or np.abs(self.value) <= sigma * self._dvalue
 
    
 
 
@@ -3520,15 +3598,15 @@ Number of standard errors used for the check.
    - 
    442    def is_zero(self, atol=1e-10):
-443        """Checks whether the observable is zero within a given tolerance.
-444
-445        Parameters
-446        ----------
-447        atol : float
-448            Absolute tolerance (for details see numpy documentation).
-449        """
-450        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())
+            
    457    def is_zero(self, atol=1e-10):
+458        """Checks whether the observable is zero within a given tolerance.
+459
+460        Parameters
+461        ----------
+462        atol : float
+463            Absolute tolerance (for details see numpy documentation).
+464        """
+465        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())
 
    
 
 
@@ -3555,45 +3633,45 @@ Absolute tolerance (for details see numpy documentation).
    - 
    452    def plot_tauint(self, save=None):
-453        """Plot integrated autocorrelation time for each ensemble.
-454
-455        Parameters
-456        ----------
-457        save : str
-458            saves the figure to a file named 'save' if.
-459        """
-460        if not hasattr(self, 'e_dvalue'):
-461            raise Exception('Run the gamma method first.')
-462
-463        for e, e_name in enumerate(self.mc_names):
-464            fig = plt.figure()
-465            plt.xlabel(r'$W$')
-466            plt.ylabel(r'$\tau_\mathrm{int}$')
-467            length = int(len(self.e_n_tauint[e_name]))
-468            if self.tau_exp[e_name] > 0:
-469                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
-470                x_help = np.arange(2 * self.tau_exp[e_name])
-471                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
-472                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
-473                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
-474                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
-475                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
-476                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
-477                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
-478            else:
-479                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
-480                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
-481
-482            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)
-483            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
-484            plt.legend()
-485            plt.xlim(-0.5, xmax)
-486            ylim = plt.ylim()
-487            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
-488            plt.draw()
-489            if save:
-490                fig.savefig(save + "_" + str(e))
+            
    467    def plot_tauint(self, save=None):
+468        """Plot integrated autocorrelation time for each ensemble.
+469
+470        Parameters
+471        ----------
+472        save : str
+473            saves the figure to a file named 'save' if.
+474        """
+475        if not hasattr(self, 'e_dvalue'):
+476            raise Exception('Run the gamma method first.')
+477
+478        for e, e_name in enumerate(self.mc_names):
+479            fig = plt.figure()
+480            plt.xlabel(r'$W$')
+481            plt.ylabel(r'$\tau_\mathrm{int}$')
+482            length = int(len(self.e_n_tauint[e_name]))
+483            if self.tau_exp[e_name] > 0:
+484                base = self.e_n_tauint[e_name][self.e_windowsize[e_name]]
+485                x_help = np.arange(2 * self.tau_exp[e_name])
+486                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
+487                x_arr = np.arange(self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name])
+488                plt.plot(x_arr, y_help, 'C' + str(e), linewidth=1, ls='--', marker=',')
+489                plt.errorbar([self.e_windowsize[e_name] + 2 * self.tau_exp[e_name]], [self.e_tauint[e_name]],
+490                             yerr=[self.e_dtauint[e_name]], fmt='C' + str(e), linewidth=1, capsize=2, marker='o', mfc=plt.rcParams['axes.facecolor'])
+491                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+492                label = e_name + r', $\tau_\mathrm{exp}$=' + str(np.around(self.tau_exp[e_name], decimals=2))
+493            else:
+494                label = e_name + ', S=' + str(np.around(self.S[e_name], decimals=2))
+495                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+496
+497            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)
+498            plt.axvline(x=self.e_windowsize[e_name], color='C' + str(e), alpha=0.5, marker=',', ls='--')
+499            plt.legend()
+500            plt.xlim(-0.5, xmax)
+501            ylim = plt.ylim()
+502            plt.ylim(bottom=0.0, top=max(1.0, ylim[1]))
+503            plt.draw()
+504            if save:
+505                fig.savefig(save + "_" + str(e))
 
    
 
 
@@ -3620,36 +3698,36 @@ saves the figure to a file named 'save' if.
    - 
    492    def plot_rho(self, save=None):
-493        """Plot normalized autocorrelation function time for each ensemble.
-494
-495        Parameters
-496        ----------
-497        save : str
-498            saves the figure to a file named 'save' if.
-499        """
-500        if not hasattr(self, 'e_dvalue'):
-501            raise Exception('Run the gamma method first.')
-502        for e, e_name in enumerate(self.mc_names):
-503            fig = plt.figure()
-504            plt.xlabel('W')
-505            plt.ylabel('rho')
-506            length = int(len(self.e_drho[e_name]))
-507            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
-508            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
-509            if self.tau_exp[e_name] > 0:
-510                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
-511                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
-512                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
-513                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
-514            else:
-515                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
-516                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
-517            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
-518            plt.xlim(-0.5, xmax)
-519            plt.draw()
-520            if save:
-521                fig.savefig(save + "_" + str(e))
+            
    507    def plot_rho(self, save=None):
+508        """Plot normalized autocorrelation function time for each ensemble.
+509
+510        Parameters
+511        ----------
+512        save : str
+513            saves the figure to a file named 'save' if.
+514        """
+515        if not hasattr(self, 'e_dvalue'):
+516            raise Exception('Run the gamma method first.')
+517        for e, e_name in enumerate(self.mc_names):
+518            fig = plt.figure()
+519            plt.xlabel('W')
+520            plt.ylabel('rho')
+521            length = int(len(self.e_drho[e_name]))
+522            plt.errorbar(np.arange(length), self.e_rho[e_name][:length], yerr=self.e_drho[e_name][:], linewidth=1, capsize=2)
+523            plt.axvline(x=self.e_windowsize[e_name], color='r', alpha=0.25, ls='--', marker=',')
+524            if self.tau_exp[e_name] > 0:
+525                plt.plot([self.e_windowsize[e_name] + 1, self.e_windowsize[e_name] + 1 + 2 * self.tau_exp[e_name]],
+526                         [self.e_rho[e_name][self.e_windowsize[e_name] + 1], 0], 'k-', lw=1)
+527                xmax = self.e_windowsize[e_name] + 2 * self.tau_exp[e_name] + 1.5
+528                plt.title('Rho ' + e_name + r', tau\_exp=' + str(np.around(self.tau_exp[e_name], decimals=2)))
+529            else:
+530                xmax = max(10.5, 2 * self.e_windowsize[e_name] - 0.5)
+531                plt.title('Rho ' + e_name + ', S=' + str(np.around(self.S[e_name], decimals=2)))
+532            plt.plot([-0.5, xmax], [0, 0], 'k--', lw=1)
+533            plt.xlim(-0.5, xmax)
+534            plt.draw()
+535            if save:
+536                fig.savefig(save + "_" + str(e))
 
    
 
 
@@ -3676,27 +3754,27 @@ saves the figure to a file named 'save' if.
    - 
    523    def plot_rep_dist(self):
-524        """Plot replica distribution for each ensemble with more than one replicum."""
-525        if not hasattr(self, 'e_dvalue'):
-526            raise Exception('Run the gamma method first.')
-527        for e, e_name in enumerate(self.mc_names):
-528            if len(self.e_content[e_name]) == 1:
-529                print('No replica distribution for a single replicum (', e_name, ')')
-530                continue
-531            r_length = []
-532            sub_r_mean = 0
-533            for r, r_name in enumerate(self.e_content[e_name]):
-534                r_length.append(len(self.deltas[r_name]))
-535                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
-536            e_N = np.sum(r_length)
-537            sub_r_mean /= e_N
-538            arr = np.zeros(len(self.e_content[e_name]))
-539            for r, r_name in enumerate(self.e_content[e_name]):
-540                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
-541            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
-542            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
-543            plt.draw()
+            
    538    def plot_rep_dist(self):
+539        """Plot replica distribution for each ensemble with more than one replicum."""
+540        if not hasattr(self, 'e_dvalue'):
+541            raise Exception('Run the gamma method first.')
+542        for e, e_name in enumerate(self.mc_names):
+543            if len(self.e_content[e_name]) == 1:
+544                print('No replica distribution for a single replicum (', e_name, ')')
+545                continue
+546            r_length = []
+547            sub_r_mean = 0
+548            for r, r_name in enumerate(self.e_content[e_name]):
+549                r_length.append(len(self.deltas[r_name]))
+550                sub_r_mean += self.shape[r_name] * self.r_values[r_name]
+551            e_N = np.sum(r_length)
+552            sub_r_mean /= e_N
+553            arr = np.zeros(len(self.e_content[e_name]))
+554            for r, r_name in enumerate(self.e_content[e_name]):
+555                arr[r] = (self.r_values[r_name] - sub_r_mean) / (self.e_dvalue[e_name] * np.sqrt(e_N / self.shape[r_name] - 1))
+556            plt.hist(arr, rwidth=0.8, bins=len(self.e_content[e_name]))
+557            plt.title('Replica distribution' + e_name + ' (mean=0, var=1)')
+558            plt.draw()
 
    
 
 
@@ -3716,37 +3794,37 @@ saves the figure to a file named 'save' if.
    - 
    545    def plot_history(self, expand=True):
-546        """Plot derived Monte Carlo history for each ensemble
-547
-548        Parameters
-549        ----------
-550        expand : bool
-551            show expanded history for irregular Monte Carlo chains (default: True).
-552        """
-553        for e, e_name in enumerate(self.mc_names):
-554            plt.figure()
-555            r_length = []
-556            tmp = []
-557            tmp_expanded = []
-558            for r, r_name in enumerate(self.e_content[e_name]):
-559                tmp.append(self.deltas[r_name] + self.r_values[r_name])
-560                if expand:
-561                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name])
-562                    r_length.append(len(tmp_expanded[-1]))
-563                else:
-564                    r_length.append(len(tmp[-1]))
-565            e_N = np.sum(r_length)
-566            x = np.arange(e_N)
-567            y_test = np.concatenate(tmp, axis=0)
-568            if expand:
-569                y = np.concatenate(tmp_expanded, axis=0)
-570            else:
-571                y = y_test
-572            plt.errorbar(x, y, fmt='.', markersize=3)
-573            plt.xlim(-0.5, e_N - 0.5)
-574            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})')
-575            plt.draw()
+            
    560    def plot_history(self, expand=True):
+561        """Plot derived Monte Carlo history for each ensemble
+562
+563        Parameters
+564        ----------
+565        expand : bool
+566            show expanded history for irregular Monte Carlo chains (default: True).
+567        """
+568        for e, e_name in enumerate(self.mc_names):
+569            plt.figure()
+570            r_length = []
+571            tmp = []
+572            tmp_expanded = []
+573            for r, r_name in enumerate(self.e_content[e_name]):
+574                tmp.append(self.deltas[r_name] + self.r_values[r_name])
+575                if expand:
+576                    tmp_expanded.append(_expand_deltas(self.deltas[r_name], list(self.idl[r_name]), self.shape[r_name]) + self.r_values[r_name])
+577                    r_length.append(len(tmp_expanded[-1]))
+578                else:
+579                    r_length.append(len(tmp[-1]))
+580            e_N = np.sum(r_length)
+581            x = np.arange(e_N)
+582            y_test = np.concatenate(tmp, axis=0)
+583            if expand:
+584                y = np.concatenate(tmp_expanded, axis=0)
+585            else:
+586                y = y_test
+587            plt.errorbar(x, y, fmt='.', markersize=3)
+588            plt.xlim(-0.5, e_N - 0.5)
+589            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})')
+590            plt.draw()
 
    
 
 
@@ -3773,29 +3851,29 @@ show expanded history for irregular Monte Carlo chains (default: True).
    - 
    577    def plot_piechart(self, save=None):
-578        """Plot piechart which shows the fractional contribution of each
-579        ensemble to the error and returns a dictionary containing the fractions.
-580
-581        Parameters
-582        ----------
-583        save : str
-584            saves the figure to a file named 'save' if.
-585        """
-586        if not hasattr(self, 'e_dvalue'):
-587            raise Exception('Run the gamma method first.')
-588        if np.isclose(0.0, self._dvalue, atol=1e-15):
-589            raise Exception('Error is 0.0')
-590        labels = self.e_names
-591        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
-592        fig1, ax1 = plt.subplots()
-593        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
-594        ax1.axis('equal')
-595        plt.draw()
-596        if save:
-597            fig1.savefig(save)
-598
-599        return dict(zip(self.e_names, sizes))
+            
    592    def plot_piechart(self, save=None):
+593        """Plot piechart which shows the fractional contribution of each
+594        ensemble to the error and returns a dictionary containing the fractions.
+595
+596        Parameters
+597        ----------
+598        save : str
+599            saves the figure to a file named 'save' if.
+600        """
+601        if not hasattr(self, 'e_dvalue'):
+602            raise Exception('Run the gamma method first.')
+603        if np.isclose(0.0, self._dvalue, atol=1e-15):
+604            raise Exception('Error is 0.0')
+605        labels = self.e_names
+606        sizes = [self.e_dvalue[name] ** 2 for name in labels] / self._dvalue ** 2
+607        fig1, ax1 = plt.subplots()
+608        ax1.pie(sizes, labels=labels, startangle=90, normalize=True)
+609        ax1.axis('equal')
+610        plt.draw()
+611        if save:
+612            fig1.savefig(save)
+613
+614        return dict(zip(self.e_names, sizes))
 
    
 
 
@@ -3823,34 +3901,34 @@ saves the figure to a file named 'save' if.
    - 
    601    def dump(self, filename, datatype="json.gz", description="", **kwargs):
-602        """Dump the Obs to a file 'name' of chosen format.
-603
-604        Parameters
-605        ----------
-606        filename : str
-607            name of the file to be saved.
-608        datatype : str
-609            Format of the exported file. Supported formats include
-610            "json.gz" and "pickle"
-611        description : str
-612            Description for output file, only relevant for json.gz format.
-613        path : str
-614            specifies a custom path for the file (default '.')
-615        """
-616        if 'path' in kwargs:
-617            file_name = kwargs.get('path') + '/' + filename
-618        else:
-619            file_name = filename
-620
-621        if datatype == "json.gz":
-622            from .input.json import dump_to_json
-623            dump_to_json([self], file_name, description=description)
-624        elif datatype == "pickle":
-625            with open(file_name + '.p', 'wb') as fb:
-626                pickle.dump(self, fb)
-627        else:
-628            raise Exception("Unknown datatype " + str(datatype))
+            
    616    def dump(self, filename, datatype="json.gz", description="", **kwargs):
+617        """Dump the Obs to a file 'name' of chosen format.
+618
+619        Parameters
+620        ----------
+621        filename : str
+622            name of the file to be saved.
+623        datatype : str
+624            Format of the exported file. Supported formats include
+625            "json.gz" and "pickle"
+626        description : str
+627            Description for output file, only relevant for json.gz format.
+628        path : str
+629            specifies a custom path for the file (default '.')
+630        """
+631        if 'path' in kwargs:
+632            file_name = kwargs.get('path') + '/' + filename
+633        else:
+634            file_name = filename
+635
+636        if datatype == "json.gz":
+637            from .input.json import dump_to_json
+638            dump_to_json([self], file_name, description=description)
+639        elif datatype == "pickle":
+640            with open(file_name + '.p', 'wb') as fb:
+641                pickle.dump(self, fb)
+642        else:
+643            raise Exception("Unknown datatype " + str(datatype))
 
    
 
 
@@ -3884,31 +3962,31 @@ specifies a custom path for the file (default '.')
    - 
    630    def export_jackknife(self):
-631        """Export jackknife samples from the Obs
-632
-633        Returns
-634        -------
-635        numpy.ndarray
-636            Returns a numpy array of length N + 1 where N is the number of samples
-637            for the given ensemble and replicum. The zeroth entry of the array contains
-638            the mean value of the Obs, entries 1 to N contain the N jackknife samples
-639            derived from the Obs. The current implementation only works for observables
-640            defined on exactly one ensemble and replicum. The derived jackknife samples
-641            should agree with samples from a full jackknife analysis up to O(1/N).
-642        """
-643
-644        if len(self.names) != 1:
-645            raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
-646
-647        name = self.names[0]
-648        full_data = self.deltas[name] + self.r_values[name]
-649        n = full_data.size
-650        mean = self.value
-651        tmp_jacks = np.zeros(n + 1)
-652        tmp_jacks[0] = mean
-653        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
-654        return tmp_jacks
+            
    645    def export_jackknife(self):
+646        """Export jackknife samples from the Obs
+647
+648        Returns
+649        -------
+650        numpy.ndarray
+651            Returns a numpy array of length N + 1 where N is the number of samples
+652            for the given ensemble and replicum. The zeroth entry of the array contains
+653            the mean value of the Obs, entries 1 to N contain the N jackknife samples
+654            derived from the Obs. The current implementation only works for observables
+655            defined on exactly one ensemble and replicum. The derived jackknife samples
+656            should agree with samples from a full jackknife analysis up to O(1/N).
+657        """
+658
+659        if len(self.names) != 1:
+660            raise Exception("'export_jackknife' is only implemented for Obs defined on one ensemble and replicum.")
+661
+662        name = self.names[0]
+663        full_data = self.deltas[name] + self.r_values[name]
+664        n = full_data.size
+665        mean = self.value
+666        tmp_jacks = np.zeros(n + 1)
+667        tmp_jacks[0] = mean
+668        tmp_jacks[1:] = (n * mean - full_data) / (n - 1)
+669        return tmp_jacks
 
    
 
 
@@ -3939,8 +4017,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    781    def sqrt(self):
-782        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
+            
    796    def sqrt(self):
+797        return derived_observable(lambda x, **kwargs: np.sqrt(x[0]), [self], man_grad=[1 / 2 / np.sqrt(self.value)])
 
    
 
 
@@ -3958,8 +4036,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    784    def log(self):
-785        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
+            
    799    def log(self):
+800        return derived_observable(lambda x, **kwargs: np.log(x[0]), [self], man_grad=[1 / self.value])
 
    
 
 
@@ -3977,8 +4055,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    787    def exp(self):
-788        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
+            
    802    def exp(self):
+803        return derived_observable(lambda x, **kwargs: np.exp(x[0]), [self], man_grad=[np.exp(self.value)])
 
    
 
 
@@ -3996,8 +4074,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    790    def sin(self):
-791        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
+            
    805    def sin(self):
+806        return derived_observable(lambda x, **kwargs: np.sin(x[0]), [self], man_grad=[np.cos(self.value)])
 
    
 
 
@@ -4015,8 +4093,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    793    def cos(self):
-794        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
+            
    808    def cos(self):
+809        return derived_observable(lambda x, **kwargs: np.cos(x[0]), [self], man_grad=[-np.sin(self.value)])
 
    
 
 
@@ -4034,8 +4112,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    796    def tan(self):
-797        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
+            
    811    def tan(self):
+812        return derived_observable(lambda x, **kwargs: np.tan(x[0]), [self], man_grad=[1 / np.cos(self.value) ** 2])
 
    
 
 
@@ -4053,8 +4131,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    799    def arcsin(self):
-800        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
+            
    814    def arcsin(self):
+815        return derived_observable(lambda x: anp.arcsin(x[0]), [self])
 
    
 
 
@@ -4072,8 +4150,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    802    def arccos(self):
-803        return derived_observable(lambda x: anp.arccos(x[0]), [self])
+            
    817    def arccos(self):
+818        return derived_observable(lambda x: anp.arccos(x[0]), [self])
 
    
 
 
@@ -4091,8 +4169,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    805    def arctan(self):
-806        return derived_observable(lambda x: anp.arctan(x[0]), [self])
+            
    820    def arctan(self):
+821        return derived_observable(lambda x: anp.arctan(x[0]), [self])
 
    
 
 
@@ -4110,8 +4188,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    808    def sinh(self):
-809        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
+            
    823    def sinh(self):
+824        return derived_observable(lambda x, **kwargs: np.sinh(x[0]), [self], man_grad=[np.cosh(self.value)])
 
    
 
 
@@ -4129,8 +4207,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    811    def cosh(self):
-812        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
+            
    826    def cosh(self):
+827        return derived_observable(lambda x, **kwargs: np.cosh(x[0]), [self], man_grad=[np.sinh(self.value)])
 
    
 
 
@@ -4148,8 +4226,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    814    def tanh(self):
-815        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
+            
    829    def tanh(self):
+830        return derived_observable(lambda x, **kwargs: np.tanh(x[0]), [self], man_grad=[1 / np.cosh(self.value) ** 2])
 
    
 
 
@@ -4167,8 +4245,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    817    def arcsinh(self):
-818        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
+            
    832    def arcsinh(self):
+833        return derived_observable(lambda x: anp.arcsinh(x[0]), [self])
 
    
 
 
@@ -4186,8 +4264,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    820    def arccosh(self):
-821        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
+            
    835    def arccosh(self):
+836        return derived_observable(lambda x: anp.arccosh(x[0]), [self])
 
    
 
 
@@ -4205,8 +4283,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    823    def arctanh(self):
-824        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
+            
    838    def arctanh(self):
+839        return derived_observable(lambda x: anp.arctanh(x[0]), [self])
 
    
 
 
@@ -4357,115 +4435,115 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    827class CObs:
-828    """Class for a complex valued observable."""
-829    __slots__ = ['_real', '_imag', 'tag']
-830
-831    def __init__(self, real, imag=0.0):
-832        self._real = real
-833        self._imag = imag
-834        self.tag = None
-835
-836    @property
-837    def real(self):
-838        return self._real
-839
-840    @property
-841    def imag(self):
-842        return self._imag
-843
-844    def gamma_method(self, **kwargs):
-845        """Executes the gamma_method for the real and the imaginary part."""
-846        if isinstance(self.real, Obs):
-847            self.real.gamma_method(**kwargs)
-848        if isinstance(self.imag, Obs):
-849            self.imag.gamma_method(**kwargs)
+            
    842class CObs:
+843    """Class for a complex valued observable."""
+844    __slots__ = ['_real', '_imag', 'tag']
+845
+846    def __init__(self, real, imag=0.0):
+847        self._real = real
+848        self._imag = imag
+849        self.tag = None
 850
-851    def is_zero(self):
-852        """Checks whether both real and imaginary part are zero within machine precision."""
-853        return self.real == 0.0 and self.imag == 0.0
+851    @property
+852    def real(self):
+853        return self._real
 854
-855    def conjugate(self):
-856        return CObs(self.real, -self.imag)
-857
-858    def __add__(self, other):
-859        if isinstance(other, np.ndarray):
-860            return other + self
-861        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-862            return CObs(self.real + other.real,
-863                        self.imag + other.imag)
-864        else:
-865            return CObs(self.real + other, self.imag)
-866
-867    def __radd__(self, y):
-868        return self + y
+855    @property
+856    def imag(self):
+857        return self._imag
+858
+859    def gamma_method(self, **kwargs):
+860        """Executes the gamma_method for the real and the imaginary part."""
+861        if isinstance(self.real, Obs):
+862            self.real.gamma_method(**kwargs)
+863        if isinstance(self.imag, Obs):
+864            self.imag.gamma_method(**kwargs)
+865
+866    def is_zero(self):
+867        """Checks whether both real and imaginary part are zero within machine precision."""
+868        return self.real == 0.0 and self.imag == 0.0
 869
-870    def __sub__(self, other):
-871        if isinstance(other, np.ndarray):
-872            return -1 * (other - self)
-873        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-874            return CObs(self.real - other.real, self.imag - other.imag)
-875        else:
-876            return CObs(self.real - other, self.imag)
-877
-878    def __rsub__(self, other):
-879        return -1 * (self - other)
-880
-881    def __mul__(self, other):
-882        if isinstance(other, np.ndarray):
-883            return other * self
-884        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-885            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
-886                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
-887                                               [self.real, other.real, self.imag, other.imag],
-888                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
-889                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
-890                                               [self.real, other.real, self.imag, other.imag],
-891                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
-892            elif getattr(other, 'imag', 0) != 0:
-893                return CObs(self.real * other.real - self.imag * other.imag,
-894                            self.imag * other.real + self.real * other.imag)
-895            else:
-896                return CObs(self.real * other.real, self.imag * other.real)
-897        else:
-898            return CObs(self.real * other, self.imag * other)
-899
-900    def __rmul__(self, other):
-901        return self * other
-902
-903    def __truediv__(self, other):
-904        if isinstance(other, np.ndarray):
-905            return 1 / (other / self)
-906        elif hasattr(other, 'real') and hasattr(other, 'imag'):
-907            r = other.real ** 2 + other.imag ** 2
-908            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
-909        else:
-910            return CObs(self.real / other, self.imag / other)
-911
-912    def __rtruediv__(self, other):
-913        r = self.real ** 2 + self.imag ** 2
-914        if hasattr(other, 'real') and hasattr(other, 'imag'):
-915            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
-916        else:
-917            return CObs(self.real * other / r, -self.imag * other / r)
-918
-919    def __abs__(self):
-920        return np.sqrt(self.real**2 + self.imag**2)
-921
-922    def __pos__(self):
-923        return self
-924
-925    def __neg__(self):
-926        return -1 * self
-927
-928    def __eq__(self, other):
-929        return self.real == other.real and self.imag == other.imag
-930
-931    def __str__(self):
-932        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
+870    def conjugate(self):
+871        return CObs(self.real, -self.imag)
+872
+873    def __add__(self, other):
+874        if isinstance(other, np.ndarray):
+875            return other + self
+876        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+877            return CObs(self.real + other.real,
+878                        self.imag + other.imag)
+879        else:
+880            return CObs(self.real + other, self.imag)
+881
+882    def __radd__(self, y):
+883        return self + y
+884
+885    def __sub__(self, other):
+886        if isinstance(other, np.ndarray):
+887            return -1 * (other - self)
+888        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+889            return CObs(self.real - other.real, self.imag - other.imag)
+890        else:
+891            return CObs(self.real - other, self.imag)
+892
+893    def __rsub__(self, other):
+894        return -1 * (self - other)
+895
+896    def __mul__(self, other):
+897        if isinstance(other, np.ndarray):
+898            return other * self
+899        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+900            if all(isinstance(i, Obs) for i in [self.real, self.imag, other.real, other.imag]):
+901                return CObs(derived_observable(lambda x, **kwargs: x[0] * x[1] - x[2] * x[3],
+902                                               [self.real, other.real, self.imag, other.imag],
+903                                               man_grad=[other.real.value, self.real.value, -other.imag.value, -self.imag.value]),
+904                            derived_observable(lambda x, **kwargs: x[2] * x[1] + x[0] * x[3],
+905                                               [self.real, other.real, self.imag, other.imag],
+906                                               man_grad=[other.imag.value, self.imag.value, other.real.value, self.real.value]))
+907            elif getattr(other, 'imag', 0) != 0:
+908                return CObs(self.real * other.real - self.imag * other.imag,
+909                            self.imag * other.real + self.real * other.imag)
+910            else:
+911                return CObs(self.real * other.real, self.imag * other.real)
+912        else:
+913            return CObs(self.real * other, self.imag * other)
+914
+915    def __rmul__(self, other):
+916        return self * other
+917
+918    def __truediv__(self, other):
+919        if isinstance(other, np.ndarray):
+920            return 1 / (other / self)
+921        elif hasattr(other, 'real') and hasattr(other, 'imag'):
+922            r = other.real ** 2 + other.imag ** 2
+923            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.imag * other.real - self.real * other.imag) / r)
+924        else:
+925            return CObs(self.real / other, self.imag / other)
+926
+927    def __rtruediv__(self, other):
+928        r = self.real ** 2 + self.imag ** 2
+929        if hasattr(other, 'real') and hasattr(other, 'imag'):
+930            return CObs((self.real * other.real + self.imag * other.imag) / r, (self.real * other.imag - self.imag * other.real) / r)
+931        else:
+932            return CObs(self.real * other / r, -self.imag * other / r)
 933
-934    def __repr__(self):
-935        return 'CObs[' + str(self) + ']'
+934    def __abs__(self):
+935        return np.sqrt(self.real**2 + self.imag**2)
+936
+937    def __pos__(self):
+938        return self
+939
+940    def __neg__(self):
+941        return -1 * self
+942
+943    def __eq__(self, other):
+944        return self.real == other.real and self.imag == other.imag
+945
+946    def __str__(self):
+947        return '(' + str(self.real) + int(self.imag >= 0.0) * '+' + str(self.imag) + 'j)'
+948
+949    def __repr__(self):
+950        return 'CObs[' + str(self) + ']'
 
    
 
 
@@ -4483,10 +4561,10 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    831    def __init__(self, real, imag=0.0):
-832        self._real = real
-833        self._imag = imag
-834        self.tag = None
+            
    846    def __init__(self, real, imag=0.0):
+847        self._real = real
+848        self._imag = imag
+849        self.tag = None
 
    
 
 
@@ -4537,12 +4615,12 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    844    def gamma_method(self, **kwargs):
-845        """Executes the gamma_method for the real and the imaginary part."""
-846        if isinstance(self.real, Obs):
-847            self.real.gamma_method(**kwargs)
-848        if isinstance(self.imag, Obs):
-849            self.imag.gamma_method(**kwargs)
+            
    859    def gamma_method(self, **kwargs):
+860        """Executes the gamma_method for the real and the imaginary part."""
+861        if isinstance(self.real, Obs):
+862            self.real.gamma_method(**kwargs)
+863        if isinstance(self.imag, Obs):
+864            self.imag.gamma_method(**kwargs)
 
    
 
 
@@ -4562,9 +4640,9 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    851    def is_zero(self):
-852        """Checks whether both real and imaginary part are zero within machine precision."""
-853        return self.real == 0.0 and self.imag == 0.0
+            
    866    def is_zero(self):
+867        """Checks whether both real and imaginary part are zero within machine precision."""
+868        return self.real == 0.0 and self.imag == 0.0
 
    
 
 
@@ -4584,8 +4662,8 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    855    def conjugate(self):
-856        return CObs(self.real, -self.imag)
+            
    870    def conjugate(self):
+871        return CObs(self.real, -self.imag)
 
    
 
 
@@ -4604,184 +4682,184 @@ should agree with samples from a full jackknife analysis up to O(1/N).
    - 
    1104def derived_observable(func, data, array_mode=False, **kwargs):
-1105    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
-1106
-1107    Parameters
-1108    ----------
-1109    func : object
-1110        arbitrary function of the form func(data, **kwargs). For the
-1111        automatic differentiation to work, all numpy functions have to have
-1112        the autograd wrapper (use 'import autograd.numpy as anp').
-1113    data : list
-1114        list of Obs, e.g. [obs1, obs2, obs3].
-1115    num_grad : bool
-1116        if True, numerical derivatives are used instead of autograd
-1117        (default False). To control the numerical differentiation the
-1118        kwargs of numdifftools.step_generators.MaxStepGenerator
-1119        can be used.
-1120    man_grad : list
-1121        manually supply a list or an array which contains the jacobian
-1122        of func. Use cautiously, supplying the wrong derivative will
-1123        not be intercepted.
-1124
-1125    Notes
-1126    -----
-1127    For simple mathematical operations it can be practical to use anonymous
-1128    functions. For the ratio of two observables one can e.g. use
-1129
-1130    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
-1131    """
-1132
-1133    data = np.asarray(data)
-1134    raveled_data = data.ravel()
-1135
-1136    # Workaround for matrix operations containing non Obs data
-1137    if not all(isinstance(x, Obs) for x in raveled_data):
-1138        for i in range(len(raveled_data)):
-1139            if isinstance(raveled_data[i], (int, float)):
-1140                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
-1141
-1142    allcov = {}
-1143    for o in raveled_data:
-1144        for name in o.cov_names:
-1145            if name in allcov:
-1146                if not np.allclose(allcov[name], o.covobs[name].cov):
-1147                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
-1148            else:
-1149                allcov[name] = o.covobs[name].cov
+            
    1119def derived_observable(func, data, array_mode=False, **kwargs):
+1120    """Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
+1121
+1122    Parameters
+1123    ----------
+1124    func : object
+1125        arbitrary function of the form func(data, **kwargs). For the
+1126        automatic differentiation to work, all numpy functions have to have
+1127        the autograd wrapper (use 'import autograd.numpy as anp').
+1128    data : list
+1129        list of Obs, e.g. [obs1, obs2, obs3].
+1130    num_grad : bool
+1131        if True, numerical derivatives are used instead of autograd
+1132        (default False). To control the numerical differentiation the
+1133        kwargs of numdifftools.step_generators.MaxStepGenerator
+1134        can be used.
+1135    man_grad : list
+1136        manually supply a list or an array which contains the jacobian
+1137        of func. Use cautiously, supplying the wrong derivative will
+1138        not be intercepted.
+1139
+1140    Notes
+1141    -----
+1142    For simple mathematical operations it can be practical to use anonymous
+1143    functions. For the ratio of two observables one can e.g. use
+1144
+1145    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
+1146    """
+1147
+1148    data = np.asarray(data)
+1149    raveled_data = data.ravel()
 1150
-1151    n_obs = len(raveled_data)
-1152    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
-1153    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
-1154    new_sample_names = sorted(set(new_names) - set(new_cov_names))
-1155
-1156    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}
-1157    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
-1158
-1159    if data.ndim == 1:
-1160        values = np.array([o.value for o in data])
-1161    else:
-1162        values = np.vectorize(lambda x: x.value)(data)
-1163
-1164    new_values = func(values, **kwargs)
+1151    # Workaround for matrix operations containing non Obs data
+1152    if not all(isinstance(x, Obs) for x in raveled_data):
+1153        for i in range(len(raveled_data)):
+1154            if isinstance(raveled_data[i], (int, float)):
+1155                raveled_data[i] = cov_Obs(raveled_data[i], 0.0, "###dummy_covobs###")
+1156
+1157    allcov = {}
+1158    for o in raveled_data:
+1159        for name in o.cov_names:
+1160            if name in allcov:
+1161                if not np.allclose(allcov[name], o.covobs[name].cov):
+1162                    raise Exception('Inconsistent covariance matrices for %s!' % (name))
+1163            else:
+1164                allcov[name] = o.covobs[name].cov
 1165
-1166    multi = int(isinstance(new_values, np.ndarray))
-1167
-1168    new_r_values = {}
-1169    new_idl_d = {}
-1170    for name in new_sample_names:
-1171        idl = []
-1172        tmp_values = np.zeros(n_obs)
-1173        for i, item in enumerate(raveled_data):
-1174            tmp_values[i] = item.r_values.get(name, item.value)
-1175            tmp_idl = item.idl.get(name)
-1176            if tmp_idl is not None:
-1177                idl.append(tmp_idl)
-1178        if multi > 0:
-1179            tmp_values = np.array(tmp_values).reshape(data.shape)
-1180        new_r_values[name] = func(tmp_values, **kwargs)
-1181        new_idl_d[name] = _merge_idx(idl)
-1182        if not is_merged[name]:
-1183            is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]])))
-1184
-1185    if 'man_grad' in kwargs:
-1186        deriv = np.asarray(kwargs.get('man_grad'))
-1187        if new_values.shape + data.shape != deriv.shape:
-1188            raise Exception('Manual derivative does not have correct shape.')
-1189    elif kwargs.get('num_grad') is True:
-1190        if multi > 0:
-1191            raise Exception('Multi mode currently not supported for numerical derivative')
-1192        options = {
-1193            'base_step': 0.1,
-1194            'step_ratio': 2.5}
-1195        for key in options.keys():
-1196            kwarg = kwargs.get(key)
-1197            if kwarg is not None:
-1198                options[key] = kwarg
-1199        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
-1200        if tmp_df.size == 1:
-1201            deriv = np.array([tmp_df.real])
-1202        else:
-1203            deriv = tmp_df.real
-1204    else:
-1205        deriv = jacobian(func)(values, **kwargs)
-1206
-1207    final_result = np.zeros(new_values.shape, dtype=object)
-1208
-1209    if array_mode is True:
-1210
-1211        class _Zero_grad():
-1212            def __init__(self, N):
-1213                self.grad = np.zeros((N, 1))
-1214
-1215        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]))
-1216        d_extracted = {}
-1217        g_extracted = {}
-1218        for name in new_sample_names:
-1219            d_extracted[name] = []
-1220            ens_length = len(new_idl_d[name])
-1221            for i_dat, dat in enumerate(data):
-1222                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, )))
-1223        for name in new_cov_names:
-1224            g_extracted[name] = []
-1225            zero_grad = _Zero_grad(new_covobs_lengths[name])
-1226            for i_dat, dat in enumerate(data):
-1227                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)))
-1228
-1229    for i_val, new_val in np.ndenumerate(new_values):
-1230        new_deltas = {}
-1231        new_grad = {}
-1232        if array_mode is True:
-1233            for name in new_sample_names:
-1234                ens_length = d_extracted[name][0].shape[-1]
-1235                new_deltas[name] = np.zeros(ens_length)
-1236                for i_dat, dat in enumerate(d_extracted[name]):
-1237                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1238            for name in new_cov_names:
-1239                new_grad[name] = 0
-1240                for i_dat, dat in enumerate(g_extracted[name]):
-1241                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
-1242        else:
-1243            for j_obs, obs in np.ndenumerate(data):
-1244                for name in obs.names:
-1245                    if name in obs.cov_names:
-1246                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
-1247                    else:
-1248                        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])
-1249
-1250        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
-1251
-1252        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
-1253            raise Exception('The same name has been used for deltas and covobs!')
-1254        new_samples = []
-1255        new_means = []
-1256        new_idl = []
-1257        new_names_obs = []
-1258        for name in new_names:
-1259            if name not in new_covobs:
-1260                if is_merged[name]:
-1261                    filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name])
-1262                else:
-1263                    filtered_deltas = new_deltas[name]
-1264                    filtered_idl_d = new_idl_d[name]
-1265
-1266                new_samples.append(filtered_deltas)
-1267                new_idl.append(filtered_idl_d)
-1268                new_means.append(new_r_values[name][i_val])
-1269                new_names_obs.append(name)
-1270        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
-1271        for name in new_covobs:
-1272            final_result[i_val].names.append(name)
-1273        final_result[i_val]._covobs = new_covobs
-1274        final_result[i_val]._value = new_val
-1275        final_result[i_val].is_merged = is_merged
-1276        final_result[i_val].reweighted = reweighted
-1277
-1278    if multi == 0:
-1279        final_result = final_result.item()
+1166    n_obs = len(raveled_data)
+1167    new_names = sorted(set([y for x in [o.names for o in raveled_data] for y in x]))
+1168    new_cov_names = sorted(set([y for x in [o.cov_names for o in raveled_data] for y in x]))
+1169    new_sample_names = sorted(set(new_names) - set(new_cov_names))
+1170
+1171    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}
+1172    reweighted = len(list(filter(lambda o: o.reweighted is True, raveled_data))) > 0
+1173
+1174    if data.ndim == 1:
+1175        values = np.array([o.value for o in data])
+1176    else:
+1177        values = np.vectorize(lambda x: x.value)(data)
+1178
+1179    new_values = func(values, **kwargs)
+1180
+1181    multi = int(isinstance(new_values, np.ndarray))
+1182
+1183    new_r_values = {}
+1184    new_idl_d = {}
+1185    for name in new_sample_names:
+1186        idl = []
+1187        tmp_values = np.zeros(n_obs)
+1188        for i, item in enumerate(raveled_data):
+1189            tmp_values[i] = item.r_values.get(name, item.value)
+1190            tmp_idl = item.idl.get(name)
+1191            if tmp_idl is not None:
+1192                idl.append(tmp_idl)
+1193        if multi > 0:
+1194            tmp_values = np.array(tmp_values).reshape(data.shape)
+1195        new_r_values[name] = func(tmp_values, **kwargs)
+1196        new_idl_d[name] = _merge_idx(idl)
+1197        if not is_merged[name]:
+1198            is_merged[name] = (1 != len(set([len(idx) for idx in [*idl, new_idl_d[name]]])))
+1199
+1200    if 'man_grad' in kwargs:
+1201        deriv = np.asarray(kwargs.get('man_grad'))
+1202        if new_values.shape + data.shape != deriv.shape:
+1203            raise Exception('Manual derivative does not have correct shape.')
+1204    elif kwargs.get('num_grad') is True:
+1205        if multi > 0:
+1206            raise Exception('Multi mode currently not supported for numerical derivative')
+1207        options = {
+1208            'base_step': 0.1,
+1209            'step_ratio': 2.5}
+1210        for key in options.keys():
+1211            kwarg = kwargs.get(key)
+1212            if kwarg is not None:
+1213                options[key] = kwarg
+1214        tmp_df = nd.Gradient(func, order=4, **{k: v for k, v in options.items() if v is not None})(values, **kwargs)
+1215        if tmp_df.size == 1:
+1216            deriv = np.array([tmp_df.real])
+1217        else:
+1218            deriv = tmp_df.real
+1219    else:
+1220        deriv = jacobian(func)(values, **kwargs)
+1221
+1222    final_result = np.zeros(new_values.shape, dtype=object)
+1223
+1224    if array_mode is True:
+1225
+1226        class _Zero_grad():
+1227            def __init__(self, N):
+1228                self.grad = np.zeros((N, 1))
+1229
+1230        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]))
+1231        d_extracted = {}
+1232        g_extracted = {}
+1233        for name in new_sample_names:
+1234            d_extracted[name] = []
+1235            ens_length = len(new_idl_d[name])
+1236            for i_dat, dat in enumerate(data):
+1237                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, )))
+1238        for name in new_cov_names:
+1239            g_extracted[name] = []
+1240            zero_grad = _Zero_grad(new_covobs_lengths[name])
+1241            for i_dat, dat in enumerate(data):
+1242                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)))
+1243
+1244    for i_val, new_val in np.ndenumerate(new_values):
+1245        new_deltas = {}
+1246        new_grad = {}
+1247        if array_mode is True:
+1248            for name in new_sample_names:
+1249                ens_length = d_extracted[name][0].shape[-1]
+1250                new_deltas[name] = np.zeros(ens_length)
+1251                for i_dat, dat in enumerate(d_extracted[name]):
+1252                    new_deltas[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1253            for name in new_cov_names:
+1254                new_grad[name] = 0
+1255                for i_dat, dat in enumerate(g_extracted[name]):
+1256                    new_grad[name] += np.tensordot(deriv[i_val + (i_dat, )], dat)
+1257        else:
+1258            for j_obs, obs in np.ndenumerate(data):
+1259                for name in obs.names:
+1260                    if name in obs.cov_names:
+1261                        new_grad[name] = new_grad.get(name, 0) + deriv[i_val + j_obs] * obs.covobs[name].grad
+1262                    else:
+1263                        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])
+1264
+1265        new_covobs = {name: Covobs(0, allcov[name], name, grad=new_grad[name]) for name in new_grad}
+1266
+1267        if not set(new_covobs.keys()).isdisjoint(new_deltas.keys()):
+1268            raise Exception('The same name has been used for deltas and covobs!')
+1269        new_samples = []
+1270        new_means = []
+1271        new_idl = []
+1272        new_names_obs = []
+1273        for name in new_names:
+1274            if name not in new_covobs:
+1275                if is_merged[name]:
+1276                    filtered_deltas, filtered_idl_d = _filter_zeroes(new_deltas[name], new_idl_d[name])
+1277                else:
+1278                    filtered_deltas = new_deltas[name]
+1279                    filtered_idl_d = new_idl_d[name]
 1280
-1281    return final_result
+1281                new_samples.append(filtered_deltas)
+1282                new_idl.append(filtered_idl_d)
+1283                new_means.append(new_r_values[name][i_val])
+1284                new_names_obs.append(name)
+1285        final_result[i_val] = Obs(new_samples, new_names_obs, means=new_means, idl=new_idl)
+1286        for name in new_covobs:
+1287            final_result[i_val].names.append(name)
+1288        final_result[i_val]._covobs = new_covobs
+1289        final_result[i_val]._value = new_val
+1290        final_result[i_val].is_merged = is_merged
+1291        final_result[i_val].reweighted = reweighted
+1292
+1293    if multi == 0:
+1294        final_result = final_result.item()
+1295
+1296    return final_result
 
    
 
 
@@ -4828,47 +4906,47 @@ functions. For the ratio of two observables one can e.g. use
    - 
    1321def reweight(weight, obs, **kwargs):
-1322    """Reweight a list of observables.
-1323
-1324    Parameters
-1325    ----------
-1326    weight : Obs
-1327        Reweighting factor. An Observable that has to be defined on a superset of the
-1328        configurations in obs[i].idl for all i.
-1329    obs : list
-1330        list of Obs, e.g. [obs1, obs2, obs3].
-1331    all_configs : bool
-1332        if True, the reweighted observables are normalized by the average of
-1333        the reweighting factor on all configurations in weight.idl and not
-1334        on the configurations in obs[i].idl.
-1335    """
-1336    result = []
-1337    for i in range(len(obs)):
-1338        if len(obs[i].cov_names):
-1339            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
-1340        if not set(obs[i].names).issubset(weight.names):
-1341            raise Exception('Error: Ensembles do not fit')
-1342        for name in obs[i].names:
-1343            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
-1344                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
-1345        new_samples = []
-1346        w_deltas = {}
-1347        for name in sorted(obs[i].names):
-1348            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
-1349            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
-1350        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
-1351
-1352        if kwargs.get('all_configs'):
-1353            new_weight = weight
-1354        else:
-1355            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)])
-1356
-1357        result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs))
-1358        result[-1].reweighted = True
-1359        result[-1].is_merged = obs[i].is_merged
-1360
-1361    return result
+            
    1336def reweight(weight, obs, **kwargs):
+1337    """Reweight a list of observables.
+1338
+1339    Parameters
+1340    ----------
+1341    weight : Obs
+1342        Reweighting factor. An Observable that has to be defined on a superset of the
+1343        configurations in obs[i].idl for all i.
+1344    obs : list
+1345        list of Obs, e.g. [obs1, obs2, obs3].
+1346    all_configs : bool
+1347        if True, the reweighted observables are normalized by the average of
+1348        the reweighting factor on all configurations in weight.idl and not
+1349        on the configurations in obs[i].idl. Default False.
+1350    """
+1351    result = []
+1352    for i in range(len(obs)):
+1353        if len(obs[i].cov_names):
+1354            raise Exception('Error: Not possible to reweight an Obs that contains covobs!')
+1355        if not set(obs[i].names).issubset(weight.names):
+1356            raise Exception('Error: Ensembles do not fit')
+1357        for name in obs[i].names:
+1358            if not set(obs[i].idl[name]).issubset(weight.idl[name]):
+1359                raise Exception('obs[%d] has to be defined on a subset of the configs in weight.idl[%s]!' % (i, name))
+1360        new_samples = []
+1361        w_deltas = {}
+1362        for name in sorted(obs[i].names):
+1363            w_deltas[name] = _reduce_deltas(weight.deltas[name], weight.idl[name], obs[i].idl[name])
+1364            new_samples.append((w_deltas[name] + weight.r_values[name]) * (obs[i].deltas[name] + obs[i].r_values[name]))
+1365        tmp_obs = Obs(new_samples, sorted(obs[i].names), idl=[obs[i].idl[name] for name in sorted(obs[i].names)])
+1366
+1367        if kwargs.get('all_configs'):
+1368            new_weight = weight
+1369        else:
+1370            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)])
+1371
+1372        result.append(derived_observable(lambda x, **kwargs: x[0] / x[1], [tmp_obs, new_weight], **kwargs))
+1373        result[-1].reweighted = True
+1374        result[-1].is_merged = obs[i].is_merged
+1375
+1376    return result
 
    
 
 
@@ -4885,7 +4963,7 @@ list of Obs, e.g. [obs1, obs2, obs3].
 
  • all_configs (bool):
 if True, the reweighted observables are normalized by the average of
 the reweighting factor on all configurations in weight.idl and not
-on the configurations in obs[i].idl.
    • 
+on the configurations in obs[i].idl. Default False.
    @@ -4902,48 +4980,48 @@ on the configurations in obs[i].idl. - 
    1364def correlate(obs_a, obs_b):
-1365    """Correlate two observables.
-1366
-1367    Parameters
-1368    ----------
-1369    obs_a : Obs
-1370        First observable
-1371    obs_b : Obs
-1372        Second observable
-1373
-1374    Notes
-1375    -----
-1376    Keep in mind to only correlate primary observables which have not been reweighted
-1377    yet. The reweighting has to be applied after correlating the observables.
-1378    Currently only works if ensembles are identical (this is not strictly necessary).
-1379    """
-1380
-1381    if sorted(obs_a.names) != sorted(obs_b.names):
-1382        raise Exception('Ensembles do not fit')
-1383    if len(obs_a.cov_names) or len(obs_b.cov_names):
-1384        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
-1385    for name in obs_a.names:
-1386        if obs_a.shape[name] != obs_b.shape[name]:
-1387            raise Exception('Shapes of ensemble', name, 'do not fit')
-1388        if obs_a.idl[name] != obs_b.idl[name]:
-1389            raise Exception('idl of ensemble', name, 'do not fit')
-1390
-1391    if obs_a.reweighted is True:
-1392        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
-1393    if obs_b.reweighted is True:
-1394        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
+            
    1379def correlate(obs_a, obs_b):
+1380    """Correlate two observables.
+1381
+1382    Parameters
+1383    ----------
+1384    obs_a : Obs
+1385        First observable
+1386    obs_b : Obs
+1387        Second observable
+1388
+1389    Notes
+1390    -----
+1391    Keep in mind to only correlate primary observables which have not been reweighted
+1392    yet. The reweighting has to be applied after correlating the observables.
+1393    Currently only works if ensembles are identical (this is not strictly necessary).
+1394    """
 1395
-1396    new_samples = []
-1397    new_idl = []
-1398    for name in sorted(obs_a.names):
-1399        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
-1400        new_idl.append(obs_a.idl[name])
-1401
-1402    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
-1403    o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names}
-1404    o.reweighted = obs_a.reweighted or obs_b.reweighted
-1405    return o
+1396    if sorted(obs_a.names) != sorted(obs_b.names):
+1397        raise Exception('Ensembles do not fit')
+1398    if len(obs_a.cov_names) or len(obs_b.cov_names):
+1399        raise Exception('Error: Not possible to correlate Obs that contain covobs!')
+1400    for name in obs_a.names:
+1401        if obs_a.shape[name] != obs_b.shape[name]:
+1402            raise Exception('Shapes of ensemble', name, 'do not fit')
+1403        if obs_a.idl[name] != obs_b.idl[name]:
+1404            raise Exception('idl of ensemble', name, 'do not fit')
+1405
+1406    if obs_a.reweighted is True:
+1407        warnings.warn("The first observable is already reweighted.", RuntimeWarning)
+1408    if obs_b.reweighted is True:
+1409        warnings.warn("The second observable is already reweighted.", RuntimeWarning)
+1410
+1411    new_samples = []
+1412    new_idl = []
+1413    for name in sorted(obs_a.names):
+1414        new_samples.append((obs_a.deltas[name] + obs_a.r_values[name]) * (obs_b.deltas[name] + obs_b.r_values[name]))
+1415        new_idl.append(obs_a.idl[name])
+1416
+1417    o = Obs(new_samples, sorted(obs_a.names), idl=new_idl)
+1418    o.is_merged = {name: (obs_a.is_merged.get(name, False) or obs_b.is_merged.get(name, False)) for name in o.names}
+1419    o.reweighted = obs_a.reweighted or obs_b.reweighted
+1420    return o
 
    
 
 
@@ -4978,71 +5056,71 @@ Currently only works if ensembles are identical (this is not strictly necessary)
    - 
    1408def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
-1409    r'''Calculates the error covariance matrix of a set of observables.
-1410
-1411    The gamma method has to be applied first to all observables.
-1412
-1413    Parameters
-1414    ----------
-1415    obs : list or numpy.ndarray
-1416        List or one dimensional array of Obs
-1417    visualize : bool
-1418        If True plots the corresponding normalized correlation matrix (default False).
-1419    correlation : bool
-1420        If True the correlation matrix instead of the error covariance matrix is returned (default False).
-1421    smooth : None or int
-1422        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
-1423        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
-1424        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
-1425        small ones.
-1426
-1427    Notes
-1428    -----
-1429    The error covariance is defined such that it agrees with the squared standard error for two identical observables
-1430    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
-1431    in the absence of autocorrelation.
-1432    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
-1433    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
-1434    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.
-1435    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
-1436    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
-1437    '''
-1438
-1439    length = len(obs)
-1440
-1441    max_samples = np.max([o.N for o in obs])
-1442    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
-1443        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)
-1444
-1445    cov = np.zeros((length, length))
-1446    for i in range(length):
-1447        for j in range(i, length):
-1448            cov[i, j] = _covariance_element(obs[i], obs[j])
-1449    cov = cov + cov.T - np.diag(np.diag(cov))
-1450
-1451    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
-1452
-1453    if isinstance(smooth, int):
-1454        corr = _smooth_eigenvalues(corr, smooth)
+            
    1423def covariance(obs, visualize=False, correlation=False, smooth=None, **kwargs):
+1424    r'''Calculates the error covariance matrix of a set of observables.
+1425
+1426    The gamma method has to be applied first to all observables.
+1427
+1428    Parameters
+1429    ----------
+1430    obs : list or numpy.ndarray
+1431        List or one dimensional array of Obs
+1432    visualize : bool
+1433        If True plots the corresponding normalized correlation matrix (default False).
+1434    correlation : bool
+1435        If True the correlation matrix instead of the error covariance matrix is returned (default False).
+1436    smooth : None or int
+1437        If smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue
+1438        smoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the
+1439        largest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely
+1440        small ones.
+1441
+1442    Notes
+1443    -----
+1444    The error covariance is defined such that it agrees with the squared standard error for two identical observables
+1445    $$\operatorname{cov}(a,a)=\sum_{s=1}^N\delta_a^s\delta_a^s/N^2=\Gamma_{aa}(0)/N=\operatorname{var}(a)/N=\sigma_a^2$$
+1446    in the absence of autocorrelation.
+1447    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
+1448    $$\sum_{i,j}v_i\Gamma_{ij}(0)v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i,j}v_i\delta_i^s\delta_j^s v_j=\frac{1}{N}\sum_{s=1}^N\sum_{i}|v_i\delta_i^s|^2\geq 0\,,$$ for every $v\in\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.
+1449    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.
+1450    $$\tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}$$
+1451    This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
+1452    '''
+1453
+1454    length = len(obs)
 1455
-1456    if visualize:
-1457        plt.matshow(corr, vmin=-1, vmax=1)
-1458        plt.set_cmap('RdBu')
-1459        plt.colorbar()
-1460        plt.draw()
-1461
-1462    if correlation is True:
-1463        return corr
-1464
-1465    errors = [o.dvalue for o in obs]
-1466    cov = np.diag(errors) @ corr @ np.diag(errors)
+1456    max_samples = np.max([o.N for o in obs])
+1457    if max_samples <= length and not [item for sublist in [o.cov_names for o in obs] for item in sublist]:
+1458        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)
+1459
+1460    cov = np.zeros((length, length))
+1461    for i in range(length):
+1462        for j in range(i, length):
+1463            cov[i, j] = _covariance_element(obs[i], obs[j])
+1464    cov = cov + cov.T - np.diag(np.diag(cov))
+1465
+1466    corr = np.diag(1 / np.sqrt(np.diag(cov))) @ cov @ np.diag(1 / np.sqrt(np.diag(cov)))
 1467
-1468    eigenvalues = np.linalg.eigh(cov)[0]
-1469    if not np.all(eigenvalues >= 0):
-1470        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
-1471
-1472    return cov
+1468    if isinstance(smooth, int):
+1469        corr = _smooth_eigenvalues(corr, smooth)
+1470
+1471    if visualize:
+1472        plt.matshow(corr, vmin=-1, vmax=1)
+1473        plt.set_cmap('RdBu')
+1474        plt.colorbar()
+1475        plt.draw()
+1476
+1477    if correlation is True:
+1478        return corr
+1479
+1480    errors = [o.dvalue for o in obs]
+1481    cov = np.diag(errors) @ corr @ np.diag(errors)
+1482
+1483    eigenvalues = np.linalg.eigh(cov)[0]
+1484    if not np.all(eigenvalues >= 0):
+1485        warnings.warn("Covariance matrix is not positive semi-definite (Eigenvalues: " + str(eigenvalues) + ")", RuntimeWarning)
+1486
+1487    return cov
 
    
 
 
@@ -5091,24 +5169,24 @@ This construction ensures that the estimated covariance matrix is positive semi-
    - 
    1552def import_jackknife(jacks, name, idl=None):
-1553    """Imports jackknife samples and returns an Obs
-1554
-1555    Parameters
-1556    ----------
-1557    jacks : numpy.ndarray
-1558        numpy array containing the mean value as zeroth entry and
-1559        the N jackknife samples as first to Nth entry.
-1560    name : str
-1561        name of the ensemble the samples are defined on.
-1562    """
-1563    length = len(jacks) - 1
-1564    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
-1565    samples = jacks[1:] @ prj
-1566    mean = np.mean(samples)
-1567    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
-1568    new_obs._value = jacks[0]
-1569    return new_obs
+            
    1567def import_jackknife(jacks, name, idl=None):
+1568    """Imports jackknife samples and returns an Obs
+1569
+1570    Parameters
+1571    ----------
+1572    jacks : numpy.ndarray
+1573        numpy array containing the mean value as zeroth entry and
+1574        the N jackknife samples as first to Nth entry.
+1575    name : str
+1576        name of the ensemble the samples are defined on.
+1577    """
+1578    length = len(jacks) - 1
+1579    prj = (np.ones((length, length)) - (length - 1) * np.identity(length))
+1580    samples = jacks[1:] @ prj
+1581    mean = np.mean(samples)
+1582    new_obs = Obs([samples - mean], [name], idl=idl, means=[mean])
+1583    new_obs._value = jacks[0]
+1584    return new_obs
 
    
 
 
@@ -5138,35 +5216,35 @@ name of the ensemble the samples are defined on.
    - 
    1572def merge_obs(list_of_obs):
-1573    """Combine all observables in list_of_obs into one new observable
-1574
-1575    Parameters
-1576    ----------
-1577    list_of_obs : list
-1578        list of the Obs object to be combined
-1579
-1580    Notes
-1581    -----
-1582    It is not possible to combine obs which are based on the same replicum
-1583    """
-1584    replist = [item for obs in list_of_obs for item in obs.names]
-1585    if (len(replist) == len(set(replist))) is False:
-1586        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
-1587    if any([len(o.cov_names) for o in list_of_obs]):
-1588        raise Exception('Not possible to merge data that contains covobs!')
-1589    new_dict = {}
-1590    idl_dict = {}
-1591    for o in list_of_obs:
-1592        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
-1593                        for key in set(o.deltas) | set(o.r_values)})
-1594        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
-1595
-1596    names = sorted(new_dict.keys())
-1597    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
-1598    o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names}
-1599    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
-1600    return o
+            
    1587def merge_obs(list_of_obs):
+1588    """Combine all observables in list_of_obs into one new observable
+1589
+1590    Parameters
+1591    ----------
+1592    list_of_obs : list
+1593        list of the Obs object to be combined
+1594
+1595    Notes
+1596    -----
+1597    It is not possible to combine obs which are based on the same replicum
+1598    """
+1599    replist = [item for obs in list_of_obs for item in obs.names]
+1600    if (len(replist) == len(set(replist))) is False:
+1601        raise Exception('list_of_obs contains duplicate replica: %s' % (str(replist)))
+1602    if any([len(o.cov_names) for o in list_of_obs]):
+1603        raise Exception('Not possible to merge data that contains covobs!')
+1604    new_dict = {}
+1605    idl_dict = {}
+1606    for o in list_of_obs:
+1607        new_dict.update({key: o.deltas.get(key, 0) + o.r_values.get(key, 0)
+1608                        for key in set(o.deltas) | set(o.r_values)})
+1609        idl_dict.update({key: o.idl.get(key, 0) for key in set(o.deltas)})
+1610
+1611    names = sorted(new_dict.keys())
+1612    o = Obs([new_dict[name] for name in names], names, idl=[idl_dict[name] for name in names])
+1613    o.is_merged = {name: np.any([oi.is_merged.get(name, False) for oi in list_of_obs]) for name in o.names}
+1614    o.reweighted = np.max([oi.reweighted for oi in list_of_obs])
+1615    return o
 
    
 
 
@@ -5197,47 +5275,47 @@ list of the Obs object to be combined
    - 
    1603def cov_Obs(means, cov, name, grad=None):
-1604    """Create an Obs based on mean(s) and a covariance matrix
-1605
-1606    Parameters
-1607    ----------
-1608    mean : list of floats or float
-1609        N mean value(s) of the new Obs
-1610    cov : list or array
-1611        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
-1612    name : str
-1613        identifier for the covariance matrix
-1614    grad : list or array
-1615        Gradient of the Covobs wrt. the means belonging to cov.
-1616    """
-1617
-1618    def covobs_to_obs(co):
-1619        """Make an Obs out of a Covobs
+            
    1618def cov_Obs(means, cov, name, grad=None):
+1619    """Create an Obs based on mean(s) and a covariance matrix
 1620
-1621        Parameters
-1622        ----------
-1623        co : Covobs
-1624            Covobs to be embedded into the Obs
-1625        """
-1626        o = Obs([], [], means=[])
-1627        o._value = co.value
-1628        o.names.append(co.name)
-1629        o._covobs[co.name] = co
-1630        o._dvalue = np.sqrt(co.errsq())
-1631        return o
+1621    Parameters
+1622    ----------
+1623    mean : list of floats or float
+1624        N mean value(s) of the new Obs
+1625    cov : list or array
+1626        2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
+1627    name : str
+1628        identifier for the covariance matrix
+1629    grad : list or array
+1630        Gradient of the Covobs wrt. the means belonging to cov.
+1631    """
 1632
-1633    ol = []
-1634    if isinstance(means, (float, int)):
-1635        means = [means]
-1636
-1637    for i in range(len(means)):
-1638        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
-1639    if ol[0].covobs[name].N != len(means):
-1640        raise Exception('You have to provide %d mean values!' % (ol[0].N))
-1641    if len(ol) == 1:
-1642        return ol[0]
-1643    return ol
+1633    def covobs_to_obs(co):
+1634        """Make an Obs out of a Covobs
+1635
+1636        Parameters
+1637        ----------
+1638        co : Covobs
+1639            Covobs to be embedded into the Obs
+1640        """
+1641        o = Obs([], [], means=[])
+1642        o._value = co.value
+1643        o.names.append(co.name)
+1644        o._covobs[co.name] = co
+1645        o._dvalue = np.sqrt(co.errsq())
+1646        return o
+1647
+1648    ol = []
+1649    if isinstance(means, (float, int)):
+1650        means = [means]
+1651
+1652    for i in range(len(means)):
+1653        ol.append(covobs_to_obs(Covobs(means[i], cov, name, pos=i, grad=grad)))
+1654    if ol[0].covobs[name].N != len(means):
+1655        raise Exception('You have to provide %d mean values!' % (ol[0].N))
+1656    if len(ol) == 1:
+1657        return ol[0]
+1658    return ol
 
    
 
 
diff --git a/docs/search.js b/docs/search.js
index c543f081..964105b7 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 liner 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
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    print(my_corr[3])\n> 0.3227(33)\n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    o.covobs[k].grad\n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n\n
    Citing
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.\nand
      • \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.\nwhere applicable.
      • \n
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue')", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n   'fit' fits a constant to the plateau region\n   'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None,\n    title=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
    \n", "signature": "(self, print_range=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n\n
    Second mode:
    \n\n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
    \n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
    \n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
    \n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
    \n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
    \n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "type": "module", "doc": "
    What is pyerrors?
    \n\n
    pyerrors is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the gamma method arXiv:hep-lat/0306017. Some of its features are:
    \n\n
      \n
    • automatic differentiation for exact liner 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
    There exist similar publicly available implementations of gamma method error analysis suites in Fortran, Julia and Python.
    \n\n
    Basic example
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object\nmy_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object\nmy_new_obs.gamma_method()                     # Estimate the statistical error\nprint(my_new_obs)                             # Print the result to stdout\n> 0.31498(72)\n
    \n\n
    The Obs class
    \n\n
    pyerrors introduces a new datatype, Obs, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn Obs object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble.
    \n\n
    import pyerrors as pe\n\nmy_obs = pe.Obs([samples], ['ensemble_name'])\n
    \n\n
    Error propagation
    \n\n
    When performing mathematical operations on Obs objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in arXiv:hep-lat/0306017.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in arXiv:1809.01289.
    \n\n
    The Obs class is designed such that mathematical numpy functions can be used on Obs just as for regular floats.
    \n\n
    import numpy as np\nimport pyerrors as pe\n\nmy_obs1 = pe.Obs([samples1], ['ensemble_name'])\nmy_obs2 = pe.Obs([samples2], ['ensemble_name'])\n\nmy_sum = my_obs1 + my_obs2\n\nmy_m_eff = np.log(my_obs1 / my_obs2)\n\niamzero = my_m_eff - my_m_eff\n# Check that value and fluctuations are zero within machine precision\nprint(iamzero == 0.0)\n> True\n
    \n\n
    Error estimation
    \n\n
    The error estimation within pyerrors is based on the gamma method introduced in arXiv:hep-lat/0306017.\nAfter having arrived at the derived quantity of interest the gamma_method can be called as detailed in the following example.
    \n\n
    my_sum.gamma_method()\nprint(my_sum)\n> 1.70(57)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)\n>  t_int         2.71422900e+00 +/- 6.40320983e-01 S = 2.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    We use the following definition of the integrated autocorrelation time established in Madras & Sokal 1988\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in arXiv:hep-lat/0306017.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the gamma_method as parameter.
    \n\n
    my_sum.gamma_method(S=3.0)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)\n>  t_int         3.29909703e+00 +/- 9.77310102e-01 S = 3.00\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods pyerrors.obs.Obs.plot_tauint and pyerrors.obs.Obs.plot_tauint.
    \n\n
    If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the windowsize is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.
    \n\n
    Exponential tails
    \n\n
    Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in arXiv:1009.5228. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the gamma_method as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.
    \n\n
    my_sum.gamma_method(tau_exp=7.2)\nmy_sum.details()\n> Result         1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)\n>  t_int         3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1\n> 1000 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)\n
    \n\n
    For the full API see pyerrors.obs.Obs.gamma_method.
    \n\n
    Multiple ensembles/replica
    \n\n
    Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their name.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1'])\nobs2 = pe.Obs([samples2], ['ensemble2'])\n\nmy_sum = obs1 + obs2\nmy_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 2 ensembles:\n>   \u00b7 Ensemble 'ensemble1' : 1000 configurations (from 1 to 1000)\n>   \u00b7 Ensemble 'ensemble2' : 500 configurations (from 1 to 500)\n
    \n\n
    pyerrors identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar | in the name of the data set.
    \n\n
    obs1 = pe.Obs([samples1], ['ensemble1|r01'])\nobs2 = pe.Obs([samples2], ['ensemble1|r02'])\n\n> my_sum = obs1 + obs2\n> my_sum.details()\n> Result   2.00697958e+00\n> 1500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1'\n>     \u00b7 Replicum 'r01' : 1000 configurations (from 1 to 1000)\n>     \u00b7 Replicum 'r02' : 500 configurations (from 1 to 500)\n
    \n\n
    Error estimation for multiple ensembles
    \n\n
    In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.
    \n\n
    pe.Obs.S_dict['ensemble1'] = 2.5\npe.Obs.tau_exp_dict['ensemble2'] = 8.0\npe.Obs.tau_exp_dict['ensemble3'] = 2.0\n
    \n\n
    In case the gamma_method is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the gamma_method still dominates over the dictionaries.
    \n\n
    Irregular Monte Carlo chains
    \n\n
    Obs objects defined on irregular Monte Carlo chains can be initialized with the parameter idl.
    \n\n
    # Observable defined on configurations 20 to 519\nobs1 = pe.Obs([samples1], ['ensemble1'], idl=[range(20, 520)])\nobs1.details()\n> Result         9.98319881e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 20 to 519)\n\n# Observable defined on every second configuration between 5 and 1003\nobs2 = pe.Obs([samples2], ['ensemble1'], idl=[range(5, 1005, 2)])\nobs2.details()\n> Result         9.99100712e-01\n> 500 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 500 configurations (from 5 to 1003 in steps of 2)\n\n# Observable defined on configurations 2, 9, 28, 29 and 501\nobs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])\nobs3.details()\n> Result         1.01718064e+00\n> 5 samples in 1 ensemble:\n>   \u00b7 Ensemble 'ensemble1' : 5 configurations (irregular range)\n
    \n\n
    Obs objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.
    \n\n
    Warning: Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. pyerrors.obs.Obs.plot_rho or pyerrors.obs.Obs.plot_tauint.
    \n\n
    For the full API see pyerrors.obs.Obs.
    \n\n
    Correlators
    \n\n
    When one is not interested in single observables but correlation functions, pyerrors offers the Corr class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a Corr objects one needs to arrange the data as a list of Obs
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0      0.7957(80)\n> 1      0.5156(51)\n> 2      0.3227(33)\n> 3      0.2041(21)\n
    \n\n
    In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.
    \n\n
    my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])\nprint(my_corr)\n> x0/a  Corr(x0/a)\n> ------------------\n> 0\n> 1      0.7957(80)\n> 2      0.5156(51)\n> 3      0.3227(33)\n> 4      0.2041(21)\n> 5\n
    \n\n
    The individual entries of a correlator can be accessed via slicing
    \n\n
    print(my_corr[3])\n> 0.3227(33)\n
    \n\n
    Error propagation with the Corr class works very similar to Obs objects. Mathematical operations are overloaded and Corr objects can be computed together with other Corr objects, Obs objects or real numbers and integers.
    \n\n
    my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr\n
    \n\n
    pyerrors provides the user with a set of regularly used methods for the manipulation of correlator objects:
    \n\n
      \n
    • Corr.gamma_method applies the gamma method to all entries of the correlator.
      • \n
    • Corr.m_eff to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.
      • \n
    • Corr.deriv returns the first derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.second_deriv returns the second derivative of the correlator as Corr. Different discretizations of the numerical derivative are available.
      • \n
    • Corr.symmetric symmetrizes parity even correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.anti_symmetric anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.
      • \n
    • Corr.T_symmetry averages a correlator with its time symmetry partner, assuming fixed boundary conditions.
      • \n
    • Corr.plateau extracts a plateau value from the correlator in a given range.
      • \n
    • Corr.roll periodically shifts the correlator.
      • \n
    • Corr.reverse reverses the time ordering of the correlator.
      • \n
    • Corr.correlate constructs a disconnected correlation function from the correlator and another Corr or Obs object.
      • \n
    • Corr.reweight reweights the correlator.
      • \n
    \n\n
    pyerrors can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see pyerrors.correlators.Corr.GEVP).
    \n\n
    For the full API see pyerrors.correlators.Corr.
    \n\n
    Complex valued observables
    \n\n
    pyerrors can handle complex valued observables via the class pyerrors.obs.CObs.\nCObs are initialized with a real and an imaginary part which both can be Obs valued.
    \n\n
    my_real_part = pe.Obs([samples1], ['ensemble1'])\nmy_imag_part = pe.Obs([samples2], ['ensemble1'])\n\nmy_cobs = pe.CObs(my_real_part, my_imag_part)\nmy_cobs.gamma_method()\nprint(my_cobs)\n> (0.9959(91)+0.659(28)j)\n
    \n\n
    Elementary mathematical operations are overloaded and samples are properly propagated as for the Obs class.
    \n\n
    my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)\nmy_derived_cobs.gamma_method()\nprint(my_derived_cobs)\n> (1.668(23)+0.0j)\n
    \n\n
    The Covobs class
    \n\n
    In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The Covobs class allows to define such quantities in pyerrors. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.
    \n\n
    This concept is built into the definition of Covobs. In pyerrors, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters cov_Obs, since the second argument of this function is the covariance matrix of the Covobs.
    \n\n
    import pyerrors.obs as pe\n\nmpi = pe.cov_Obs(134.9768, 0.0005**2, 'pi^0 mass')\nmpi.gamma_method()\nmpi.details()\n> Result         1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)\n>  pi^0 mass     5.00000000e-04\n> 0 samples in 1 ensemble:\n>   \u00b7 Covobs   'pi^0 mass'\n
    \n\n
    The resulting object mpi is an Obs that contains a Covobs. In the following, it may be handled as any other Obs. The contribution of the covariance matrix to the error of an Obs is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the Obs with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.
    \n\n
    Correlated auxiliary data is defined similarly to above, e.g., via
    \n\n
    RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], 'R_AP, 1906.03445, (5.3a)')\nprint(RAP)\n> [Obs[16.7(1.9)], Obs[-19.0(3.3)]]\n
    \n\n
    where RAP now is a list of two Obs that contains the two correlated parameters.
    \n\n
    Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the Covobs class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an Obs o with respect to a covariance matrix with the identifying string k may be accessed via
    \n\n
    o.covobs[k].grad\n
    \n\n
    Error propagation in iterative algorithms
    \n\n
    pyerrors supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in arXiv:1809.01289.
    \n\n
    Least squares fits
    \n\n
    Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with pyerrors.fits.least_squares. As default solver the Levenberg-Marquardt algorithm implemented in scipy is used.
    \n\n
    Fit functions have to be of the following form
    \n\n
    import autograd.numpy as anp\n\ndef func(a, x):\n    return a[1] * anp.exp(-a[0] * x)\n
    \n\n
    It is important that numerical functions refer to autograd.numpy instead of numpy for the automatic differentiation in iterative algorithms to work properly.
    \n\n
    Fits can then be performed via
    \n\n
    fit_result = pe.fits.least_squares(x, y, func)\nprint("\\n", fit_result)\n> Fit with 2 parameters\n> Method: Levenberg-Marquardt\n> `ftol` termination condition is satisfied.\n> chisquare/d.o.f.: 0.9593035785160936\n\n>  Goodness of fit:\n> \u03c7\u00b2/d.o.f. = 0.959304\n> p-value   = 0.5673\n> Fit parameters:\n> 0      0.0548(28)\n> 1      1.933(64)\n
    \n\n
    where x is a list or numpy.array of floats and y is a list or numpy.array of Obs.
    \n\n
    Data stored in Corr objects can be fitted directly using the Corr.fit method.
    \n\n
    my_corr = pe.Corr(y)\nfit_result = my_corr.fit(func, fitrange=[12, 25])\n
    \n\n
    this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.
    \n\n
    For fit functions with multiple independent variables the fit function can be of the form
    \n\n
    def func(a, x):\n    (x1, x2) = x\n    return a[0] * x1 ** 2 + a[1] * x2\n
    \n\n
    pyerrors also supports correlated fits which can be triggered via the parameter correlated_fit=True.\nDetails about how the required covariance matrix is estimated can be found in pyerrors.obs.covariance.
    \n\n
    Direct visualizations of the performed fits can be triggered via resplot=True or qqplot=True. For all available options see pyerrors.fits.least_squares.
    \n\n
    Total least squares fits
    \n\n
    pyerrors can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in scipy, see pyerrors.fits.least_squares. The syntax is identical to the standard least squares case, the only diffrence being that x also has to be a list or numpy.array of Obs.
    \n\n
    For the full API see pyerrors.fits for fits and pyerrors.roots for finding roots of functions.
    \n\n
    Matrix operations
    \n\n
    pyerrors provides wrappers for Obs- and CObs-valued matrix operations based on numpy.linalg. The supported functions include:
    \n\n
      \n
    • inv for the matrix inverse.
      • \n
    • cholseky for the Cholesky decomposition.
      • \n
    • det for the matrix determinant.
      • \n
    • eigh for eigenvalues and eigenvectors of hermitean matrices.
      • \n
    • eig for eigenvalues of general matrices.
      • \n
    • pinv for the Moore-Penrose pseudoinverse.
      • \n
    • svd for the singular-value-decomposition.
      • \n
    \n\n
    For the full API see pyerrors.linalg.
    \n\n
    Export data
    \n\n
    The preferred exported file format within pyerrors is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:
    \n\n
      \n
    • What observables are stored? Possibly: How exactly are they defined.
      • \n
    • How does each single ensemble or external quantity contribute to the error of the observable?
      • \n
    • Who did write the file when and on which machine?
      • \n
    \n\n
    This can be achieved by storing all information in one single file. The export routines of pyerrors are written such that as much information as possible is written automatically as described in the following example
    \n\n
    my_obs = pe.Obs([samples], ["test_ensemble"])\nmy_obs.tag = "My observable"\n\npe.input.json.dump_to_json(my_obs, "test_output_file", description="This file contains a test observable")\n# For a single observable one can equivalently use the class method dump\nmy_obs.dump("test_output_file", description="This file contains a test observable")\n\ncheck = pe.input.json.load_json("test_output_file")\n\nprint(my_obs == check)\n> True\n
    \n\n
    The format also allows to directly write out the content of Corr objects or lists and arrays of Obs objects by passing the desired data to pyerrors.input.json.dump_to_json.
    \n\n
    json.gz format specification
    \n\n
    The first entries of the file provide optional auxiliary information:
    \n\n
      \n
    • program is a string that indicates which program was used to write the file.
      • \n
    • version is a string that specifies the version of the format.
      • \n
    • who is a string that specifies the user name of the creator of the file.
      • \n
    • date is a string and contains the creation date of the file.
      • \n
    • host is a string and contains the hostname of the machine where the file has been written.
      • \n
    • description contains information on the content of the file. This field is not filled automatically in pyerrors. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.
      • \n
    \n\n
    The only necessary entry of the file is the field\n-obsdata, an array that contains the actual data.
    \n\n
    Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of Obs, list, numpy.ndarray, Corr. All Obs inside a structure (with dimension > 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array obsdata, are treated independently. Each entry of the array obsdata has the following required entries:
    \n\n
      \n
    • type is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.
      • \n
    • value is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:
      • \n
    • layout is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).
      • \n
    • tag is any JSON type. It contains additional information concerning the structure. The tag of an Obs in pyerrors is written here.
      • \n
    • reweighted is a Bool that may be used to specify, whether the Obs in the structure have been reweighted.
      • \n
    • data is an array that contains the data from MC chains. We will define it below.
      • \n
    • cdata is an array that contains the data from external quantities with an error (Covobs in pyerrors). We will define it below.
      • \n
    \n\n
    The array data contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:
    \n\n
      \n
    • id, a string that contains the name of the ensemble
      • \n
    • replica, an array that contains an entry per replica of the ensemble.
      • \n
    \n\n
    Each entry of replica contains\nname, a string that contains the name of the replica\ndeltas, an array that contains the actual data.
    \n\n
    Each entry in deltas corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each Obs inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.
    \n\n
    The array cdata contains information about the contribution of auxiliary observables, represented by Covobs in pyerrors, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:
    \n\n
      \n
    • id, a string that identifies the covariance matrix
      • \n
    • layout, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").
      • \n
    • cov, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.
      • \n
    • grad, an array that contains N entries, one for each Obs inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.
      • \n
    \n\n
    A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.
    \n\n
    Julia I/O routines for the json.gz format, compatible with ADerrors.jl, can be found here.
    \n\n
    Citing
    \n\n
    If you use pyerrors for research that leads to a publication please consider citing:
    \n\n
      \n
    • Ulli Wolff, Monte Carlo errors with less errors. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).
      • \n
    • Alberto Ramos, Automatic differentiation for error analysis of Monte Carlo data. Comput.Phys.Commun. 238 (2019) 19-35.\nand
      • \n
    • Stefan Schaefer, Rainer Sommer, Francesco Virotta, Critical slowing down and error analysis in lattice QCD simulations. Nucl.Phys.B 845 (2011) 93-119.\nwhere applicable.
      • \n
    \n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "type": "module", "doc": "
    \n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "class", "doc": "
    The class for a correlator (time dependent sequence of pe.Obs).
    \n\n
    Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.
    \n\n
    The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.
    \n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "
    Initialize a Corr object.
    \n\n
    Parameters
    \n\n
      \n
    • data_input (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs
      • \n
    • padding (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.
      • \n
    • prange (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.
      • \n
    \n", "signature": "(self, data_input, padding=[0, 0], prange=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "
    Apply the gamma method to the content of the Corr.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "
    We need to project the Correlator with a Vector to get a single value at each timeslice.
    \n\n
    The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to
    \n", "signature": "(self, vector_l=None, vector_r=None, normalize=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "
    Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.
    \n\n
    Parameters
    \n\n
      \n
    • i (int):\nFirst index to be picked.
      • \n
    • j (int):\nSecond index to be picked.
      • \n
    \n", "signature": "(self, i, j)", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "function", "doc": "
    Outputs the correlator in a plotable format.
    \n\n
    Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "
    Symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "
    Anti-symmetrize the correlator around x0=0.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "
    Symmetrizes the correlator matrices on every timeslice.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "
    Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.
    \n\n
    The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing
    \n\n
    C.GEVP(t0=2)[0]  # Ground state vector(s)\nC.GEVP(t0=2)[:3]  # Vectors for the lowest three states\n
    \n\n
    Parameters
    \n\n
      \n
    • t0 (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$
      • \n
    • ts (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.
      • \n
    • sort (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n
        \n
      • \"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.
        • \n
      • \"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.
        • \n
      • \n
    \n\n
    Other Parameters
    \n\n
      \n
    • state (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.
      • \n
    \n", "signature": "(self, t0, ts=None, sort='Eigenvalue', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "
    Determines the eigenvalue of the GEVP by solving and projecting the correlator
    \n\n
    Parameters
    \n\n
      \n
    • state (int):\nThe state one is interested in ordered by energy. The lowest state is zero.
      • \n
    • All other parameters are identical to the ones of Corr.GEVP.
      • \n
    \n", "signature": "(self, t0, ts=None, state=0, sort='Eigenvalue')", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "
    Constructs an NxN Hankel matrix
    \n\n
    C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))
    \n\n
    Parameters
    \n\n
      \n
    • N (int):\nDimension of the Hankel matrix
      • \n
    • periodic (bool, optional):\ndetermines whether the matrix is extended periodically
      • \n
    \n", "signature": "(self, N, periodic=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "function", "doc": "
    Periodically shift the correlator by dt timeslices
    \n\n
    Parameters
    \n\n
      \n
    • dt (int):\nnumber of timeslices
      • \n
    \n", "signature": "(self, dt)", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "
    Reverse the time ordering of the Corr
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "
    Thin out a correlator to suppress correlations
    \n\n
    Parameters
    \n\n
      \n
    • spacing (int):\nKeep only every 'spacing'th entry of the correlator
      • \n
    • offset (int):\nOffset the equal spacing
      • \n
    \n", "signature": "(self, spacing=2, offset=0)", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "function", "doc": "
    Correlate the correlator with another correlator or Obs
    \n\n
    Parameters
    \n\n
      \n
    • partner (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.
      • \n
    \n", "signature": "(self, partner)", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "function", "doc": "
    Reweight the correlator.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.
      • \n
    \n", "signature": "(self, weight, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "function", "doc": "
    Return the time symmetry average of the correlator and its partner
    \n\n
    Parameters
    \n\n
      \n
    • partner (Corr):\nTime symmetry partner of the Corr
      • \n
    • partity (int):\nParity quantum number of the correlator, can be +1 or -1
      • \n
    \n", "signature": "(self, partner, parity=1)", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "function", "doc": "
    Return the first derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "
    Return the second derivative of the correlator with respect to x0.
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric
      • \n
    \n", "signature": "(self, variant='symmetric')", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "function", "doc": "
    Returns the effective mass of the correlator as correlator object
    \n\n
    Parameters
    \n\n
      \n
    • variant (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicitiy of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicitiy of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)
      • \n
    • guess (float):\nguess for the root finder, only relevant for the root variant
      • \n
    \n", "signature": "(self, variant='log', guess=1.0)", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "function", "doc": "
    Fits function to the data
    \n\n
    Parameters
    \n\n
      \n
    • function (obj):\nfunction to fit to the data. See fits.least_squares for details.
      • \n
    • fitrange (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\nfitrange=[4, 6] corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.
      • \n
    • silent (bool):\nDecides whether output is printed to the standard output.
      • \n
    \n", "signature": "(self, function, fitrange=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "function", "doc": "
    Extract a plateau value from a Corr object
    \n\n
    Parameters
    \n\n
      \n
    • plateau_range (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.
      • \n
    • method (str):\nmethod to extract the plateau.\n   'fit' fits a constant to the plateau region\n   'avg', 'average' or 'mean' just average over the given timeslices.
      • \n
    • auto_gamma (bool):\napply gamma_method with default parameters to the Corr. Defaults to None
      • \n
    \n", "signature": "(self, plateau_range=None, method='fit', auto_gamma=False)", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "
    Sets the attribute prange of the Corr object.
    \n", "signature": "(self, prange)", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "
    Plots the correlator using the tag of the correlator as label if available.
    \n\n
    Parameters
    \n\n
      \n
    • x_range (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].
      • \n
    • comp (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.
      • \n
    • logscale (bool):\nSets y-axis to logscale.
      • \n
    • plateau (Obs):\nPlateau value to be visualized in the figure.
      • \n
    • fit_res (Fit_result):\nFit_result object to be visualized.
      • \n
    • ylabel (str):\nLabel for the y-axis.
      • \n
    • save (str):\npath to file in which the figure should be saved.
      • \n
    • auto_gamma (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.
      • \n
    • hide_sigma (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.
      • \n
    • references (list):\nList of floating point values that are displayed as horizontal lines for reference.
      • \n
    • title (string):\nOptional title of the figure.
      • \n
    \n", "signature": "(\n    self,\n    x_range=None,\n    comp=None,\n    y_range=None,\n    logscale=False,\n    plateau=None,\n    fit_res=None,\n    ylabel=None,\n    save=None,\n    auto_gamma=False,\n    hide_sigma=None,\n    references=None,\n    title=None\n)", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "
    Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.
    \n\n
    Parameters
    \n\n
      \n
    • logscale (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.
      • \n
    \n", "signature": "(self, logscale=True)", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "
    Dumps the Corr into a file of chosen type
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nName of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', **kwargs)", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "
    \n", "signature": "(self, print_range=None)", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "
    Project large correlation matrix to lowest states
    \n\n
    This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.
    \n\n
    Parameters
    \n\n
      \n
    • Ntrunc (int):\nRank of the target matrix.
      • \n
    • tproj (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.
      • \n
    • t0proj (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.
      • \n
    • basematrix (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.
      • \n
    \n\n
    Notes
    \n\n
    We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.
    \n", "signature": "(self, Ntrunc, tproj=3, t0proj=2, basematrix=None)", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "type": "module", "doc": "
    \n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "
    \n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "function", "doc": "
    Initialize Covobs object.
    \n\n
    Parameters
    \n\n
      \n
    • mean (float):\nMean value of the new Obs
      • \n
    • cov (list or array):\n2d Covariance matrix or 1d diagonal entries
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • pos (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(self, mean, cov, name, pos=None, grad=None)", "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "
    Return the variance (= square of the error) of the Covobs
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "type": "variable", "doc": "
    \n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "type": "variable", "doc": "
    \n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "
    \n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "
    Rank-3 epsilon tensor
    \n\n
    Based on https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k)", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "
    Rank-4 epsilon tensor
    \n\n
    Extension of https://codegolf.stackexchange.com/a/160375
    \n", "signature": "(i, j, k, o)", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "
    Returns gamma matrix in Grid labeling.
    \n", "signature": "(gamma_tag)", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "type": "module", "doc": "
    \n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "class", "doc": "
    Represents fit results.
    \n\n
    Attributes
    \n\n
      \n
    • fit_parameters (list):\nresults for the individual fit parameters,\nalso accessible via indices.
      • \n
    \n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "
    Apply the gamma method to all fit parameters
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x).
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of floats.
      • \n
    • y (list):\nlist of Obs.
      • \n
    • func (object):\nfit function, has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • priors (list, optional):\npriors has to be a list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.
      • \n
    • method (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.
      • \n
    • correlated_fit (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see pyerrors.obs.covariance.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for prior==None and when no method is given.
      • \n
    • expected_chisquare (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).
      • \n
    • resplot (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).
      • \n
    • qqplot (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).
      • \n
    \n", "signature": "(x, y, func, priors=None, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "function", "doc": "
    Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nlist of Obs, or a tuple of lists of Obs
      • \n
    • y (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.
      • \n
    • func (object):\nfunc has to be of the form
      \n\n
      import autograd.numpy as anp\n\ndef func(a, x):\n   return a[0] + a[1] * x + a[2] * anp.sinh(x)\n
      \n\n
      For multiple x values func can be of the form
      \n\n
      def func(a, x):\n   (x1, x2) = x\n   return a[0] * x1 ** 2 + a[1] * x2\n
      \n\n
      It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.
      • \n
    • silent (bool, optional):\nIf true all output to the console is omitted (default False).
      • \n
    • initial_guess (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.
      • \n
    • expected_chisquare (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).
      • \n
    \n\n
    Notes
    \n\n
    Based on the orthogonal distance regression module of scipy
    \n", "signature": "(x, y, func, silent=False, **kwargs)", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "
    Performs a linear fit to y = n + m * x and returns two Obs n, m.
    \n\n
    Parameters
    \n\n
      \n
    • x (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.
      • \n
    • y (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.
      • \n
    \n", "signature": "(x, y, **kwargs)", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "
    Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.
    \n", "signature": "(x, o_y, func, p)", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "
    Generates a plot which compares the fit to the data and displays the corresponding residuals
    \n", "signature": "(x, y, func, fit_res)", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "
    Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.
    \n", "signature": "(x, func, beta)", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "
    Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.
    \n\n
    Parameters
    \n\n
      \n
    • objects (list):\nList of fit results to include in the analysis (optional).
      • \n
    \n", "signature": "(objects=None)", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "
    pyerrors includes an input submodule in which input routines and parsers for the output of various numerical programs are contained.
    \n\n
    Jackknife samples
    \n\n
    For comparison with other analysis workflows pyerrors can also generate jackknife samples from an Obs object or import jackknife samples into an Obs object.\nSee pyerrors.obs.Obs.export_jackknife and pyerrors.obs.import_jackknife for details.
    \n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "type": "module", "doc": "
    \n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "function", "doc": "
    Extract generic MCMC data from a bdio file
    \n\n
    read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "function", "doc": "
    Write Obs to a bdio file according to ADerrors conventions
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path -- path to the bdio file
      • \n
    • bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    \n", "signature": "(obs_list, file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "function", "doc": "
    Extract mesons data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)
    \n\n
    read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "function", "doc": "
    Extract dSdm data from a bdio file and return it as a dictionary
    \n\n
    The dictionary can be accessed with a tuple consisting of (type, kappa)
    \n\n
    read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to
    \n\n
    all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/
    \n\n
    Parameters
    \n\n
      \n
    • file_path (str):\npath to the bdio file
      • \n
    • bdio_path (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)
      • \n
    • start (int):\nThe first configuration to be read (default 1)
      • \n
    • stop (int):\nThe last configuration to be read (default None)
      • \n
    • step (int):\nFixed step size between two measurements (default 1)
      • \n
    • alternative_ensemble_name (str):\nManually overwrite ensemble name
      • \n
    \n", "signature": "(file_path, bdio_path='./libbdio.so', **kwargs)", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "
    \n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    \n", "signature": "(obsl, name, spec='', origin='', symbol=[], enstag=None)", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • enstag (str):\nEnstag that is written to pobs. If None, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='',\n    origin='',\n    symbol=[],\n    enstag=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen pobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.
      • \n
    \n", "signature": "(fname, full_output=False, gz=True, separator_insertion=None)", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "
    Import a list of Obs from a string in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • content (str):\nXML string containing the data
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(content, noempty=False, full_output=False, separator_insertion=True)", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "
    Import a list of Obs from an xml.gz file in the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • noemtpy (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.
      • \n
    • separatior_insertion (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.
      • \n
    \n", "signature": "(\n    fname,\n    noempty=False,\n    full_output=False,\n    gz=True,\n    separator_insertion=True\n)", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator |is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    \n", "signature": "(\n    obsl,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None\n)", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.
    \n\n
    Tags are not written or recovered automatically. The separator | is removed from the replica names.
    \n\n
    Parameters
    \n\n
      \n
    • obsl (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • name (str):\nThe name of the observable.
      • \n
    • spec (str):\nOptional string that describes the contents of the file.
      • \n
    • origin (str):\nSpecify where the data has its origin.
      • \n
    • symbol (list):\nA list of symbols that describe the observables to be written. May be empty.
      • \n
    • who (str):\nProvide the name of the person that exports the data.
      • \n
    • enstags (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.
      • \n
    • gz (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.
      • \n
    \n", "signature": "(\n    obsl,\n    fname,\n    name,\n    spec='dobs v1.0',\n    origin='',\n    symbol=[],\n    who=None,\n    enstags=None,\n    gz=True\n)", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "type": "module", "doc": "
    \n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "function", "doc": "
    Read hadrons meson hdf5 file and extract the meson labeled 'meson'
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • meson (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.
      • \n
    • gammas (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, meson='meson_0', idl=None, gammas=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "
    Read hadrons DistillationContraction hdf5 files in given directory structure
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the directories to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • diagrams (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, ens_id, diagrams=['direct'], idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "class", "doc": "
    ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)
    \n\n
    An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)
    \n\n
    Arrays should be constructed using array, zeros or empty (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (ndarray(...)) for instantiating an array.
    \n\n
    For more information, refer to the numpy module and examine the\nmethods and attributes of an array.
    \n\n
    Parameters
    \n\n
      \n
    • (for the __new__ method; see Notes below)
      • \n
    • shape (tuple of ints):\nShape of created array.
      • \n
    • dtype (data-type, optional):\nAny object that can be interpreted as a numpy data type.
      • \n
    • buffer (object exposing buffer interface, optional):\nUsed to fill the array with data.
      • \n
    • offset (int, optional):\nOffset of array data in buffer.
      • \n
    • strides (tuple of ints, optional):\nStrides of data in memory.
      • \n
    • order ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.
      • \n
    \n\n
    Attributes
    \n\n
      \n
    • T (ndarray):\nTranspose of the array.
      • \n
    • data (buffer):\nThe array's elements, in memory.
      • \n
    • dtype (dtype object):\nDescribes the format of the elements in the array.
      • \n
    • flags (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      • \n
    • flat (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., x.flat = 3 (See ndarray.flat for\nassignment examples; TODO).
      • \n
    • imag (ndarray):\nImaginary part of the array.
      • \n
    • real (ndarray):\nReal part of the array.
      • \n
    • size (int):\nNumber of elements in the array.
      • \n
    • itemsize (int):\nThe memory use of each array element in bytes.
      • \n
    • nbytes (int):\nThe total number of bytes required to store the array data,\ni.e., itemsize * size.
      • \n
    • ndim (int):\nThe array's number of dimensions.
      • \n
    • shape (tuple of ints):\nShape of the array.
      • \n
    • strides (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous (3, 4) array of type\nint16 in C-order has strides (8, 2).  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(2 * 4).
      • \n
    • ctypes (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.
      • \n
    • base (ndarray):\nIf the array is a view into another array, that array is its base\n(unless that array is also a view).  The base array is where the\narray data is actually stored.
      • \n
    \n\n
    See Also
    \n\n
    array:  Construct an array. 
    \nzeros:  Create an array, each element of which is zero. 
    \nempty:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\"). 
    \ndtype:  Create a data-type. 
    \nnumpy.typing.NDArray:  An ndarray alias :term:generic <generic type>\nw.r.t. its dtype.type <numpy.dtype.type>.  
    \n\n
    Notes
    \n\n
    There are two modes of creating an array using __new__:
    \n\n
      \n
    1. If buffer is None, then only shape, dtype, and order\nare used.
      2. \n
    2. If buffer is an object exposing the buffer interface, then\nall keywords are interpreted.
      3. \n
    \n\n
    No __init__ method is needed because the array is fully initialized\nafter the __new__ method.
    \n\n
    Examples
    \n\n
    These examples illustrate the low-level ndarray constructor.  Refer\nto the See Also section above for easier ways of constructing an\nndarray.
    \n\n
    First mode, buffer is None:
    \n\n
    >>> np.ndarray(shape=(2,2), dtype=float, order='F')\narray([[0.0e+000, 0.0e+000], # random\n       [     nan, 2.5e-323]])\n
    \n\n
    Second mode:
    \n\n
    >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n...            offset=np.int_().itemsize,\n...            dtype=int) # offset = 1*itemsize, i.e. skip first element\narray([2, 3])\n
    \n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "
    \n", "signature": "()", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "variable", "doc": "
    Gamma_5 hermitean conjugate
    \n\n
    Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.
    \n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "type": "function", "doc": "
    Read hadrons ExternalLeg hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "function", "doc": "
    Read hadrons Bilinear hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None)", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "function", "doc": "
    Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the files to read
      • \n
    • filestem (str):\nnamestem of the files to read
      • \n
    • ens_id (str):\nname of the ensemble, required for internal bookkeeping
      • \n
    • idl (range):\nIf specified only configurations in the given range are read in.
      • \n
    • vertices (list):\nVertex functions to be extracted.
      • \n
    \n", "signature": "(path, filestem, ens_id, idl=None, vertices=['VA', 'AV'])", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "type": "module", "doc": "
    \n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "type": "function", "doc": "
    Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    \n", "signature": "(ol, description='', indent=1)", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "
    Export a list of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • ol (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(ol, fname, description='', indent=1, gz=True)", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "
    Reconstruct a list of Obs or structures containing Obs from a json string.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • json_string (str):\njson string containing the data.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(json_string, verbose=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "function", "doc": "
    Import a list of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False)", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "
    Export a dict of Obs or structures containing Obs to a .json(.gz) file
    \n\n
    Parameters
    \n\n
      \n
    • od (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.
      • \n
    • fname (str):\nFilename of the output file.
      • \n
    • description (str):\nOptional string that describes the contents of the json file.
      • \n
    • indent (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.
      • \n
    • gz (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.
      • \n
    \n", "signature": "(od, fname, description='', indent=1, reps='DICTOBS', gz=True)", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "
    Import a dict of Obs or structures containing Obs from a .json(.gz) file.
    \n\n
    The following structures are supported: Obs, list, numpy.ndarray, Corr
    \n\n
    Parameters
    \n\n
      \n
    • fname (str):\nFilename of the input file.
      • \n
    • verbose (bool):\nPrint additional information that was written to the file.
      • \n
    • gz (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.
      • \n
    • full_output (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.
      • \n
    • reps (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.
      • \n
    \n", "signature": "(fname, verbose=True, gz=True, full_output=False, reps='DICTOBS')", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "type": "module", "doc": "
    \n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "
    Read pbp format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    \n", "signature": "(path, prefix, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "type": "module", "doc": "
    \n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "function", "doc": "
    Read rwms format from given folder structure. Returns a list of length nrw
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath that contains the data files
      • \n
    • prefix (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.
      • \n
    • version (str):\nversion of openQCD, default 2.0
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • postfix (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • print_err (bool):\nPrint additional information that is useful for debugging.
      • \n
    \n", "signature": "(path, prefix, version='2.0', names=None, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "
    Extract t0 from given .ms.dat files. Returns t0 as Obs.
    \n\n
    It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2 - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.
    \n\n
    It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\nPath to .ms.dat files
      • \n
    • prefix (str):\nEnsemble prefix
      • \n
    • dtr_read (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.
      • \n
    • xmin (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.
      • \n
    • spatial_extent (int):\nspatial extent of the lattice, required for normalization.
      • \n
    • fit_range (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • r_step (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.
      • \n
    • plaquette (bool):\nIf true extract the plaquette estimate of t0 instead.
      • \n
    • names (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!
      • \n
    • files (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.
      • \n
    • plot_fit (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.
      • \n
    • assume_thermalization (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference
      • \n
    \n", "signature": "(path, prefix, dtr_read, xmin, spatial_extent, fit_range=5, **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "
    Read the topologial charge based on openQCD gradient flow measurements.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nEither openQCD or sfqcd, depending on the data.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\nlist which contains the first config to be read for each replicum.
      • \n
    • r_stop (list):\nlist which contains the last config to be read for each replicum.
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    • integer_charge (bool):\nIf True, the charge is rounded towards the nearest integer on each config.
      • \n
    \n", "signature": "(path, prefix, c, dtr_cnfg=1, version='openQCD', **kwargs)", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "
    Returns the projection to the topological charge sector defined by target.
    \n\n
    Parameters
    \n\n
      \n
    • path (Obs):\nTopological charge.
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    \n", "signature": "(qtop, target=0)", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "
    Constructs reweighting factors to a specified topological sector.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath of the measurement files
      • \n
    • prefix (str):\nprefix of the measurement files, e.g. _id0_r0.ms.dat
      • \n
    • c (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L
      • \n
    • target (int):\nSpecifies the topological sector to be reweighted to (default 0)
      • \n
    • dtr_cnfg (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.
      • \n
    • steps (int):\n(optional) Distance between two configurations in units of trajectories /\ncycles. Assumed to be the distance between two measurements * dtr_cnfg if not given
      • \n
    • version (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.
      • \n
    • L (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header
      • \n
    • r_start (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs
      • \n
    • r_stop (list):\nlast configurations that need to be read (per replicum)
      • \n
    • files (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • Zeuthen_flow (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.
      • \n
    \n", "signature": "(path, prefix, c, target=0, **kwargs)", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "type": "module", "doc": "
    \n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "
    Read sfcf c format from given folder structure.
    \n\n
    Parameters
    \n\n
      \n
    • quarks (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version
      • \n
    • noffset (int):\nOffset of the source (only relevant when wavefunctions are used)
      • \n
    • wf (int):\nID of wave function
      • \n
    • wf2 (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)
      • \n
    • im (bool):\nif True, read imaginary instead of real part\nof the correlation function.
      • \n
    • corr_type (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types
      • \n
    • names (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length
      • \n
    • ens_name (str):\nreplaces the name of the ensemble
      • \n
    • version (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version
      • \n
    • cfg_separator (str):\nString that separates the ensemble identifier from the configuration number (default 'n').
      • \n
    • replica (list):\nlist of replica to be read, default is all
      • \n
    • files (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.
      • \n
    • check_configs:: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs
      • \n
    \n", "signature": "(\n    path,\n    prefix,\n    name,\n    quarks='.*',\n    corr_type='bi',\n    noffset=0,\n    wf=0,\n    wf2=0,\n    version='1.0c',\n    cfg_separator='n',\n    **kwargs\n)", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "
    Utilities for the input
    \n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "
    Checks if list of configurations is contained in an idl
    \n\n
    Parameters
    \n\n
      \n
    • idl (range or list):\nidl of the current replicum
      • \n
    • che (list):\nlist of configurations to be checked against
      • \n
    \n", "signature": "(idl, che)", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "type": "module", "doc": "
    \n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "function", "doc": "
    Matrix multiply all operands.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • This implementation is faster compared to standard multiplication via the @ operator.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "function", "doc": "
    Matrix multiply both operands making use of the jackknife approximation.
    \n\n
    Parameters
    \n\n
      \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    • For large matrices this is considerably faster compared to matmul.
      • \n
    \n", "signature": "(*operands)", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "function", "doc": "
    Wrapper for numpy.einsum
    \n\n
    Parameters
    \n\n
      \n
    • subscripts (str):\nSubscripts for summation (see numpy documentation for details)
      • \n
    • operands (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.
      • \n
    \n", "signature": "(subscripts, *operands)", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "
    Inverse of Obs or CObs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "
    Cholesky decomposition of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "
    Determinant of Obs valued matrices.
    \n", "signature": "(x)", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "
    Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "
    Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "
    Computes the Moore-Penrose pseudoinverse of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "
    Computes the singular value decomposition of a matrix of Obs.
    \n", "signature": "(obs, **kwargs)", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "type": "module", "doc": "
    \n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "function", "doc": "
    Dump object into pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • obj (object):\nobject to be saved in the pickle file
      • \n
    • name (str):\nname of the file
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(obj, name, **kwargs)", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "function", "doc": "
    Load object from pickle file.
    \n\n
    Parameters
    \n\n
      \n
    • path (str):\npath to the file
      • \n
    \n", "signature": "(path)", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "
    Generate an Obs object with given value, dvalue and name for test purposes
    \n\n
    Parameters
    \n\n
      \n
    • value (float):\ncentral value of the Obs to be generated.
      • \n
    • dvalue (float):\nerror of the Obs to be generated.
      • \n
    • name (str):\nname of the ensemble for which the Obs is to be generated.
      • \n
    • samples (int):\nnumber of samples for the Obs (default 1000).
      • \n
    \n", "signature": "(value, dvalue, name, samples=1000)", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "function", "doc": "
    Generate observables with given covariance and autocorrelation times.
    \n\n
    Parameters
    \n\n
      \n
    • means (list):\nlist containing the mean value of each observable.
      • \n
    • cov (numpy.ndarray):\ncovariance matrix for the data to be generated.
      • \n
    • name (str):\nensemble name for the data to be geneated.
      • \n
    • tau (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.
      • \n
    • samples (int):\nnumber of samples to be generated for each observable.
      • \n
    \n", "signature": "(means, cov, name, tau=0.5, samples=1000)", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "type": "module", "doc": "
    \n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "function", "doc": "
    Matrix pencil method to extract k energy levels from data
    \n\n
    Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)
    \n\n
    Parameters
    \n\n
      \n
    • data (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.
      • \n
    • k (int):\nNumber of states to extract (default 1).
      • \n
    • p (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).
      • \n
    \n", "signature": "(corrs, k=1, p=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "type": "module", "doc": "
    \n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "class", "doc": "
    Class for a general observable.
    \n\n
    Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.
    \n\n
    Attributes
    \n\n
      \n
    • S_global (float):\nStandard value for S (default 2.0)
      • \n
    • S_dict (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.
      • \n
    • tau_exp_global (float):\nStandard value for tau_exp (default 0.0)
      • \n
    • tau_exp_dict (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    • N_sigma_global (float):\nStandard value for N_sigma (default 1.0)
      • \n
    • N_sigma_dict (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.
      • \n
    \n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "type": "function", "doc": "
    Initialize Obs object.
    \n\n
    Parameters
    \n\n
      \n
    • samples (list):\nlist of numpy arrays containing the Monte Carlo samples
      • \n
    • names (list):\nlist of strings labeling the individual samples
      • \n
    • idl (list, optional):\nlist of ranges or lists on which the samples are defined
      • \n
    \n", "signature": "(self, samples, names, idl=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "
    \n", "default_value": " = 2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "
    \n", "default_value": " = 0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "
    \n", "default_value": " = 1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "
    \n", "default_value": " = {}"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "
    \n", "default_value": " = 1e-10"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "function", "doc": "
    Estimate the error and related properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • S (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.
      • \n
    • tau_exp (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).
      • \n
    • N_sigma (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).
      • \n
    • fft (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)
      • \n
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "function", "doc": "
    Output detailed properties of the Obs.
    \n\n
    Parameters
    \n\n
      \n
    • ens_content (bool):\nprint details about the ensembles and replica if true.
      • \n
    \n", "signature": "(self, ens_content=True)", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "type": "function", "doc": "
    Reweight the obs with given rewighting factors.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(self, rw)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "type": "function", "doc": "
    Checks whether the observable is zero within 'sigma' standard errors.
    \n\n
    Parameters
    \n\n
      \n
    • sigma (int):\nNumber of standard errors used for the check.
      • \n
    • Works only properly when the gamma method was run.
      • \n
    \n", "signature": "(self, sigma=1)", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "function", "doc": "
    Checks whether the observable is zero within a given tolerance.
    \n\n
    Parameters
    \n\n
      \n
    • atol (float):\nAbsolute tolerance (for details see numpy documentation).
      • \n
    \n", "signature": "(self, atol=1e-10)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "function", "doc": "
    Plot integrated autocorrelation time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "
    Plot normalized autocorrelation function time for each ensemble.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "
    Plot replica distribution for each ensemble with more than one replicum.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "function", "doc": "
    Plot derived Monte Carlo history for each ensemble
    \n\n
    Parameters
    \n\n
      \n
    • expand (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).
      • \n
    \n", "signature": "(self, expand=True)", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "function", "doc": "
    Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.
    \n\n
    Parameters
    \n\n
      \n
    • save (str):\nsaves the figure to a file named 'save' if.
      • \n
    \n", "signature": "(self, save=None)", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "
    Dump the Obs to a file 'name' of chosen format.
    \n\n
    Parameters
    \n\n
      \n
    • filename (str):\nname of the file to be saved.
      • \n
    • datatype (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"
      • \n
    • description (str):\nDescription for output file, only relevant for json.gz format.
      • \n
    • path (str):\nspecifies a custom path for the file (default '.')
      • \n
    \n", "signature": "(self, filename, datatype='json.gz', description='', **kwargs)", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "function", "doc": "
    Export jackknife samples from the Obs
    \n\n
    Returns
    \n\n
      \n
    • numpy.ndarray: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).
      • \n
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "class", "doc": "
    Class for a complex valued observable.
    \n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "type": "function", "doc": "
    \n", "signature": "(self, real, imag=0.0)", "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "
    \n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "
    Executes the gamma_method for the real and the imaginary part.
    \n", "signature": "(self, **kwargs)", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "
    Checks whether both real and imaginary part are zero within machine precision.
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "
    \n", "signature": "(self)", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "function", "doc": "
    Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.
    \n\n
    Parameters
    \n\n
      \n
    • func (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').
      • \n
    • data (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • num_grad (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.
      • \n
    • man_grad (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.
      • \n
    \n\n
    Notes
    \n\n
    For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use
    \n\n
    new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])
    \n", "signature": "(func, data, array_mode=False, **kwargs)", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "function", "doc": "
    Reweight a list of observables.
    \n\n
    Parameters
    \n\n
      \n
    • weight (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.
      • \n
    • obs (list):\nlist of Obs, e.g. [obs1, obs2, obs3].
      • \n
    • all_configs (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.
      • \n
    \n", "signature": "(weight, obs, **kwargs)", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "function", "doc": "
    Correlate two observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs_a (Obs):\nFirst observable
      • \n
    • obs_b (Obs):\nSecond observable
      • \n
    \n\n
    Notes
    \n\n
    Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).
    \n", "signature": "(obs_a, obs_b)", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "
    Calculates the error covariance matrix of a set of observables.
    \n\n
    The gamma method has to be applied first to all observables.
    \n\n
    Parameters
    \n\n
      \n
    • obs (list or numpy.ndarray):\nList or one dimensional array of Obs
      • \n
    • visualize (bool):\nIf True plots the corresponding normalized correlation matrix (default False).
      • \n
    • correlation (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).
      • \n
    • smooth (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.
      • \n
    \n\n
    Notes
    \n\n
    The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).
    \n", "signature": "(obs, visualize=False, correlation=False, smooth=None, **kwargs)", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "function", "doc": "
    Imports jackknife samples and returns an Obs
    \n\n
    Parameters
    \n\n
      \n
    • jacks (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.
      • \n
    • name (str):\nname of the ensemble the samples are defined on.
      • \n
    \n", "signature": "(jacks, name, idl=None)", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "
    Combine all observables in list_of_obs into one new observable
    \n\n
    Parameters
    \n\n
      \n
    • list_of_obs (list):\nlist of the Obs object to be combined
      • \n
    \n\n
    Notes
    \n\n
    It is not possible to combine obs which are based on the same replicum
    \n", "signature": "(list_of_obs)", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "function", "doc": "
    Create an Obs based on mean(s) and a covariance matrix
    \n\n
    Parameters
    \n\n
      \n
    • mean (list of floats or float):\nN mean value(s) of the new Obs
      • \n
    • cov (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance
      • \n
    • name (str):\nidentifier for the covariance matrix
      • \n
    • grad (list or array):\nGradient of the Covobs wrt. the means belonging to cov.
      • \n
    \n", "signature": "(means, cov, name, grad=None)", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "type": "module", "doc": "
    \n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "function", "doc": "
    Finds the root of the function func(x, d) where d is an Obs.
    \n\n
    Parameters
    \n\n
      \n
    • d (Obs):\nObs passed to the function.
      • \n
    • func (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\npython\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n
      • \n
    • guess (float):\nInitial guess for the minimization.
      • \n
    \n\n
    Returns
    \n\n
      \n
    • Obs: Obs valued root of the function.
      • \n
    \n", "signature": "(d, func, guess=1.0, **kwargs)", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "
    \n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 7922}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 108}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 10, "bases": 0, "doc": 94}, "pyerrors.correlators.Corr.reweighted": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr.gamma_method": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 4, "bases": 0, "doc": 13}, "pyerrors.correlators.Corr.projected": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 11, "bases": 0, "doc": 64}, "pyerrors.correlators.Corr.item": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 5, "bases": 0, "doc": 53}, "pyerrors.correlators.Corr.plottable": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 31}, "pyerrors.correlators.Corr.symmetric": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 9}, "pyerrors.correlators.Corr.anti_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.matrix_symmetric": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, "signature": 3, "bases": 0, "doc": 10}, "pyerrors.correlators.Corr.GEVP": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, "signature": 9, "bases": 0, "doc": 324}, "pyerrors.correlators.Corr.Eigenvalue": {"qualname": 2, "fullname": 4, "annotation": 0, "default_value": 0, 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