diff --git a/pyerrors/__init__.py b/pyerrors/__init__.py index 74f87b14..d121f1f5 100644 --- a/pyerrors/__init__.py +++ b/pyerrors/__init__.py @@ -61,9 +61,41 @@ my_m_eff = np.log(my_obs1 / my_obs2) The error propagation is based on the gamma method introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017). +After having arrived at + +Example: +```python +my_sum.gamma_method() +my_sum.details() +``` + +The standard value for the automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the `gamma_method` as parameter. + +Example: +```python +my_sum.gamma_method(S=3.0) +my_sum.details() +``` + +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`. + +Example: +```python +my_sum.plot_tauint() +my_sum.plot_rho() +``` + +### Exponential tails + +Slow modes in the Monte Carlo history can be accounted for by attaching and exponntial tail to the autocorrelation function $\rho$ as suggested in [arXiv:1009.5228](https://arxiv.org/abs/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. + +Example: +```python +my_sum.gamma_method(tau_exp=4.2) +my_sum.details() +``` For the full API see `pyerrors.obs.Obs.gamma_method` -### Exponential tails ## Multiple ensembles/replica @@ -97,6 +129,18 @@ obs2 = pe.Obs([samples2], ['ensemble1|r02']) > · Replicum 'r01' : 1000 configurations (from 1 to 1000) > · Replicum 'r02' : 500 configurations (from 1 to 500) ``` + +### Error estimation for multiple ensembles + +In order to keep track of different error analyis parameters for different ensembles one can make use of global dictionaries as detailed in the following example. + +Example: +```python +pe.Obs.S_dict['ensemble1'] = 2.5 +pe.Obs.tau_exp_dict['ensemble2'] = 8.0 +pe.Obs.tau_exp_dict['ensemble3'] = 2.0 +``` + ## Irregular Monte Carlo chains Irregular Monte Carlo chains can be initilized with the parameter `idl`.