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docs: gamma_method explanation extended

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Fabian Joswig 2021-11-15 10:42:34 +00:00
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pyerrors/__init__.py
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@ -67,6 +67,10 @@ Example:
```python
my_sum.gamma_method()
my_sum.details()
> Result 1.70000000e+00 +/- 3.89934513e+00 +/- 5.84901770e-01 (229.373%)
> t_int 3.72133617e+00 +/- 9.81032454e-01 S = 2.00
> 1000 samples in 1 ensemble:
> · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
```
The standard value for the automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the `gamma_method` as parameter.
@ -75,6 +79,11 @@ Example:
```python
my_sum.gamma_method(S=3.0)
my_sum.details()
> Result 1.70000000e+00 +/- 3.77151850e+00 +/- 6.47779576e-01 (221.854%)
> t_int 3.48135280e+00 +/- 1.06547679e+00 S = 3.00
> 1000 samples in 1 ensemble:
> · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
```
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`.
@ -91,8 +100,12 @@ Slow modes in the Monte Carlo history can be accounted for by attaching and expo
Example:
```python
my_sum.gamma_method(tau_exp=4.2)
my_sum.gamma_method(tau_exp=7.2)
my_sum.details()
> Result 1.70000000e+00 +/- 3.77806247e+00 +/- 3.48320149e-01 (222.239%)
> t_int 3.49344429e+00 +/- 7.62747210e-01 tau_exp = 7.20, N_sigma = 1
> 1000 samples in 1 ensemble:
> · Ensemble 'ensemble_name' : 1000 configurations (from 1 to 1000)
```
For the full API see `pyerrors.obs.Obs.gamma_method`
@ -141,6 +154,10 @@ pe.Obs.tau_exp_dict['ensemble2'] = 8.0
pe.Obs.tau_exp_dict['ensemble3'] = 2.0
```
In case the `gamma_method` is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.
Passing arguments to the `gamma_method` still dominates over the dictionaries.
## Irregular Monte Carlo chains
Irregular Monte Carlo chains can be initilized with the parameter `idl`.