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Merge branch 'develop' into documentation

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fjosw 2021-11-16 11:50:15 +00:00
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pyerrors/__init__.py
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@ -14,10 +14,10 @@ It is based on the **gamma method** [arXiv:hep-lat/0306017](https://arxiv.org/ab
import numpy as np
import pyerrors as pe
my_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object with Monte Carlo samples
my_obs = pe.Obs([samples], ['ensemble_name']) # Initialize an Obs object
my_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object
my_new_obs.gamma_method() # Estimate the error with the gamma_method
print(my_new_obs) # Print the result to stdout
my_new_obs.gamma_method() # Estimate the statistical error
print(my_new_obs) # Print the result to stdout
> 0.31498(72)
```
@ -40,7 +40,6 @@ my_obs = pe.Obs([samples], ['ensemble_name'])
When performing mathematical operations on `Obs` objects the correct error propagation is intrinsically taken care using a first order Taylor expansion
$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$
as introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).
The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).
The `Obs` class is designed such that mathematical numpy functions can be used on `Obs` just as for regular floats.