diff --git a/pyerrors/__init__.py b/pyerrors/__init__.py index a91b3e11..22efa8f4 100644 --- a/pyerrors/__init__.py +++ b/pyerrors/__init__.py @@ -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.