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pyerrors/__init__.py
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@ -21,13 +21,50 @@ my_new_obs.details()
print(my_new_obs)
```
# The `Obs` class
`pyerrors.obs.Obs`
`pyerrors` introduces a new datatype, `Obs`, which simplifies error propagation and estimation for auto- and cross-correlated data.
An `Obs` object can be initialized with two arguments, the first is a list containining the samples for an Observable from a Monte Carlo chain.
The samples can either be provided as python list or as numpy array.
The 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.
Example:
```python
import pyerrors as pe
my_obs = pe.Obs([samples], ['ensemble_name'])
```
## Error propagation
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.
Example:
```python
import numpy as np
import pyerrors as pe
my_obs1 = pe.Obs([samples1], ['ensemble_name'])
my_obs2 = pe.Obs([samples2], ['ensemble_name'])
my_sum = my_obs1 + my_obs2
my_m_eff = np.log(my_obs1 / my_obs2)
```
## Error estimation
The error propagation is based on the gamma method introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).
For the full API see `pyerrors.obs.Obs.gamma_method`
### Exponential tails
## Multiple ensembles/replica
Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handeled automatically. Ensembles are uniquely identified by their `name`.
@ -78,40 +115,18 @@ obs3 = pe.Obs([samples3], ['ensemble1'], idl=[[2, 9, 28, 29, 501]])
**Warning:** Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.
Make sure to check the with e.g. `pyerrors.obs.Obs.plot_rho` or `pyerrors.obs.Obs.plot_tauint`.
# Error propagation
Automatic differentiation, [arXiv:1809.01289](https://arxiv.org/abs/1809.01289)
numpy overloaded
```python
import numpy as np
import pyerrors as pe
my_obs = pe.Obs([samples], ['ensemble_name'])
my_new_obs = 2 * np.log(my_obs) / my_obs
my_new_obs.gamma_method()
my_new_obs.details()
```
# Error estimation
`pyerrors.obs.Obs.gamma_method`
$\delta_i\delta_j$
## Exponential tails
## Covariance
For the full API see `pyerrors.obs.Obs`
# Correlators
`pyerrors.correlators.Corr`
For the full API see `pyerrors.correlators.Corr`
# Complex observables
`pyerrors.obs.CObs`
# Optimization / fits / roots
`pyerrors.fits`
`pyerrors.roots`
# Complex observables
`pyerrors.obs.CObs`
# Matrix operations
`pyerrors.linalg`