From 773fd8e4c5ad557b4364a8dd7b27aca406cbccb9 Mon Sep 17 00:00:00 2001 From: Fabian Joswig Date: Thu, 23 Dec 2021 16:42:53 +0100 Subject: [PATCH] docs: documentation of Corr objects added --- pyerrors/__init__.py | 50 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 50 insertions(+) diff --git a/pyerrors/__init__.py b/pyerrors/__init__.py index 9c427818..856b5178 100644 --- a/pyerrors/__init__.py +++ b/pyerrors/__init__.py @@ -193,6 +193,56 @@ Make sure to check the autocorrelation time with e.g. `pyerrors.obs.Obs.plot_rho For the full API see `pyerrors.obs.Obs`. # Correlators +When one is not interested in single observables but correlation functions, `pyerrors` offers the `Corr` class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a `Corr` objects one needs to arrange the data as a list of `Obs´ +```python +my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3]) +print(my_corr) +> x0/a Corr(x0/a) +> ------------------ +> 0 0.7957(80) +> 1 0.5156(51) +> 2 0.3227(33) +> 3 0.2041(21) +``` +In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced. +```python +my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding_front=1, padding_back=1) +print(my_corr) +> x0/a Corr(x0/a) +> ------------------ +> 0 +> 1 0.7957(80) +> 2 0.5156(51) +> 3 0.3227(33) +> 4 0.2041(21) +> 5 +``` +The individual entries of a correlator can be accessed via slicing +```python +print(my_corr[3]) +> 0.3227(33) +``` +Error propagation with the `Corr` class works very similar to `Obs` objects. Mathematical operations are overloaded and `Corr` objects can be computed together with other `Corr` objects, `Obs` objects or real numbers and integers. +```python +my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr +``` + +`pyerrors` provides the user with a set of regularly used methods for the manipulation of correlator objects: +- `Corr.gamma_method` applies the gamma method to all entries of the correlator. +- `Corr.m_eff` to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available. +- `Corr.deriv` returns the first derivative of the correlator as `Corr`. Different discretizations of the numerical derivative are available. +- `Corr.second_deriv` returns the second derivative of the correlator as `Corr`. Different discretizations of the numerical derivative are available. +- `Corr.symmetric` symmetrizes parity even correlations functions, assuming periodic boundary conditions. +- `Corr.anti_symmetric` anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions. +- `Corr.T_symmetry` averages a correlator with its time symmetry partner, assuming fixed boundary conditions. +- `Corr.plateau` extracts a plateau value from the correlator in a given range. +- `Corr.roll` periodically shifts the correlator. +- `Corr.reverse` reverses the time ordering of the correlator. +- `Corr.correlate` constructs a disconnected correlation function from the correlator and another `Corr` or `Obs` object. +- `Corr.reweight` reweights the correlator. + +`pyerrors` can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see `pyerrors.correlators.Corr.GEVP). + For the full API see `pyerrors.correlators.Corr`. # Complex observables