[![flake8](https://github.com/fjosw/pyerrors/actions/workflows/flake8.yml/badge.svg)](https://github.com/fjosw/pyerrors/actions/workflows/flake8.yml) [![CI](https://github.com/fjosw/pyerrors/actions/workflows/CI.yml/badge.svg)](https://github.com/fjosw/pyerrors/actions/workflows/CI.yml) [![](https://img.shields.io/badge/python-3.6+-blue.svg)](https://www.python.org/downloads/) # pyerrors `pyerrors` is a python package for error computation and propagation of Markov chain Monte Carlo data. It is based on the **gamma method** [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017). Some of its features are: * **automatic differentiation** as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289) (partly based on the [autograd](https://github.com/HIPS/autograd) package) * **treatment of slow modes** in the simulation as suggested in [arXiv:1009.5228](https://arxiv.org/abs/1009.5228) * coherent **error propagation** for data from **different Markov chains** * **non-linear fits with x- and y-errors** and exact linear error propagation based on automatic differentiation as introduced in [arXiv:1809.01289] * **real and complex matrix operations** and their error propagation based on automatic differentiation (cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...) There exist similar implementations of gamma method error analysis suites in - [Fortran](https://gitlab.ift.uam-csic.es/alberto/aderrors) - [Julia](https://gitlab.ift.uam-csic.es/alberto/aderrors.jl) - [Python 3](https://github.com/mbruno46/pyobs) ## Installation To install the most recent release of `pyerrors` run ```bash pip install git+https://github.com/fjosw/pyerrors.git ``` ## Usage The basic objects of a pyerrors analysis are instances of the class `Obs`. They can be initialized with an array of Monte Carlo data (e.g. `samples1`) and a name for the given ensemble (e.g. `'ensemble1'`). The `gamma_method` can then be used to compute the statistical error, taking into account autocorrelations. The `print` method outputs a human readable result. ```python import pyerrors as pe obs1 = pe.Obs([samples1], ['ensemble1']) obs1.gamma_method() obs1.print() ``` Often one is interested in secondary observables which can be arbitrary functions of primary observables. `pyerrors` overloads most basic math operations and `numpy` functions such that the user can work with `Obs` objects as if they were floats ```python import numpy as np obs3 = 12.0 / obs1 ** 2 - np.exp(-1.0 / obs2) obs3.gamma_method() obs3.print() ``` More detailed examples can be found in the `examples` folder: * [01_basic_example](examples/01_basic_example.ipynb) * [02_correlators](examples/02_correlators.ipynb) * [03_pcac_example](examples/03_pcac_example.ipynb) * [04_fit_example](examples/04_fit_example.ipynb) * [05_matrix_operations](examples/05_matrix_operations.ipynb) ## License [MIT](https://choosealicense.com/licenses/mit/)