[![flake8 Lint](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-3.5+-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) * the treatment of slow modes in the simulation as suggested in [arXiv:1009.5228](https://arxiv.org/abs/1009.5228) * multi ensemble analyses * non-linear fits with y-errors and exact linear error propagation based on automatic differentiation as introduced in [arXiv:1809.01289] * non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation * matrix valued operations and their error propagation based on automatic differentiation (cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...) * implementation of the matrix-pencil-method [IEEE Trans. Acoust. 38, 814-824 (1990)](https://ieeexplore.ieee.org/document/56027) for the extraction of energy levels, especially suited for noisy data and excited states 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 Install the package for the local user: ```bash pip install . --user ``` ## 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 numpy as np 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 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/)