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[![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/) [![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
pyerrors is a python package for error computation and propagation of Markov Chain Monte Carlo data. `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: 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) * **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) * **treatment of slow modes** in the simulation as suggested in [arXiv:1009.5228](https://arxiv.org/abs/1009.5228)
* multi ensemble analyses * coherent **error propagation** for data from **different Markov chains**
* 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 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...)
* 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 There exist similar implementations of gamma method error analysis suites in
- [Fortran](https://gitlab.ift.uam-csic.es/alberto/aderrors) - [Fortran](https://gitlab.ift.uam-csic.es/alberto/aderrors)