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# 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
`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]
* **matrix valued 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)