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pyerrors/__init__.py
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# What is pyerrors? # What is 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 for exact liner error propagation 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 for exact linear error propagation 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). - 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. - 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](https://arxiv.org/abs/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](https://arxiv.org/abs/1809.01289).
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# Error propagation in iterative algorithms # Error propagation in iterative algorithms
`pyerrors` supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures fits or root finding. The derivatives required for the error propagation are calculated as described in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289). `pyerrors` supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).
## Least squares fits ## Least squares fits
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Direct visualizations of the performed fits can be triggered via `resplot=True` or `qqplot=True`. For all available options see `pyerrors.fits.least_squares`. Direct visualizations of the performed fits can be triggered via `resplot=True` or `qqplot=True`. For all available options see `pyerrors.fits.least_squares`.
## Total least squares fits ## Total least squares fits
`pyerrors` can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in [scipy](https://docs.scipy.org/doc/scipy/reference/odr.html), see `pyerrors.fits.least_squares`. The syntax is identical to the standard least squares case, the only diffrence being that `x` also has to be a `list` or `numpy.array` of `Obs`. `pyerrors` can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in [scipy](https://docs.scipy.org/doc/scipy/reference/odr.html), see `pyerrors.fits.least_squares`. The syntax is identical to the standard least squares case, the only difference being that `x` also has to be a `list` or `numpy.array` of `Obs`.
For the full API see `pyerrors.fits` for fits and `pyerrors.roots` for finding roots of functions. For the full API see `pyerrors.fits` for fits and `pyerrors.roots` for finding roots of functions.