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57 lines
2.8 KiB
Markdown
57 lines
2.8 KiB
Markdown
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# pyerrors
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pyerrors is a python package for error computation and propagation of Markov Chain Monte Carlo data.
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It is based on the gamma method [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017). Some of its features are:
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* 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)
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* the treatment of slow modes in the simulation as suggested in [arXiv:1009.5228](https://arxiv.org/abs/1009.5228)
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* multi ensemble analyses
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* non-linear fits with y-errors and exact linear error propagation based on automatic differentiation as introduced in [arXiv:1809.01289]
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* non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation
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* matrix valued operations and their error propagation based on automatic differentiation (cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...)
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* 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
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There exist similar implementations of gamma method error analysis suites in
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- [Fortran](https://gitlab.ift.uam-csic.es/alberto/aderrors).
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- [Julia](https://gitlab.ift.uam-csic.es/alberto/aderrors.jl)
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- [Python 3](https://github.com/mbruno46/pyobs)
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## Installation
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pyerrors requires python versions >= 3.5.0
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Install the package for the local user:
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```bash
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pip install . --user
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```
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Run tests to verify the installation:
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```bash
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pytest .
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```
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## Usage
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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.
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```python
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import numpy as np
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import pyerrors as pe
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observable1 = pe.Obs([samples1], ['ensemble1'])
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observable1.gamma_method()
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observable1.print()
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```
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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
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```python
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observable3 = 12.0 / observable1 ** 2 - np.exp(-1.0 / observable2)
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observable3.gamma_method()
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observable3.print()
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```
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More detailed examples can be found in the `/examples` folder:
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* [01_basic_example](examples/01_basic_example.ipynb)
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* [02_pcac_example](examples/02_pcac_example.ipynb)
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* [03_fit_example](examples/03_fit_example.ipynb)
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* [04_matrix_operations](examples/04_matrix_operations.ipynb)
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## License
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[MIT](https://choosealicense.com/licenses/mit/)
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