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. Some of its features are:

• automatic differentiation as suggested in arXiv:1809.01289 (partly based on the autograd package)
• the treatment of slow modes in the simulation as suggested in arXiv: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) 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
• Julia
• Python 3

Installation

pyerrors requires python versions >= 3.5.0

Install the package for the local user:

pip install . --user

Run tests to verify the installation:

pytest .

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.

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

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
• 02_correlators
• 03_pcac_example
• 04_fit_example
• 05_matrix_operations

License

MIT