A python library for calculating Allan deviation and related time & frequency statistics. LGPL v3+ license.

• Development at https://github.com/aewallin/allantools
• Installation package at https://pypi.python.org/pypi/AllanTools
• Discussion group at https://groups.google.com/d/forum/allantools
• Documentation available at https://allantools.readthedocs.org

Input data should be evenly spaced observations of either fractional frequency, or phase in seconds. Deviations are calculated for given tau values in seconds.

Parallel accelerated versions are also available for improved performance on large datasets:

Noise generators for creating synthetic datasets are also included:

• violet noise with f^2 PSD
• white noise with f^0 PSD
• pink noise with f^-1 PSD
• Brownian or random walk noise with f^-2 PSD

More details on available statistics and noise generators : full list of available functions

see /tests for tests that compare allantools output to other (e.g. Stable32) programs. More test data, benchmarks, ipython notebooks, and comparisons to known-good algorithms are welcome!

Install from pypi:

pip install allantools

Latest version + examples, tests, test data, iPython notebooks : clone from github, then from the cloned repository install

pip install .

(see pip install -h for install options)

These commands should be run as root for system-wide installation, or you can use the --user option to install for your account only. Exact command names may vary depending on your OS / package manager / target python version. If command pip is not available or does not install the package in the expected python version, python -m pip install . is equivalent.

We can call allantools with only one parameter - an array of phase data. This is suitable for time-interval measurements at 1 Hz, for example from a time-interval-counter measuring the 1PPS output of two clocks.

>>> import allantools
>>> x = allantools.noise.white(10000)        # Generate some phase data, in seconds.
>>> (taus, adevs, errors, ns) = allantools.oadev(x)

when only one input parameter is given, phase data in seconds is assumed when no rate parameter is given, rate=1.0 is the default when no taus parameter is given, taus='octave' is the default

Note that allantools assumes non-dimensional frequency data input. Normalization, by e.g. dividing all data points with the average frequency, is left to the user.

>>> import allantools
>>> import pylab as plt
>>> import numpy as np
>>> t = np.logspace(0, 3, 50)  # tau values from 1 to 1000
>>> y = allantools.noise.white(10000)  # Generate some frequency data
>>> r = 12.3  # sample rate in Hz of the input data
>>> (t2, ad, ade, adn) = allantools.oadev(y, rate=r, data_type="freq", taus=t)  # Compute the overlapping ADEV
>>> fig = plt.loglog(t2, ad) # Plot the results
>>> # plt.show()

New in 2016.11 : simple top-level API, using dedicated classes for data handling and plotting.

import allantools # https://github.com/aewallin/allantools/
import numpy as np

# Compute a deviation using the Dataset class
a = allantools.Dataset(data=np.random.rand(1000))
a.compute("mdev")

# New in 2019.7 : write results to file
a.write_results("output.dat")

# Plot it using the Plot class
b = allantools.Plot()
# New in 2019.7 : additional keyword arguments are passed to
# matplotlib.pyplot.plot()
b.plot(a, errorbars=True, grid=True)
# You can override defaults before "show" if needed
b.ax.set_xlabel("Tau (s)")
b.show()

For large datasets, parallel accelerated versions can provide significant performance improvements:

import allantools
import numpy as np

# Generate large dataset
data = np.random.rand(1000000)
rate = 100.0

# Use parallel version with parallel=True
from allantools.allantools_parallel import poadev
taus, devs, errs, ns = poadev(data, rate=rate, taus="octave", parallel=True)

# Or use default serial execution
taus, devs, errs, ns = poadev(data, rate=rate, taus="octave", parallel=False)

Parallel functions automatically fall back to serial execution for small datasets where parallelization overhead would exceed benefits. All parallel functions have the same API as their original counterparts.

Available parallel functions: padev, poadev, pmdev, ptdev, phdev, pohdev, ppdev, pgradev, pgcodev.

Jupyter notebooks are interactive python scripts, embedded in a browser, allowing you to manipulate data and display plots like easily. For guidance on installing jupyter, please refer to https://jupyter.org/install.

See /examples for some examples in notebook format.

github formats the notebooks into nice web-pages, for example

• https://github.com/aewallin/allantools/blob/master/examples/noise-color-demo.ipynb
• https://github.com/aewallin/allantools/blob/master/examples/three-cornered-hat-demo.ipynb

• Anders E.E. Wallin, anders.e.e.wallin "at" gmail.com , https://github.com/aewallin
• Danny Price, https://github.com/telegraphic
• Cantwell G. Carson, carsonc "at" gmail.com
• Frédéric Meynadier, https://github.com/fmeynadier
• Yan Xie, https://github.com/yxie-git
• Erik Benkler, https://github.com/EBenkler