LombScargle.jl

Introduction

LombScargle.jl is a package for a fast multi-threaded estimation of the frequency spectrum of a periodic signal with the Lomb–Scargle periodogram. This is written in Julia, a modern high-level, high-performance dynamic programming language designed for technical computing.

Another Julia package that provides tools to perform spectral analysis of signals is DSP.jl, but its methods require that the signal has been sampled at equally spaced times. Instead, the Lomb–Scargle periodogram enables you to analyze unevenly sampled data as well, which is a fairly common case in astronomy, a field where this periodogram is widely used.

The algorithms used in this package are reported in the following papers:

Other relevant papers are:

The package provides facilities to:

• compute the periodogram using different methods (with different speeds) and different normalizations. This is one of the fastest implementations of these methods available as free software. If Julia is run with more than one thread, computation is automatically multi-threaded, further speeding up calculations;
• access the frequency and period grid of the resulting periodogram, together with the power spectrum;
• find the maximum power in the periodogram and the frequency and period corresponding to the peak. All these queries can be restricted to a specified region, in order to search a local maximum, instead of the global one;
• calculate the probability that a peak arises from noise only (false-alarm probability) using analytic formulas, in order to assess the significance of the peak;
• perform bootstrap resamplings in order to compute the false-alarm probability with a statistical method;
• determine the best-fitting Lomb–Scargle model for the given data set at the given frequency.

Contents

• LombScargle.jl
• • Introduction
  • Contents
  • Installation
  • Performance
  • Development
  • • History
  • License
  • • Acknowledgements
  • References

Installation

LombScargle.jl is available for Julia 1.0 and later versions, and can be installed with Julia's built-in package manager. In a Julia session run the commands

julia> import Pkg
julia> Pkg.add("LombScargle")

Older versions are also available for Julia 0.4-0.6.

For instructions on using the package, please see the Usage page.

Performance

A pre-planned periodogram in LombScargle.jl computed in single thread mode with the fast method is more than 2 times faster than the implementation of the same algorithm provided by AstroPy, and more than 4 times faster if 4 FFTW threads are used (on machines with at least 4 physical CPUs).

The following plot shows a comparison between the times needed to compute a periodogram for a signal with N datapoints using LombScargle.jl, with 1 or 4 FFTW threads (with flags = FFTW.MEASURE for better performance), and the single-threaded Astropy implementation. (Julia version: 1.6.0; LombScargle.jl version: 1.0.0; Python version: 3.8.6; Astropy version: 4.1. CPU: Intel(R) Core(TM) i7-4870HQ CPU @ 2.50GHz.)

Note that this comparison is unfair, as Astropy doesn’t support pre-planning a periodogram nor multi-threading, and it pads vectors for FFT to a length which is a power of 2, while by default LombScargle.jl uses length which are multiples of 2, 3, 5, 7. A non-planned periodogram in single thread mode in LombScargle.jl is still twice as fast as Astropy.

Development

The package is developed at https://github.com/JuliaAstro/LombScargle.jl. There you can submit bug reports, make suggestions, and propose pull requests.

History

The ChangeLog of the package is available in NEWS.md file in top directory.

License

The LombScargle.jl package is licensed under the BSD 3-clause "New" or "Revised" License. The original author is Mosè Giordano.

Acknowledgements

This package adapts the implementation in Astropy of the the fast Lomb–Scargle method by Press and Rybicki (1989). We claim no endorsement nor promotion by the Astropy Team.

References