GitHub

PicardLefschetzIntegration

Documentation for PicardLefschetzIntegration. This package numerically evaluates multidimensional oscillatory integrals of the form

\[I = \int e^{i f(\bm{x})}\mathrm{d}\bm{x}\,,\]

for meromorphic functions $f$ using Picard Lefschetz theory. We deform the original integration domain in the complex plane onto the Lefschetz thimbles and numerically evaluate the integral.

Installation

The PicardLefschetzIntegration package can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add PicardLefschetzIntegration

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("PicardLefschetzIntegration")

Usage

Please have a look at the Tutorial page for details on how to use this package.

Citation

When using this package, please cite the paper Oscillatory path integrals for radio astronomy (2023) by Feldbrugge, Pen and Turok and the Zenodo link DOI:10.5281/zenodo.20683184. You can use the BibTeX entries

@ARTICLE{2023AnPhy.45169255F,
       author = {{Feldbrugge}, Job and {Pen}, Ue-Li and {Turok}, Neil},
        title = "{Oscillatory path integrals for radio astronomy}",
      journal = {Annals of Physics},
     keywords = {Interference, Lensing, Wave optics, Kirchhoff-Fresnel integral},
         year = 2023,
        month = apr,
       volume = {451},
          eid = {169255},
        pages = {169255},
          doi = {10.1016/j.aop.2023.169255},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2023AnPhy.45169255F},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@software{job_feldbrugge_2026_20683184,
  author       = {Job Feldbrugge},
  title        = {jfeldbrugge/PicardLefschetzIntegration.jl:
                   PicardLefschetzIntegration.jl
                  },
  month        = jun,
  year         = 2026,
  publisher    = {Zenodo},
  version      = {v1.0.0},
  doi          = {10.5281/zenodo.20683184},
  url          = {https://doi.org/10.5281/zenodo.20683184},
  swhid        = {swh:1:dir:fc800cc333cbf38115cf7296b244a966216bc821
                   ;origin=https://doi.org/10.5281/zenodo.20683183;vi
                   sit=swh:1:snp:76f139f585a46656e9c20b2ea6fb9f47b39c
                   a968;anchor=swh:1:rel:9d817d5fe15ec8731bb7ced50c6d
                   46e824306ad4;path=jfeldbrugge-
                   PicardLefschetzIntegration.jl-ec297a8
                  },
}

Contributors

This code was written by:

Related packages for the evaluation of oscillatory integrals in the complex plane include