Code for the paper: visualizing the wavenumber content of a point pattern

To run the code, follow these steps:

1. Clone this repository
2. Open Julia and navigate to the repository (install Julia if necessary)
3. Activate the project and instantiate the packages to the correct version by running

   import Pkg
   Pkg.activate(".")
   Pkg.instantiate()

4. Build RCall if not done previously

   Pkg.build("RCall")

5. Run the file

See the Julia documentation for more details on environments.

Files

• Fig1_introexample.jl: Figure 1, a Thomas process example.
• Fig2_lgcp.jl: Figure 2, a log-Gaussian Cox process example.
• Fig3_lansingwoods.jl: Figure 3, analysis of the Lansing Woods data.
• Fig4_impulseresponse.jl: Figure 4, the impulse responses for certain regions.

Additional code

The folder src contains a minimal implementation of the isotropic spectral estimation method proposed by Rajala et al. (2023).

Note on R

Part of the simulation and the Lansing Woods data require the R package spatstat. Note that R and its packages are not version controlled by the Julia environment. For convenience, we provide the file session_info.jl which can be run from Julia to print the version of R and spatstat which is installed. A summary of the package versions we used is given below (this is the relevant subset of the output from running sessionInfo(), not the complete output)

R version 4.3.0 (2023-04-21)
Platform: x86_64-apple-darwin20 (64-bit)
Running under: macOS Ventura 13.3.1

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] spatstat_3.0-6         spatstat.linnet_3.1-1  spatstat.model_3.2-4  
[4] rpart_4.1.19           spatstat.explore_3.2-1 nlme_3.1-162          
[7] spatstat.random_3.1-5  spatstat.geom_3.2-1    spatstat.data_3.0-1   

loaded via a namespace (and not attached):
 [1] mgcv_1.8-42           Matrix_1.5-4          lattice_0.21-8       
 [4] splines_4.3.0         abind_1.4-5           polyclip_1.10-4      
 [7] deldir_1.0-9          goftest_1.2-3         spatstat.sparse_3.0-1
[10] grid_4.3.0            compiler_4.3.0        spatstat.utils_3.0-3 
[13] tensor_1.5

General implementation

Note that the methodology of the paper is in the package PointProcessFilters.jl

References

• Grainger, J. P., Rajala, T. A., Murrell, D. J., & Olhede, S. C. (2023). Visualizing the Wavenumber Content of a Point Pattern. arXiv preprint arXiv:2306.04198.
• T. A. Rajala, S. C. Olhede, J. P. Grainger, and D. J. Murrell, "What is the Fourier transform of a spatial point process?" IEEE Transactions on Information Theory, 2023.
• Jake P. Grainger. (2023). "SDS-EPFL/PointProcessFilters.jl: v0.1.0 (v0.1.0)." Zenodo. https://doi.org/10.5281/zenodo.8252035