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Healpix

Healpix.jl is a set of Julia functions that implement the HEALPix algorithms to pixelate a 2-sphere. The HEALPix pixelisation has a number of features that make it efficient for the following tasks:

• All pixels have the same area (equal-area pixelisation);
• It is efficient to compute the Fourier decomposition in spherical harmonics of a discretized signal on the sphere (using the RING ordering scheme);
• It is efficient to find neighbour pixels (using the NESTED ordering scheme);
• The base pixelisation divides the 2-sphere in 12 pixels, but each of these pixels can be divided into four sub-pixels, and the process can be continued; in principle, the size of a pixel can be reduced to arbitrarily small values.

HEALPix is widely used in cosmology to store maps of the CMB temperature and polarization anisotropies, which is the field studied by the authors of this package.

Supported platforms

The purpose of Healpix.jl, is to implement a Julia-only library, instead of providing bindings to the original implementation of the C/C++/Fortran/Python Healpix library. This means that, unlike the original implementation, Healpix.jl is fully supported on Windows systems, among with Linux and Mac OS X.

Installation

From the Julia REPL, run

import Pkg
Pkg.add("Healpix.jl")

Usage examples

Here are some code snippets that show how to use Healpix.jl. It is interesting to have a look at test/runtests.jl as well.

Refer to the documentation for more examples.

Dealing with resolutions

The resolution of a HEALPix map is uniquely determined by the NSIDE parameter. Healpix.jl precalculates a number of values from NSIDE to save time during computations; such values are saved in a Healpix.Resolution object:

import Healpix
res = Healpix.Resolution(256)
print("The pixel index is $(Healpix.ang2pixNest(res, 0.1, 0.2))\n")

Reading a map from a FITS file

This snippet loads a map named planck_70GHz.fits into an array of 64-bit floating-point numbers:

import Healpix

m = Healpix.readMapFromFITS("planck_70GHz.fits", 1, Float64)
print("average: $(mean(m.pixels))\n")

How to contribute

See the document CONTRIBUTING.md.

Citing Healpix.jl

If you have used Healpix.jl in your research and want to acknowledge the library in your academic publications, you can reference its ASCL entry through the code ascl:2109.028:

Tomasi M., Li Z. 2021 Healpix.jl: Julia-only port of the HEALPix library, 0.30, Astrophysics Source Code Library ascl:2109.028

Be sure to append ascl:2109.028 to the end of the citation, so that ADS and other bibliographic databases can create a reference to this package.

Here is a BibTeX entry ready to be used, generated by ADS:

@MISC{2021ascl.soft09028T,
       author = {{Tomasi}, Maurizio and {Li}, Zack},
        title = "{Healpix.jl: Julia-only port of the HEALPix library}",
     keywords = {Software},
      version = {3.0},     
         year = 2021,
        month = sep,
          eid = {ascl:2109.028},
        pages = {ascl:2109.028},
archivePrefix = {ascl},
       eprint = {2109.028},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2021ascl.soft09028T},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

Please update the version number (version = {…}) accordingly.

See the ASCL guidelines for more information.

License

Healpix.jl is released under the GPL license. Versions before 2.3.0 were released under a MIT license, but this was considered incompatible with the way the code has been written (#15).