B. Leistedt, A. Rassat, A. Refregier, J. -L. Starck
High precision cosmology requires analysis of large scale surveys in 3D
spherical coordinates, i.e. Fourier-Bessel decomposition. Current methods are
insufficient for future data-sets from wide-field cosmology surveys. The aim of
this paper is to present a public code for fast Fourier-Bessel decomposition
which can be applied to cosmological data or 3D data in spherical coordinates
in other scientific fields. In this paper, we present an equivalent formulation
of the Fourier-Bessel decomposition which separates radial and tangential
calculations. We propose to make use of existing pixelisation scheme HEALPix
for rapid calculation of the tangential modes. 3DEX (3D EXpansions) is a public
code for fast Fourier-Bessel decomposition of 3D all-sky surveys which takes
advantage of HEALPix for the calculation of tangential modes. We perform tests
on very large simulations and we compare precision and computation time of our
method with an optimised implementation of the Fourier-Bessel original
formulation. For surveys with millions of galaxies, computation time is reduced
by a factor 4-12 depending on the desired scales and accuracy. The formulation
is also suitable for pre-calculations and external storage of the spherical
harmonics, which allows for further speed improvements. The 3DEX code can
accommodate data with masked regions of missing data. 3DEX can also be used in
other disciplines, where 3D data is to be analysed in spherical coordinates.
The code and documentation can be downloaded at http://ixkael.com/blog/3dex.
View original:
http://arxiv.org/abs/1111.3591
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