  High-precision cosmology requires the analysis of large-scale surveys in 3D
spherical coordinates, i.e. spherical 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 spherical
Fourier-Bessel decomposition that can be applied to cosmological data or 3D
data in spherical coordinates in other scientific fields. We present an
equivalent formulation of the spherical Fourier-Bessel decomposition that
separates radial and tangential calculations. We propose the use of the
existing pixelisation scheme HEALPix for a rapid calculation of the tangential
modes. 3DEX (3D EXpansions) is a public code for fast spherical Fourier-Bessel
decomposition of 3D all-sky surveys that takes advantage of HEALPix for the
calculation of tangential modes. We perform tests on very large simulations and
we compare the precision and computation time of our method with an optimised
implementation of the spherical 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 additional 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 are to be analysed in spherical coordinates. The
code and documentation can be downloaded at http://ixkael.com/blog/3dex.
