FuGa3D: Fast full-sky analysis of Galaxy catalogues in 3D

¹ University of Helsinki, Department of Physics, PO Box 64, 00014 Helsinki, Finland
² Helsinki Institute of Physics, PO Box 64, 00014 Helsinki, Finland
³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
⁴ Department of Astronomy, University of Geneva, Ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁵ INAF – Osservatorio Astronomico di Roma, via Frascati 33, 00040 Monteporzio Catone, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 June 2025
Accepted: 16 January 2026

Abstract

We present FuGa3D, a code for fast computation of two-point statistics for galaxy-survey observables, including galaxy clustering and cosmic shear. We define the redshift–space correlation function (RCF) as the correlation function expressed in the parameter space of two redshifts and an angular separation angle. Assuming that there is no preferred direction in the sky, these parameters fully characterise the relative position of two galaxies independently of the assumed cosmological model. The conventional correlation metrics, such as the real-space clustering correlation function and its multipoles, can be constructed from the pre-computed RCF. The method provides a framework for efficient analysis of large cosmological datasets since the numerically expensive calculations only have to be carried out once and the subsequent cosmology-dependent analysis steps are cheap. We further define the redshift–space power spectrum as the harmonic counterpart of the RCF, and we show that it can be computed efficiently using the discrete galaxy coordinates. We validate the code with simulated mock catalogues, utilising a 40-core compute node. Computing the RCF and the real-space two-point correlation function up to the comoving 200 Mpc separation for a MICE simulation with 46 million galaxies at 1.5 Mpc (3 Mpc) resolution took 47 (12) node-minutes for clustering only and 7.3 (3.0) node-hours with shear analysis included.