2D-FFTLog: Efficient computation of real space covariance matrices for galaxy clustering and weak lensing

Abstract

Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate and numerically stable computation of non-Gaussian real space covariances. The 2D-FFTLog algorithm is easily extended to perform real space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a DES Y3-like and an LSST Y1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances at the flat sky limit, which are sufficiently accurate for inferring cosmological parameters.