ConKer: An algorithm for evaluating correlations of arbitrary order

Department of Physics and Astronomy, University of Rochester, 500 Joseph C. Wilson Boulevard, Rochester, NY 14627, USA
e-mail: zbrown5@ur.rochester.edu

Received: 30 July 2021
Accepted: 21 July 2022

Abstract

Context. High order correlations in the cosmic matter density have become increasingly valuable in cosmological analyses. However, computing these correlation functions is computationally expensive.

Aims. We aim to circumvent these challenges by developing a new algorithm called ConKer for estimating correlation functions.

Methods. This algorithm performs convolutions of matter distributions with spherical kernels using FFT. Since matter distributions and kernels are defined on a grid, it results in some loss of accuracy in the distance and angle definitions. We study the algorithm setting at which these limitations become critical and suggest ways to minimize them.

Results. ConKer is applied to the CMASS sample of the SDSS DR12 galaxy survey and corresponding mock catalogs, and is used to compute the correlation functions up to correlation order n = 5. We compare the n = 2 and n = 3 cases to traditional algorithms to verify the accuracy of the new algorithm. We perform a timing study of the algorithm and find that three of the four distinct processes within the algorithm are nearly independent of the catalog size N, while one subdominant component scales as O(N). The dominant portion of the calculation has complexity of O(N_c^4/3 log N_c), where N_c is the of cells in a three-dimensional grid corresponding to the matter density.

Conclusions. We find ConKer to be a fast and accurate method of probing high order correlations in the cosmic matter density, then discuss its application to upcoming surveys of large-scale structure.