ConKer: evaluating isotropic correlations of arbitrary order

TL;DR

ConKer is a novel algorithm that efficiently estimates high-order isotropic correlation functions in cosmic matter distributions using FFT convolutions, enabling analysis of large galaxy surveys with improved speed and accuracy.

Contribution

This paper introduces ConKer, a new FFT-based method for calculating high-order correlation functions, significantly reducing computational costs compared to traditional algorithms.

Findings

ConKer accurately computes correlation functions up to order 5.

The algorithm's components are scalable and efficient for large datasets.

Timing analysis shows ConKer is faster than existing methods for large catalogs.

Abstract

High order correlations in the cosmic matter density have become increasingly valuable in cosmological analyses. However, computing such correlation functions is computationally expensive. We aim to circumvent these challenges by designing a new method of estimating correlation functions. This is realized in ConKer, an algorithm that performs FFT convolutions of matter distributions with spherical kernels. ConKer is applied to the CMASS sample of the SDSS DR12 galaxy survey and used to compute the isotropic correlation up to correlation order n = 5. We also compare the n = 2 and n = 3 cases to traditional algorithms to verify the accuracy of the new method. We perform a timing study of the algorithm and find that two of the three components of the algorithm are independent of the catalog size, N, while one component is O(N), which starts dominating for catalogs larger than 10M objects. For n < 5 the dominant calculation is O(N^(4/3logN)), where N is the number of the grid cells. For higher n, the execution time is expected to be dominated by a component with time complexity O(N^((n+2)/3)). We find ConKer to be a fast and accurate method of probing high order correlations in the cosmic matter density.