Estimating N-Point Correlation Functions from Pixelized Sky Maps

Abstract

We develop, implement and test a set of algorithms for estimating N-point correlation functions from pixelized sky maps. These algorithms are slow, in the sense that they do not break the O(N_pix^N) barrier, and yet, they are fast enough for efficient analysis of data sets up to several hundred thousand pixels. The typical application of these methods is Monte Carlo analysis using several thousand realizations, and therefore we organize our programs so that the initialization cost is paid only once. The effective cost is then reduced to a few additions per pixel multiplet (pair, triplet etc.). Further, the algorithms waste no CPU time on computing undesired geometric configurations, and, finally, the computations are naturally divided into independent parts, allowing for trivial (i.e., optimal) parallelization.