sarabande: 3/4 point correlation functions with fast Fourier transforms

Abstract

AbstractWe present a new python package sarabande for measuring 3- and 4-point correlation functions (3/4 PCFs) in $\mathcal {O} (N_{\mathrm{g}}\log N_{\mathrm{g}})$ time using fast Fourier transforms (FFTs), with Ng being the number of grid points used for the FFT. sarabande can measure both projected and full 3-point correlation function and 4-point correlation function on gridded two- and three-dimensional data sets. The general technique is to generate suitable angular basis functions on an underlying grid, radially bin these to create kernels, and convolve these kernels with the original gridded data to obtain expansion coefficients about every point simultaneously. These coefficients are then combined to give us the 3/4 PCF as expanded in our basis. We apply sarabande to simulations of the interstellar medium to show the results and scaling of calculating both the full and projected 3/4 PCFs.