Papers › SARABANDE: 3/4 Point Correlation Functions with Fast Fourier Transforms
SARABANDE: 3/4 Point Correlation Functions with Fast Fourier Transforms
James Sunseri, Zachary Slepian, Stephen Portillo, Jiamin Hou, Sule Kahraman, Douglas P. Finkbeiner
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We present a new python package SARABANDE for measuring 3 & 4 Point Correlation Functions (3/4 PCFs) in 𝒪(N_g logN_g) time using Fast Fourier Transforms (FFTs), with N_g the number of grid points used for the FFT. SARABANDE can measure both projected and full 3 and 4 PCFs on gridded 2D and 3D datasets. 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 (ISM) to show the results and scaling of calculating both the full and projected 3/4 PCFs.
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