encore : an O ( N g2) estimator for galaxy N -point correlation functions
Abstract
ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $$\mathcal {O}(N_\mathrm{g}^2)$$ for Ng particles, or $$\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in $${\sim}100$$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); WFIRST; Simons Foundation; National Aeronautics and Space Administration (NASA)
- OSTI Identifier:
- 1893972
- Alternate Identifier(s):
- OSTI ID: 1859720
- Grant/Contract Number:
- SC0013718; AC02-05CH11231; PF7-180167
- Resource Type:
- Published Article
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Additional Journal Information:
- Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 509 Journal Issue: 2; Journal ID: ISSN 0035-8711
- Publisher:
- Oxford University Press
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; statistical methods; numerical methods; Cosmology; large-scale structure of Universe; theory; galaxies; statistics
Citation Formats
Philcox, Oliver H. E., Slepian, Zachary, Hou, Jiamin, Warner, Craig, Cahn, Robert N., and Eisenstein, Daniel J. encore : an O ( N g2) estimator for galaxy N -point correlation functions. United Kingdom: N. p., 2021.
Web. doi:10.1093/mnras/stab3025.
Philcox, Oliver H. E., Slepian, Zachary, Hou, Jiamin, Warner, Craig, Cahn, Robert N., & Eisenstein, Daniel J. encore : an O ( N g2) estimator for galaxy N -point correlation functions. United Kingdom. https://doi.org/10.1093/mnras/stab3025
Philcox, Oliver H. E., Slepian, Zachary, Hou, Jiamin, Warner, Craig, Cahn, Robert N., and Eisenstein, Daniel J. Wed .
"encore : an O ( N g2) estimator for galaxy N -point correlation functions". United Kingdom. https://doi.org/10.1093/mnras/stab3025.
@article{osti_1893972,
title = {encore : an O ( N g2) estimator for galaxy N -point correlation functions},
author = {Philcox, Oliver H. E. and Slepian, Zachary and Hou, Jiamin and Warner, Craig and Cahn, Robert N. and Eisenstein, Daniel J.},
abstractNote = {ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ${\sim}100$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.},
doi = {10.1093/mnras/stab3025},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 2,
volume = 509,
place = {United Kingdom},
year = {Wed Oct 20 00:00:00 EDT 2021},
month = {Wed Oct 20 00:00:00 EDT 2021}
}
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