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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | https://arxiv.org/abs/2507.15209 |
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| _version_ | 1866912835796205568 |
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| author | Ju, Wenjie Feng, Longlong Huang, Zhiqi Sun, Xin Zhu, Weishan |
| author_facet | Ju, Wenjie Feng, Longlong Huang, Zhiqi Sun, Xin Zhu, Weishan |
| contents | We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation functions, wherein spatial displacements are implemented via translation window functions. In Fourier space, these translations correspond to plane waves, whose decomposition into spherical harmonics naturally leads to a multipole expansion framework for the 3PCF. To accelerate computation, we incorporate density field reconstruction within the framework of multiresolution analysis, enabling efficient summation using either grid-based or particle-based schemes. In addition to the shared computational cost of reconstructing the multipole-decomposed density fields - scaling as $\mathcal{O}(L^2_{\text{trun}} N_g \log N_g)$ (where $N_g$ is the number of grids and $L_{\text{trun}}$ is the truncation order of the multipole expansion) - the final summation step achieves a complexity of $\mathcal{O}(D^6_{\text{sup}} N_g)$ for the grid-based approach and $\mathcal{O}(D^3_{\text{sup}} N_p)$ for the particle-based scheme (where $D_{\text{sup}}$ is the support of the basis function and $N_p$ is the number of particles). The proposed $in\, situ$ multipole algorithm is fully GPU-accelerated and implemented in the open-source $Hermes$ toolkit for cosmic statistics. This development enables fast, scalable higher-order clustering analyses for large-volume datasets from current and upcoming cosmological surveys such as Euclid, DESI, LSST, and CSST. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Optimal In-Situ Multipole Algorithm for the Isotropic Three-Point Correlation Functions Ju, Wenjie Feng, Longlong Huang, Zhiqi Sun, Xin Zhu, Weishan Cosmology and Nongalactic Astrophysics We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation functions, wherein spatial displacements are implemented via translation window functions. In Fourier space, these translations correspond to plane waves, whose decomposition into spherical harmonics naturally leads to a multipole expansion framework for the 3PCF. To accelerate computation, we incorporate density field reconstruction within the framework of multiresolution analysis, enabling efficient summation using either grid-based or particle-based schemes. In addition to the shared computational cost of reconstructing the multipole-decomposed density fields - scaling as $\mathcal{O}(L^2_{\text{trun}} N_g \log N_g)$ (where $N_g$ is the number of grids and $L_{\text{trun}}$ is the truncation order of the multipole expansion) - the final summation step achieves a complexity of $\mathcal{O}(D^6_{\text{sup}} N_g)$ for the grid-based approach and $\mathcal{O}(D^3_{\text{sup}} N_p)$ for the particle-based scheme (where $D_{\text{sup}}$ is the support of the basis function and $N_p$ is the number of particles). The proposed $in\, situ$ multipole algorithm is fully GPU-accelerated and implemented in the open-source $Hermes$ toolkit for cosmic statistics. This development enables fast, scalable higher-order clustering analyses for large-volume datasets from current and upcoming cosmological surveys such as Euclid, DESI, LSST, and CSST. |
| title | An Optimal In-Situ Multipole Algorithm for the Isotropic Three-Point Correlation Functions |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2507.15209 |