arXiv subjects

Wenjie Ju

Publications and source records attributed to Wenjie Ju.

3 recordsLinked to original sources

arXiv2026

Hermes - Towards an Optimal High-Performance Algorithm for Cosmic Statistics of Large Data Sets

We present Hermes, an in situ multiresolution framework for efficient and flexible measurements of cosmic large-scale-structure statistics from discrete catalogues. Hermes reconstructs a catalogue as a continuous density field in a compact scaling-function basis and replaces explicit counting of particle tuples with algebraic operations among window-filtered fields. Standard binning schemes for counts-in-cells, two-point and higher-order correlation functions are thereby expressed through choices of window functions, while new statistics can be constructed by modifying the kernels without redesigning the estimator. We introduce PyHermes, an open-source Python implementation combining multiresolution reconstruction, FFT-based convolution, MPI/thread parallelism, and GPU acceleration. It supports isotropic and anisotropic two-point statistics, marked correlations, standard and multipole three-point functions, filtered statistics, and differential operators for derived physical fields. Tests with cosmological N-body halo catalogues demonstrate a range of clustering measurements and quantify the computational efficiency and scalability of the approach. By separating field representation from statistical windows, a single reconstructed field can be reused for many standard and customised measurements, making Hermes well suited to large data sets from current and future galaxy surveys.

astro-ph.CO↗

arXiv2025

An Optimal In-Situ Multipole Algorithm for the Isotropic Three-Point Correlation Functions

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.

astro-ph.CO↗

arXiv2024

Pair Counting without Binning -- A New Approach to Correlation Functions in Clustering Statistics

This paper presents a novel perspective on correlation functions in the clustering analysis of the large-scale structure of the universe. We first recognise that pair counting in bins of radial separation is equivalent to evaluating counts-in-cells (CIC), which can be modelled using a filtered density field with a binning-window function. This insight leads to an in situ expression for the two-point correlation function (2PCF). Essentially, the core idea underlying our method is to introduce a window function to define the binning scheme, enabling pair-counting without binning. This approach develops a concept of generalised 2PCF, which extends beyond conventional discrete pair counting by accommodating non-sharp-edged window functions. To extend this framework to N-point correlation functions (NPCF) using current optimal edge-corrected estimators, we developed a binning scheme independent of the specific parameterisation of polyhedral configurations. In particular, we demonstrate a fast algorithm for the three-point correlation function (3PCF), where triplet counting is accomplished by assigning either a spherical tophat or a Gaussian filter to each vertex of triangles. Additionally, we derive analytical expressions for the 3PCF using a multipole expansion in Legendre polynomials, accounting for filtered field (binning) corrections. Numerical tests using several suites of N-body simulation samples show that our approach aligns remarkably well with the theoretical predictions. Our method provides an exact solution for quantifying binning effects in practical measurements and offers a high-speed algorithm, enabling high-order clustering analysis in extremely large datasets from ongoing and upcoming surveys such as Euclid, LSST, and DESI.

astro-ph.CO↗