Fast computation of temperature and polarization coupling matrices
Year: 2026
Type: article
Abstract: ABSTRACT We present a fast and exact method for computing cosmic microwave background (CMB) mode-coupling matrices based on an optimized evaluation of Wigner–$3j$ symbols. The method exploits analytic structure in the relevant Wigner–$3j$ symbol configurations appearing in temperature and polarization coupling matrices, expressing all required quantities in terms of a small set of recurrence-generated values which are pre-computed and stored in lookup tables. This approach reduces the computational cost of constructing the full coupling matrices while maintaining numerical accuracy. We demonstrate the performance of the threej_cosmo implementation using realistic survey masks from current CMB experiments. Relative to standard recursion-based approaches used in existing pseudo-$C_\ell$ pipelines, the method achieves speedups of 6–$25\times$ in practical coupling-matrix constructions, with the largest gains occurring at high multipoles. The algorithm admits efficient parallelization on both CPUs and GPUs, the latter providing additional acceleration, up to a further $\mathcal {O}(50)$ on modern hardware, without altering the underlying formalism. Beyond full matrix construction, the approach is naturally suited to applications in which only a restricted set of $\ell _3$ modes is required for each $(\ell _1,\ell _2)$ pair, such as in the computation of band-limited coupling matrices and analytic covariance terms. These features make threej_cosmo a practical backend for pseudo-$C_\ell$ estimation and related calculations in next-generation CMB analysis pipelines.
Authors: Georgia Kiddier, Steven Gratton
Institution: University of Cambridge
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,046
Awards: G1592084823, G3120427512, The DiRAC 2.5x Facility, ExCALIBUR H&ES: Intel Xeon GPU Max Pre-Exascale Testbed, Key Probes of the Extreme Universe: Accretion Discs, Gravitational Waves, CMB and Galaxy Surveys, DiRAC 2.5 Operations 2017-2020, G581313191, DiRAC 2.5 - the pathway to DiRAC Phase 3, Cambridge Centre for Doctoral Training in Data Intensive Science, Cambridge Service for Data Driven Discovery (CSD3) - A National Data Intensive Science Cloud for Converged Simulation, AI & Analytics, G7028966183, G7656762203
OpenAlex ID: W7130324576