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Fast computation of temperature and polarization coupling matrices.

Bibliographic Details
Title: Fast computation of temperature and polarization coupling matrices.
Authors: Kiddier, Georgia1 (AUTHOR), Gratton, Steven2 (AUTHOR)
Source: Monthly Notices of the Royal Astronomical Society. 7/10/2026, Vol. 549 Issue 4, p1-9. 9p.
Subject Terms: *Cosmic background radiation, *Parallel programming, *Numerical analysis
Abstract: We present a fast and exact method for computing cosmic microwave background (CMB) mode-coupling matrices based on an optimized evaluation of Wigner– 3 j symbols. The method exploits analytic structure in the relevant Wigner– 3 j 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 ℓ pipelines, the method achieves speedups of 6– 25 × 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 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 ℓ 3 modes is required for each (ℓ 1 , ℓ 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 ℓ estimation and related calculations in next-generation CMB analysis pipelines. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
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  Data: Fast computation of temperature and polarization coupling matrices.
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  Data: <searchLink fieldCode="AR" term="%22Kiddier%2C+Georgia%22">Kiddier, Georgia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Gratton%2C+Steven%22">Gratton, Steven</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Monthly+Notices+of+the+Royal+Astronomical+Society%22">Monthly Notices of the Royal Astronomical Society</searchLink>. 7/10/2026, Vol. 549 Issue 4, p1-9. 9p.
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  Data: *<searchLink fieldCode="DE" term="%22Cosmic+background+radiation%22">Cosmic background radiation</searchLink><br />*<searchLink fieldCode="DE" term="%22Parallel+programming%22">Parallel programming</searchLink><br />*<searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We present a fast and exact method for computing cosmic microwave background (CMB) mode-coupling matrices based on an optimized evaluation of Wigner– 3 j symbols. The method exploits analytic structure in the relevant Wigner– 3 j 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 ℓ pipelines, the method achieves speedups of 6– 25 × 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 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 ℓ 3 modes is required for each (ℓ 1 , ℓ 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 ℓ estimation and related calculations in next-generation CMB analysis pipelines. [ABSTRACT FROM AUTHOR]
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      – Type: doi
        Value: 10.1093/mnras/stag1075
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      – Code: eng
        Text: English
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        PageCount: 9
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        Type: general
      – SubjectFull: Parallel programming
        Type: general
      – SubjectFull: Numerical analysis
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      – TitleFull: Fast computation of temperature and polarization coupling matrices.
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            NameFull: Kiddier, Georgia
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              M: 07
              Text: 7/10/2026
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              Y: 2026
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