Randomized Matrix Computations from Few Entries and Products
Overview
Implements recent randomized algorithms that answer questions about a large positive-semidefinite matrix while touching only a small part of it. Randomly pivoted Cholesky builds a low-rank approximation from a few rows of a kernel matrix (Chen, Epperly, Tropp and Webber (2025) doi:10.1002/cpa.22234), with an accelerated variant based on rejection sampling (Epperly, Tropp and Webber (2025) doi:10.1137/24m1699048). The XTrace, XNysTrace and XDiag estimators recover the trace and diagonal of a matrix that is available only through matrix-vector products (Epperly, Tropp and Webber (2024) doi:10.1137/23m1548323), alongside the Hutch++ estimator of Meyer, Musco, Musco and Woodruff (2021) doi:10.1137/1.9781611976496.16. Randomized Nystrom preconditioning speeds up the conjugate gradient method for regularized linear systems (Frangella, Tropp and Udell (2023) doi:10.1137/21m1466244). These pieces are combined to fit restricted maximum likelihood variance-component models on genomic relationship matrices without forming or factorizing the covariance matrix.
- First release.
rpchol(): randomly pivoted Cholesky, in its simple and accelerated (rejection-sampling) forms, with greedy and uniform pivoting as baselines.trace_est()anddiag_est(): the XTrace, XNysTrace and XDiag estimators, with Hutch++ and Girard-Hutchinson for comparison.nystrom(),nystrom_precond(),effective_dim()andpcg(): randomized Nystrom preconditioning for conjugate gradients, solving many right-hand sides at once.reml_sketch()andreml_exact(): variance components by average-information REML, with the covariance matrix never formed in the sketched fit.kernel_matrix()andgrm_matrix(): kernel and genomic relationship matrices evaluated only where needed.
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- 0.1.0Latest2026-09-21 · current release
- RR 4.6.0 released · 2026-04-24
Package metadata
- First published
- 2026-09-21
- Total releases
- 1 / 1 yrs
- License
- MIT + file LICENSE OSI
- Minimum R
- ≥ 4.1.0
- Download size
- 128 KB
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