lrux documentation

Fast low-rank update (LRU) of matrix determinants and pfaffians in JAX

Installation

Requires Python 3.11+ and JAX 0.7.1+. fermix is installed automatically as a dependency.

pip install lrux

Low-rank update of determinants

det_lru(...)	Low-rank update of determinant \(\det(A_1) = \det(A_0 + vu^T)\).
init_det_carrier(A, max_delay[, max_rank])	Prepare the data and space for det_lru_delayed.
merge_det_delays(carrier)	Merge the delayed updates in the carrier.
det_lru_delayed(...)	Delayed low-rank update of determinant.

Low-rank update of pfaffians

pf_lru(...)	Low-rank update of pfaffian \(\mathrm{pf}(A_1) = \mathrm{pf}(A_0 - u J u^T)\).
init_pf_carrier(A, max_delay[, max_rank])	Prepare the data and space for pf_lru_delayed.
merge_pf_delays(carrier)	Merge the delayed updates in the carrier.
pf_lru_delayed(...)	Delayed low-rank update of pfaffian.

Utilities

The full determinants and pfaffians are computed by fermix, which provides det, slogdet, pf, and slogpf.

skew_eye(n[, dtype])

The skew-symmetric identity matrix \(J\).