librla: Randomized Linear Algebra Library

The library \texttt{librla} is a randomized linear algebra library that is specifically designed for the intermediate-sized matrices (of dimension up to roughly 10,000) that arise in applications such as reduced order modeling, fast direct solvers, least squares solves and, in some settings, data compression. \texttt{librla} is the first software package that is both stable and efficient in several high-level languages: MATLAB, Python and Julia.

It also provides increased functionality over existing software.

Specifically, it allows the user to choose to create a factorization based on a fixed rank or a desired tolerance.

The factorization options include QR, SVD and the interpolative decomposition.

Additionally, the factorization can be generated either with access to the matrix or access to a matrix-vector multiplication routine.

Numerical results compare the Python implementation with the available PyTorch and SciPy randomized factorizations.

Performance of \texttt{librla} in the three languages is comparable.