AI 中文总结
librla是为中等规模矩阵设计的随机线性代数库，能在多种高级语言中稳定高效运行，功能比现有软件更多，用户可按需求选分解方式，数值结果显示其在三种语言中性能相当。
AI 中文摘要
库librla是一个随机线性代数库，专为诸如降阶建模、快速直接求解器、最小二乘求解以及在某些情况下的数据压缩等应用中出现的中等规模矩阵（维度高达约10000）而设计。它是第一个在MATLAB、Python和Julia等几种高级语言中既稳定又高效的软件包，还提供了比现有软件更多的功能。具体而言，用户可以选择基于固定秩或所需容差创建分解。分解选项包括QR、SVD和插值分解。此外，分解可以通过访问矩阵或矩阵向量乘法例程来生成。数值结果将Python实现与可用的PyTorch和SciPy随机分解进行了比较。librla在三种语言中的性能相当。
英文摘要
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.
