<tt>pylspack</tt> : Parallel Algorithms and Data Structures for Sketching, Column Subset Selection, Regression, and Leverage Scores

We present parallel algorithms and data structures for three fundamental operations in Numerical Linear Algebra: (i) Gaussian CountSketch random projections their combination, (ii) computation of the Gram matrix (iii) squared row norms product two matrices, with a special focus on "tall-and-skinny" which arise many applications. provide detailed analysis ubiquitous transform its combination projections, accounting memory requirements, computational complexity workload balancing. also demonstrate how these results can be applied to column subset selection, least squares regression leverage scores computation. These tools have been implemented pylspack, publicly available Python package (https://github.com/IBM/pylspack) whose core is written C++ parallelized OpenMP, compatible standard SciPy NumPy. Extensive numerical experiments indicate that proposed scale well significantly outperform existing libraries tall-and-skinny matrices.