We present Sketch 'n Solve, an open-source Python package that implements efficient randomized numerical linear algebra (RandNLA) techniques for solving large-scale least squares problems. While sketch-and-solve algorithms have demonstrated theoretical promise, their practical adoption has been limited by the lack of robust, user-friendly implementations. Our package addresses this gap by providing an optimized implementation built on NumPy and SciPy, featuring both dense and sparse sketching operators with a clean API. Through extensive benchmarking, we demonstrate that our implementation achieves up to 50x speedup over traditional LSQR while maintaining high accuracy, even for ill-conditioned matrices. The package shows particular promise for applications in machine learning optimization, signal processing, and scientific computing.

Randomized Numerical Linear Algebra (RandNLA) is a powerful class of methods, widely used in High Performance Computing (HPC). RandNLA provides approximate solutions to linear algebra functions applied to large signals, at reduced computational costs. However, the randomization step for dimensionality reduction may itself become the computational bottleneck on traditional hardware. Leveraging near constant-time linear random projections delivered by LightOn Optical Processing Units we show that randomization can be significantly accelerated, at negligible precision loss, in a wide range of important RandNLA algorithms, such as RandSVD or trace estimators.