RSVDPACK: An implementation of randomized algorithms for computing the singular value, interpolative, and CUR decompositions of matrices on multi-core and GPU architectures

TL;DR

RSVDPACK is a C library that efficiently computes low-rank matrix approximations, including SVD, ID, and CUR decompositions, using randomized algorithms optimized for multi-core CPUs and GPUs.

Contribution

The paper introduces a high-performance, flexible library implementing randomized algorithms for matrix decompositions, optimized for modern multi-core and GPU architectures.

Findings

Efficient algorithms for SVD, ID, and CUR decompositions implemented

Performance improvements through algorithm modifications

Supports both CPU and GPU architectures

Abstract

RSVDPACK is a library of functions for computing low rank approximations of matrices. The library includes functions for computing standard (partial) factorizations such as the Singular Value Decomposition (SVD), and also so called "structure preserving" factorizations such as the Interpolative Decomposition (ID) and the CUR decomposition. The ID and CUR factorizations pick subsets of the rows/columns of a matrix to use as bases for its row/column space. Such factorizations preserve properties of the matrix such as sparsity or non-negativity, are helpful in data interpretation, and require in certain contexts less memory than a partial SVD. The package implements highly efficient computational algorithms based on randomized sampling, as described and analyzed in [N. Halko, P.G. Martinsson, J. Tropp, "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions," SIAM Review, 53(2), 2011], and subsequent papers. This manuscript presents some modifications to the basic algorithms that improve performance and ease of use. The library is written in C and supports both multi-core CPU and GPU architectures.