Strong Scaling of The SVD Algorithm For HPC Science: A Petsc-Based Approach

Abstract

The Singular Value Decomposition (SVD) algorithm is ubiquitous in many fields of science and technology. It may be used embedded into other advanced algorithms, solvers or data processing chains. In those scenarios dealing with large data volumes expressed as a huge matrix, there is a need for parallel SVD versions to process it efficiently. We present some ideas and results obtained within the PETSc framework, which enable to design promising HPC scalable solvers. The focused SVD implementations have been taken from the SLEPc library, which is seamless plugged into PETSc to extend its capabilities. Besides its implementation, there is also a randomized-SVD and some wrappers to interface ScaLAPACK and others packages intended to extract singular triplets. This work assesses the strong scaling behaviour attained with these SVD implementations at extracting the leading singular values of a population of both sparse and dense squared matrices. A comparison of performance is provided.