Practical Sparse Matrices in C++ with Hybrid Storage and Template-Based Expression Optimisation

Abstract

Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage format. In addition, to achieve good performance, several formats may need to be used in one program, requiring explicit selection and conversion between the formats. This can be both tedious and error-prone, especially for non-expert users. Motivated by these issues, we present a user-friendly and open-source sparse matrix class for the C++ language, with a high-level application programming interface deliberately similar to the widely used MATLAB language. This facilitates prototyping directly in C++ and aids the conversion of research code into production environments. The class internally uses two main approaches to achieve efficient execution: (i) a hybrid storage framework, which automatically and seamlessly switches between three underlying storage formats (compressed sparse column, Red-Black tree, coordinate list) depending on which format is best suited and/or available for specific operations, and (ii) a template-based meta-programming framework to automatically detect and optimise execution of common expression patterns. Empirical evaluations on large sparse matrices with various densities of non-zero elements demonstrate the advantages of the hybrid storage framework and the expression optimisation mechanism.

arXiv commentextended and revised version of an earlier conference paper arXiv:1805.03380

References in corpus (3)

• A User-Friendly Hybrid Sparse Matrix Class in C++
• Expression Templates Revisited: A Performance Analysis of the Current ET Methodology
• The non-convex Burer-Monteiro approach works on smooth semidefinite programs

Cited by in corpus (8)

• SpArch: Efficient Architecture for Sparse Matrix Multiplication
• IMSRG with flowing 3 body operators, and approximations thereof
• Polarization and charge-separation of moiré excitons in van der Waals heterostructures
• An Adaptive Solver for Systems of Linear Equations
• Determination of proton PDF uncertainties with Markov chain Monte Carlo
• Automated Synthesis of Quantum Algorithms via Classical Numerical Techniques
• Creating two-qudit maximally entangled quantum link through bulk
• A Restricted Latent Class Hidden Markov Model for Polytomous Responses, Polytomous Attributes, and Covariates: Identifiability and Application