Efficient parallel multiplication of sparse matrices is key to enabling many large-scale calculations. This article presents the DBCSR (Distributed Block Compressed Sparse Row) library for scalable sparse matrix-matrix multiplication and its use in the CP2K program for linear-scaling quantum-chemical calculations. The library combines several approaches to implement sparse matrix multiplication...

Several authors have recently considered a parallel method for solving sparse triangular systems with many right-hand sides. The method employs a partition into sparse factors of the product form of the inverse of the coefficient matrix. It is shown here that while the method can be unstable, stability is guaranteed if a certain scalar that depends on the matrix and the partition is small and t...

We present a new deep neural network architecture, motivated by sparse random matrix theory that uses a low-complexity embedding through a sparse matrix instead of a conventional stacked autoencoder. We regard autoencoders as an information-preserving dimensionality reduction method, similar to random projections in compressed sensing. Thus, exploiting recent theory on sparse matrices for dimen...

Sparse Matrix-Matrix multiplication (SpMM) is a fundamental operation over irregular data, which is widely used in graph algorithms, such as finding minimum spanning trees and shortest paths. In this work, we present a hybrid CPU and GPU-based parallel SpMM algorithm to improve the performance of SpMM. First, we improve data locality by element-wise multiplication. Second, we utilize the ordere...

The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many sparse matrix computational kernels such as sparse matrix-vector products and sparse matrix-matrix products. Solving linear systems with sparse triangular struc...

We present compiler technology for generating sparse matrix code from (i) dense matrix code and (ii) a description of the indexing structure of the sparse matrices. This technology embeds statement instances into a Cartesian product of statement iteration and data spaces, and produces efficient sparse code by identifying common enumerations for multiple references to sparse matrices. This appro...

We present compiler technology for generating sparse matrix code from (i) dense matrix code and (ii) a description of the indexing structure of the sparse matrices. This technology embeds statement instances into a Cartesian product of statement iteration and data spaces, and produces efficient sparse code by identifying common enumerations for multiple references to sparse matrices. This appro...

This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation method and uses only samples of the nonzero entries of the matrix series. The proposed approach can approximate very large matrices, unlike the current matrix...

It has been known that the sparse approximate inverse preconditioning procedures SPAI and PSAI(tol) are costly to construct preconditioners for a large sparse nonsymmetric linear system with the coefficient matrix having at least one relatively dense column. This is also true for SPAI and the recently proposed sparse approximate inverse preconditioning procedure RSAI(tol) procedure when the mat...