Abstract Repeatedly performing sparse matrix‐vector multiplication (SpMV) followed by transposed sparse matrix‐vector multiplication (SpMTV) with the same matrix is a part of several algorithms, for example, the Lanczos biorthogonalization algorithm and the biconjugate gradient method. Such algorithms can benefit from combining parallel SpMV and SpMTV into a single operation we call joint direct and transposed sparse matrix‐vector multiplication (SpMMTV). In this article, we present a parallel SpMMTV algorithm for shared‐memory CPUs. The algorithm uses a sparse matrix format that divides the stored matrix into sparse matrix blocks and compresses the row and column indices of the matrix. This sparse matrix format can be also used for SpMV, SpMTV, and similar sparse matrix‐vector operations. We expand upon existing research by suggesting new variants of the parallel SpMMTV algorithm and by extending the algorithm to efficiently support symmetric matrices. We compare the performance of the presented parallel SpMMTV algorithm with alternative approaches, which use state‐of‐the‐art sparse matrix formats and libraries, using sparse matrices from real‐world applications. The performance results indicate that the median performance of our proposed parallel SpMMTV algorithm is up to 45% higher than of the alternative approaches.

Computations with tensors are widespread in many scientific areas. Usually, the used tensors are very large but sparse, i.e., the vast majority of their elements are zero. The space complexity of sparse tensor storage formats varies significantly. For overall efficiency, it is important to reduce the execution time and additional space requirements of the initial preprocessing (i.e., converting tensors from common storage formats to the given internal format).

Abstract We propose an extension to the state‐of‐the‐art text rendering technique based on sampling a 2D signed distance field from a texture. This extension significantly improves the visual quality of sharp corners, which is the most problematic feature to reproduce for the original technique. We achieve this by using a combination of multiple distance fields in conjunction, which together provide a more thorough representation of the given glyph's (or any other 2D shape's) geometry. This multi‐channel distance field representation is described along with its application in shader‐based rendering. The rendering process itself remains very simple and efficient, and is fully compatible with previous monochrome distance fields. The introduced method of multi‐channel distance field construction requires a vector representation of the input shape. A comparative measurement of rendering quality shows that the error in the output image can be reduced by up to several orders of magnitude.

The presented study analyses 563 representative benchmark sparse matrices with respect to their partitioning into uniformly-sized blocks.The aim is to minimize memory footprints of matrices.Different block sizes and different ways of storing blocks in memory are considered and statistically evaluated.Memory footprints of partitioned matrices are additionally compared with lower bounds and the CSR storage format.The average measured memory savings against CSR in case of single and double precision are 42.3 and 28.7 percents, respectively.The corresponding worst-case savings are 25.5 and 17.1 percents.Moreover, memory footprints of partitioned matrices were in average 5 times closer to their lower bounds than CSR.Based on the obtained results, we provide generic suggestions for efficient partitioning and storage of sparse matrices in a computer memory.

Finding an optimal block size for a given sparse matrix forms an important problem for storage formats that partition matrices into uniformly-sized blocks.Finding a solution to this problem can take a significant amount of time, which, effectively, may negate the benefits that such a format brings into sparse-matrix computations.A key for an efficient solution is the ability to quickly iterate, for a particular block size, over matrix nonzero blocks.This work proposes an efficient parallel algorithm for this task and evaluate it experimentally on modern multi-core and many-core high performance computing (HPC) architectures.

Many storage formats for sparse matrices have been developed.Majority of these formats can be parametrized, so the algorithm for finding optimal parameters is crucial.For overall efficiency, it is important to reduce the execution time of this preprocessing.In this paper, we propose a new algorithm for the determination of the number of nonzero blocks of the given size in a sparse matrix.The proposed algorithm requires relatively a small amount of auxiliary memory.Our approach is based on the Morton reordering and bitwise manipulations.We also present a parallel (multithreaded) version and evaluate its performance and space complexity.