A GPU-based method for constructing symmetric matrices with compressed sparse matrices

Abstract

The embodiment of the invention discloses a symmetric matrix construction method for a compressed sparse matrix based on a GPU. The symmetric matrix construction method for the compressed sparse matrix based on the GPU comprises taking a compressed sparse matrix M in a given CSR-based storage format as an input matrix; according to the compressed sparse matrix M, converting the CSR storage format into a triple array T1 in parallel; storing each triple and a corresponding triple thereof in the triple array T1 in parallel, and carrying out parallel sorting to obtain a triple array T3; finding repeated data in the T3, constructing F-labeled repeatedly stored array elements, and deleting repeatedly stored elements with the F label of 1 in the T3 in parallel, so that a triple array T4 without repeated items is obtained; and according to the triple array T4, converting into the CSR storage format in parallel to be taken as an output matrix. By implementing the symmetric matrix construction method disclosed by the invention, processing performance of solving a symmetric matrix of the sparse matrix can be effectively improved, so that each step has parallelizability, and efficient parallel processing capacity in the GPU is played.

Description

technical field [0001] The invention relates to the technical field of matrix graphics processing, in particular to a method for constructing a symmetric matrix based on a GPU-compressed sparse matrix. Background technique [0002] A matrix is ​​a commonly used tool in scientific computing and is widely used to solve linear equations, while a sparse matrix refers to a matrix containing only a small number of non-zero elements in the matrix, which is a special case of the matrix. Since there are a large number of elements with a value of 0 in the sparse matrix, the conventional matrix storage method will bring a large number of unnecessary operations during the matrix calculation operation. Therefore, in order to improve the operational efficiency of sparse matrices, more effective storage methods are often adopted, such as CSR (CompressedRow Storage, compressed row storage) storage format (see Dongarra J.Sparse matrix storage formats[J].Templates for the Solution of Algebrai...

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Problems solved by technology

Using the CSR storage format can effectively improve the operation of sparse matrices and reduce the required storage space. However, when the traditional CPU-based operation method is faced with hundreds of thousands or even tens of millions of sparse linear equations, even if the CSR Compressed storage also requires a lot of computing time

[0003] Although Batista et al. proposed a method of accelerating multiplication based on the idea of ​​multi-core parallel processing and Mironowicz et al. utilized the high parallelism of GPU (Graphics Processing Unit, image processing unit) to accelerate matrix multiplication, all effectively reduced the matrix The storage space required for the operation improves the performance of the operation, but they all need to use a symmetric sparse matrix as the input matrix, so that when dealing with practical problems, on the one hand, the scale of the matrix to be solved is very large, and on the other hand, the input matrix is ​​often required. The matrix is ​​a symmetric matrix, so for a large asymmetric sparse matrix, solving its symmetric matrix is ​​also very time-consuming (see Mironowicz P, Dziekonski A, Mrozowski M, etal.Efficient symmetric sparse matrix-vector product on a GPU[C] / / InProceedings of Graphics Technology Conference.2014, etc.)

[0004] The existing symmetric matrix construction methods based on densely stored sparse matrices often perform transposition operations on the matrix first, and then perform Boolean union operations on the transposed matrix and the original matrix. Although the above construction methods are simple and convenient, they require a lot of of storage space

Due to the limited memory storage space of the GPU, this method is not suitable for the construction of symmetric matrices for large-scale sparse matrices on the GPU

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