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Method for storing diagonal data of sparse matrix and SpMV (Sparse Matrix Vector) realization method based on method

A sparse matrix and data storage technology, which is applied to the diagonal data storage of sparse matrix and the SpMV implementation based on it, to achieve the effect of reducing storage space requirements and memory access overhead, reducing memory access complexity, and reducing access overhead

Inactive Publication Date: 2011-08-03
INST OF SOFTWARE - CHINESE ACAD OF SCI
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Problems solved by technology

Transforming the matrix rearrangement problem into a TSP problem

Method used

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  • Method for storing diagonal data of sparse matrix and SpMV (Sparse Matrix Vector) realization method based on method
  • Method for storing diagonal data of sparse matrix and SpMV (Sparse Matrix Vector) realization method based on method
  • Method for storing diagonal data of sparse matrix and SpMV (Sparse Matrix Vector) realization method based on method

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[0075] Using the technology introduced above, we use two test platforms for verification. Test platform 1 is AMD Opteron 8378, 2.4GHz. Test platform 2 is Intel Xeon X5472 3.00G. The relevant data of the selected experimental matrices are shown in Table 2. A total of 23 matrices were selected, which are quite representative. These experimental data are based on observatory projects that have both dense and sparse diagonals that can be stored with CSD. There are less diagonal numbers of non-zero elements in the first 10 sparse matrices in table 2, and the diagonal data storage method (abbreviation DDD-SPLIT method) of the present invention is used to store; there are more pairs in the back 13 sparse matrices Diagonal lines, and the number of non-zero elements on most of the diagonal lines is small. If they are all stored in the DDD-SPLIT method, more storage space will be wasted. For these matrices, we use the same method as DIAG to process them, that is For the sparser diagon...

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Abstract

The invention discloses a method for storing diagonal data of a sparse matrix and a SpMV realization method based on the method. The storage method comprises the following steps of: (1) scanning a sparse matrix A line by line and representing a position of a non-zero-element diagonal by using number of the diagonal; (2) segmenting the matrix A into a plurality of sparse sub-matrixes by using an intersection of the non-zero-element diagonal and the lateral side of the matrix A as a horizontal line; and (3) storing elements on the non-zero-element diagonal in each sparse matrix to a val array according to the line sequence. The SpMV realization method comprises the following steps of: (1) traversing the sparse matrixes and calculating vector multiplier y=A1*x of the sparse matrix in each sparse sub-matrix; and (2) merging the vector multipliers of all sparse sub-matrixes. The data storage method disclosed by the invention is not required to store row indexes of the non-zero elements, thereby reducing access expense and requirements on a storage space; a smaller storage space is occupied by the diagonal and the index array of the x array, so that the access complexity is reduced; andall the data required for calculation are continuously accessed, so that a complier and hardware can be optimized sufficiently.

Description

technical field [0001] The invention relates to a data storage method for a sparse matrix and a SpMV realization method based on the method, in particular to a diagonal storage method for a sparse matrix and a SpMV realization method based on the method. Background technique [0002] Sparse matrix-vector multiplication (SpMV) y=A*x is an important computing kernel, widely used in scientific computing and practical applications such as signal processing, image processing, and iterative solution algorithms. But on computing platforms based on cache storage levels, Compared with dense matrix-vector multiplication, the performance of sparse matrix-vector multiplication is poor, mainly because of the complexity of the cache storage hierarchy and the irregularity of the distribution of non-zero elements of the sparse matrix. The ratio of floating-point computing operations to storage access operations is very low, especially the indirect access of vector x and the non-reusability ...

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Application Information

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IPC IPC(8): G06F17/16
Inventor 袁良张云泉孙相征王婷刘芳芳
Owner INST OF SOFTWARE - CHINESE ACAD OF SCI
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