An Alternative Compressed Storage Format for Sparse Matrices

Abstract

The handling of the sparse matrix vector product(SMVP) is a common kernel in many scientific applications. This kernel is an irregular problem, which has led to the development of several compressed storage formats such as CRS, CCS, and JDS among others. We propose an alternative storage format, the Transpose Jagged Diagonal Storage(TJDS), which is inspired from the Jagged Diagonal Storage format and makes no assumptions about the sparsity pattern of the matrix. We present a selection of sparse matrices and compare the storage requirements needed using JDS and TJDS formats, and we show that the TDJS format needs less storage space than the JDS format because the permutation array is not required. Another advantage of the proposed format is that although TJDS also suffers the drawback of indirect addressing, it does not need the permutation step after the computation of the SMVP.

Finding structurally different medical data

“…However, as is the case for text documents, the matrix is likely to be sparse. Therefore, we can eliminate the words that never occur in the data, and/or store the matrix in a compressed format such as the Compressed Column Storage (CCS) format [5]. In our experiments, we find that only about 10% of all words have some subsequence mapped to it.…”

Review of Storage Techniques for Sparse Matrices

“…Another array row_ind() is needed to store the row indices of the non-zero elements in the original matrix. Finally, a third array is also needed, tjd_ptr(), which stores the starting position of the transposed jagged diagonals in the array val() [17,18]. Although TJDS suffers the drawback of indirect addressing, it does not need the permutation step.…”

“…The Transpose Jagged Diagonal Storage (TJDS) is inspired from the Jagged Diagonal Storage format and makes no assumptions about the sparsity pattern of the matrix [17]. In TJDS all the non-zero elements are shifted upward instead of leftward as in JDS.…”

“…Instead of storing n 2 elements, it requires only (2 * N nze + N + 1) storage locations [1]. Similar to CRS is the Compressed Column Storage (CCS) (also called the Harwell-Boeing Sparse Matrix Storage Format) [17,12], which is constructed in exactly the same way as CRS but with the roles of rows and columns interchanged. One can also say that CCS is the transpose of CRS [12].…”

“…Although TJDS suffers the drawback of indirect addressing, it does not need the permutation step. This format is suitable for parallel and distributed processing [17,19]. [12].…”