Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/31/2023
Public

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents

Sparse BLAS Coordinate Matrix Storage Format

The coordinate format is the most flexible and simplest format for the sparse matrix representation. Only non-zero elements are stored, and the coordinates of each non-zero element are given explicitly. Many commercial libraries support the matrix-vector multiplication for the sparse matrices in the coordinate format.

The Intel® oneAPI Math Kernel Library coordinate format is specified by three arrays:values, rows, and column, and a parameter nnz which is number of non-zero elements in A. All three arrays have dimension nnz. The following table describes the arrays in terms of the values, row, and column positions of the non-zero elements in a sparse matrix A.

values

A real or complex array that contains the non-zero elements of A in any order.

rows

Element i of the integer array rows is the number of the row in A that contains the i-th value in the values array.

columns

Element i of the integer array columns is the number of the column in A that contains the i-th value in the values array.

NOTE:

Note that the Intel® oneAPI Math Kernel Library Sparse BLAS routines support the coordinate format both with one-based indexing and zero-based indexing.

For example, the sparse matrix C



can be represented in the coordinate format as follows:

Storage Arrays for an Example Matrix in case of the coordinate format
one-based indexing                          
values = (1 -1 -3 -2 5 4 6 4 -4 2 7 8 -5)
rows = (1 1 1 2 2 3 3 3 4 4 4 5 5)
columns = (1 2 3 1 2 3 4 5 1 3 4 2 5)
zero-based indexing                          
values = (1 -1 -3 -2 5 4 6 4 -4 2 7 8 -5)
rows = (0 0 0 1 1 2 2 2 3 3 3 4 4)
columns = (0 1 2 0 1 2 3 4 0 2 3 1 4)