Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

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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 (oneMKL) 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 (oneMKL) 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)