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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
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 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:
 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)

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