Storage format#
hipSPARSELt uses a structured sparsity storage format, which is represented by an :math:` times n` matrix, where:
m = number of rows (integer)
n = number of columns (integer)
sparsity = 50%, ratio of nnz elements in every 2:1 (int) or 4:2 (others) element along the row (4:2 means every 4 continuous elements will only have 2 nnz elements)
compressed matrix = matrix of nnz elements containing data
metadata = matrix of nnz elements containing the element indices in every 4:2 or 2:1 array along the row (contents or structure of metadata is dependent on the chosen solution by backend implementation)
Consider the following \(4 \times 4\) matrix and the structured sparsity structures using \(m = 4, n = 4\):
\[\begin{split}A = \begin{pmatrix}
1.0 & 2.0 & 0.0 & 0.0 \\
0.0 & 0.0 & 3.0 & 4.0 \\
0.0 & 6.0 & 7.0 & 0.0 \\
0.0 & 6.0 & 0.0 & 8.0 \\
\end{pmatrix}\end{split}\]
where
\[\begin{split}Compressed A = \begin{pmatrix}
1.0 & 2.0 \\
3.0 & 4.0 \\
6.0 & 7.0 \\
6.0 & 8.0 \\
\end{pmatrix}
metadata = \begin{pmatrix}
0 & 1 \\
2 & 3 \\
1 & 2 \\
1 & 3 \\
\end{pmatrix}\end{split}\]