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