Storage format

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{array}{r} A = (\begin{array}{c} 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{array}) \end{array}

where

\begin{array}{r} C o m p r e s s e d A = (\begin{array}{c} 1.0 & 2.0 \\ 3.0 & 4.0 \\ 6.0 & 7.0 \\ 6.0 & 8.0 \end{array}) m e t a d a t a = (\begin{array}{c} 0 & 1 \\ 2 & 3 \\ 1 & 2 \\ 1 & 3 \end{array}) \end{array}