Block Compressed Sparse Row (BSR) Format - 5.2 English - 68552

BSR (Block Compressed Sparse Row) is a sparse matrix storage format that groups nonzeros into fixed-size dense blocks (with zero padding if needed) and stores those blocks in a CSR-like structure. At present AOCL-Sparse only supports square blocks. Each block is of size block_dim, having bM block rows and bN block columns. The elements inside all nonzero blocks are either stored in row-major or column-major order.

The BSR format of a bM x bN block sparse matrix will have bNNZ number of blocks. It uses three arrays as follows:

• row_ptr: Array of size bM+1 that contains pointers to the start of each block row in the col_idx and (in strides of block_dim * block_dim) val arrays. The last element points to the total number of nonzero blocks.

• col_idx: Array of size bNNZ containing the block column indices of each nonzero blocks.

• val: Array of size block_dim * block_dim * bNNZ containing all the nonzero elements of the matrix stored block by block, padded with zeros to fill the incomplete blocks.

BSR format can either use 0-based indexing or 1-based indexing similar to CSR and CSC formats.

The above diagram shows a BSR matrix of block size 2 x 3 with block_dim = 2 in 0-based indexing.

• bM = 2, bN = 3, bNNZ = 4

• row_ptr[bM + 1] = {0, 1, 4}

• col_idx[bNNZ] = {1, 0, 1, 2}

Row Major:

• val[block_dim * block_dim * bNNZ] = {0, 0, 2.2, 0, 3.0, 3.4, 0, 0, 0, 0, 0, 5.4, 4.2, 0, 6.0, 0}

Column Major:

• val[block_dim * block_dim * bNNZ] = {0, 2.2, 0, 0, 3.0, 0, 3.4, 0, 0, 0, 0, 5.4, 4.2, 6.0, 0, 0}