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If the sparse matrix 
is comprised of square
dense blocks of nonzeros in some regular pattern, we can modify
the CRS (or CCS) format to exploit such block patterns. Block
matrices typically arise from the discretization of partial differential
equations in which there are several degrees of freedom associated
with a grid point. We then partition the matrix in small blocks with
a size equal to the number of degrees of freedom, and treat each
block as a dense matrix, even though it may have some zeros.
If 
is the dimension of each block and 
is the number of nonzero
blocks in the 
matrix , then the total storage
needed is 
.
The block
dimension 
of is then defined by 
.
Similar to the CRS format, we require 3 arrays for the BCRS format:
a rectangular array for floating-point numbers (
val(
,
,)) which stores the nonzero blocks in
(block) row-wise fashion, an integer array ( col_ind())
which stores the actual column indices in the original matrix of
the (
) elements of the nonzero blocks, and a pointer
array ( row_blk(
)) whose entries point to the beginning of
each block row in val(:,:,:) and col_ind(:). The
savings in storage locations and reduction in indirect addressing for
BCRS over CRS can be significant for matrices with a large .