Improve the performance of sparse matrix/dense matrix multiplication kernels

[Klaus Iglberger]

Description

The primary goal of the Blaze library is to provide maximum performance for all operations. Still, the sparse matrix/dense matrix multiplication kernels do not perform as efficiently as expected. Therefore the following kernels have been selected for a performance upgrade:

• row-major sparse/row-major dense matrix multiplication (SMatDMatMultExpr)
• row-major sparse/column-major dense matrix multiplication (SMatTDMatMultExpr)
• column-major sparse/row-major dense matrix multiplication (TSMatDMatMultExpr)
• column-major sparse/column-major dense matrix multiplication (TSMatTDMatMultExpr)

Tasks

• optimize the performance of the SMatDMatMultExpr kernel
• optimize the performance of the SMatTDMatMultExpr kernel
• optimize the performance of the TSMatDMatMultExpr kernel
• optimize the performance of the TSMatTDMatMultExpr kernel
• update symmetric refactoring operations as required
• guarantee correctness and robustness for all modified kernels

[Klaus Iglberger]

The performance of all sparse matrix/dense matrix kernels has been significantly improved. The following tables give an impression on the performance before and after the update. All results were computed on a single core of a Core i7 with 2.6 GHz and double precision element types. All results are given in MFlops:

Assignment to row-major matrices, filling degree 10%

kernel	before	after
smatdmatmult	4138.59	4138.59
smattdmatmult	2038.16	2443.15
tsmatdmatmult	1829.27	4079.71
tsmattdmatmult	811.424	2405.76

Assignment to row-major matrices, filling degree 40%

kernel	before	after
smatdmatmult	4151.3	4151.3
smattdmatmult	2507.88	3583.93
tsmatdmatmult	1761.86	4134.96
tsmattdmatmult	1086.07	3510.59

Assignment to column-major matrices, filling degree 10%

kernel	before	after
smatdmatmult	513.623	2674.4
smattdmatmult	1528.91	2178.77
tsmatdmatmult	1274.34	2682.82
tsmattdmatmult	1068.57	2147.34

Assignment to column-major matrices, filling degree 40%

kernel	before	after
smatdmatmult	531.354	2704.59
smattdmatmult	2083.3	3497.45
tsmatdmatmult	2349.02	2769.74
tsmattdmatmult	1902.57	3440.72

This improvement will be part of Blaze 2.5. Still, due to the massive performance improvement of some kernels it is recommended to use the current master revision!