Improve the performance of dense matrix/sparse matrix multiplication kernels

[Klaus Iglberger]

Description

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

• row-major dense/row-major sparse matrix multiplication (DMatSMatMultExpr)
• row-major dense/column-major sparse matrix multiplication (DMatTSMatMultExpr)
• column-major dense/row-major sparse matrix multiplication (TDMatSMatMultExpr)
• column-major dense/column-major sparse matrix multiplication (TDMatTSMatMultExpr)

Tasks

• optimize the performance of the DMatSMatMultExpr kernel
• optimize the performance of the DMatTSMatMultExpr kernel
• optimize the performance of the TDMatSMatMultExpr kernel
• optimize the performance of the TDMatTSMatMultExpr kernel
• update symmetric refactoring operations as required
• guarantee correctness and robustness for all modified kernels

[Klaus Iglberger]

The performance of all dense matrix/sparse 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 are given in MFlops:

Assignment to row-major matrices, filling degree 10%

kernel	before	after
dmatsmatmult	1315.56	2088.99
dmattsmatmult	1473.77	2072.93
tdmatsmatmult	1191.96	2618.87
tdmattsmatmult	512.772	2595.33

Assignment to row-major matrices, filling degree 40%

kernel	before	after
dmatsmatmult	2059.11	3348.41
dmattsmatmult	1531.54	3306.33
tdmatsmatmult	1803.36	2695.98
tdmattsmatmult	534.62	2663.28

Assignment to column-major matrices, filling degree 10%

kernel	before	after
dmatsmatmult	803.514	2351.86
dmattsmatmult	1344.44	2393.34
tdmatsmatmult	2304.64	4090.54
tdmattsmatmult	4113.93	4113.93

Assignment to column-major matrices, filling degree 40%

kernel	before	after
dmatsmatmult	733.848	3420.31
dmattsmatmult	1528.73	3437.07
tdmatsmatmult	2352.15	4167.31
tdmattsmatmult	4181.47	4181.47

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!