Abstract

Some level--2 and level--3 Distributed Basic Linear Algebra Subroutines (DBLAS) that have been implemented on the Connection Machine system CM--200 are described. No assumption is made on the shape or size of the operands. For matrix--matrix multiplication, both the nonsystolic and the systolic algorithms are outlined. A systolic algorithm that computes the product matrix in--place is described in detail. We show that a level--3 DBLAS yields better performance than a level--2 DBLAS. On the Connection Machine system CM--200, blocking yields a performance improvement by a factor of up to three over level--2 DBLAS. For certain matrix shapes the systolic algorithms offer both improved performance and significantly reduced temporary storage requirements compared to the nonsystolic block algorithms. We show that, in order to minimize the communication time, an algorithm that leaves the largest operand matrix stationary should be chosen for matrix--matrix multiplication. Furthermore, it is sh...

Citations