CSE5304—Project Proposal Parallel Matrix Multiplication Tian Mi

An naive version with MPI P1 P1  P2 P2  … Pi Pi  … PN PN  Result:

An naive version with MPI Pi Pi   Pi  Pi

Processor0 reads input file Processor0 distributes one matrix Processor0 broadcasts the other matrix All processors in parallel  Do the multiplication of each piece of data Processor0 gathers the result Processor0 writes result to output file

MPI_Scatter

MPI_Bcast

MPI_Gather

Data generation Data generation in R with package “igraph” Integer in range of [-1000, 1000] Matrix size: Matrix512* * * *4096 File size2.69 MB10.7 MB43.1 MB172 MB

Result Data size: 1024*1024 # ProcessorsExperiments(second)Average(s)Speedup

Result Data size: 1024*1024

Result Data size: 1024*1024

Result Data size: 2048*2048 # ProcessorsTime(s)Speedup

Result Data size: 2048*2048

Result Data size: 2048*2048

Result Data size: 4096*4096 # ProcessorsTime(s)Speedup #DIV/0! 128#DIV/0!

Analysis To see the superlinear speedup  increase the computation, which is not dominant enough larger matrix and larger integer  However, larger matrix or long integer will also increase the communication time (broadcast, scatter, gather)

Cannon's algorithm--Example

Cannon's algorithm Still Implementing and debugging No result to share at present

Thank you Questions & Comments?