1. CSE5304—Project Proposal Parallel Matrix Multiplication Tian Mi

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

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

4. 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

5. MPI_Scatter

7. MPI_Bcast

9. MPI_Gather

11. Data generation Data generation in R with package “igraph” Integer in range of [-1000, 1000] Matrix size: Matrix512*5121024*10242048*20484096*4096 File size2.69 MB10.7 MB43.1 MB172 MB

12. Result Data size: 1024*1024 # ProcessorsExperiments(second)Average(s)Speedup 1444145374241.81 22320211922211.99 4111019181614.82.82 810989 9.24.54 169911968.84.75 3281087785.23 648888885.23 1281096898.44.98

13. Result Data size: 1024*1024

14. Result Data size: 1024*1024

15. Result Data size: 2048*2048 # ProcessorsTime(s)Speedup 17511 24981.508032 42582.910853 81275.913386 16848.940476 325114.72549 645513.65455 1284815.64583

16. Result Data size: 2048*2048

17. Result Data size: 2048*2048

18. Result Data size: 4096*4096 # ProcessorsTime(s)Speedup 159201 236301.630854 428132.104515 89256.4 167457.946309 3257610.27778 64#DIV/0! 128#DIV/0!

19. 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)

20. Cannon's algorithm--Example http://www.vampire.vanderbilt.edu/education-outreach/me343_fall2008/notes/parallelMM_10_09.pdf

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

22. Thank you Questions & Comments?