Students will make short presentations of group project results in class, starting on Wednesday 02 April 2003, if any group is prepared.

CAUTION: Projects should have sufficient work to effective utilize the TCS with MPI, but should not be so time consuming as to severely affect the performance of other users. Write a group (1 < group < 2) with good load balancing among the group members) report that is a short professional paper (8 or 15 or so pages plus appendices) as if for publication, i.e., with

1. abstract (short description of problem and results)
2. executive summary (give an itemized brief summary of your paper)
3. introduction (motivate your problem for the class, citing prior work)
4. problem or method
5. results and discussion (should include theoretical explanations of interesting results and graphs; explain results whether good or bad)
6. conclusions (brief, emphasizing your main results)
7. acknowledgements (give thanks to others that helped you and to the Pittsburgh Supercomputer Center of use of the TCS if you use it: see tcs03guide.html acknowledgement.))
8. references (list articles, books and other documents that you used as sources)
9. appendices: compiler informational code listing file to identify the compiler-options command used, output files (samples if there are too many) and supporting performance timings.

WARNING: If you use test or sample floating point arrays in your project, make sure they are genuine and random floating point, i.e., do not use trivial integers or numbers with patterns. Also, make sure you MPI code represents a superproblem, else you will get slowdown rather than speedup as many unfortunately found in the TCS Starter problem because they use too small a problem size. Consult the class local user's guide for how to run a scalar job to use as a reference measurement. Also, this must be primarily be a TCS problem, although comparison can be made to a ARGO, Platinum or any of the departmental clusters. See

• Class PSC TCS Local Guide.

• PSC Terascale Computing System (TCS) Prototype.

• Class MPI Help pages Use the MPI_Wtime wall timer for measuring performance times, unless you can find a better timer.

• Class TCS MPI Example page. See QSUB job files for compiler commands, but also use the results of the TCS Starter Problem for the best choice of the optimization options.

• Class Sample Laplace-MPI C Code.

TCS Project Suggestions

1. Own Project. A PSC TCS with MPI project or your own design, such as optimization of some method connected with your thesis research area, graphical visualization, another course, or some interesting science-engineering area.
2. Statistics Project. Generate suitable sets of random numbers (make sure they are floating point), each with a different sample size N. See the TCS Local Guide or TCS man pages. Describe how you tested the randomness of your data, e.g., test for a uniform random distribution. For each set, compute basic statistics, like mean, variance and Chi-Square test in as efficient vector manner as possible Plot T versus N and T versus p. Estimate or compute and plot the Amdahl vector fraction as a function of N. Compare speedups and efficiencies relative to N. Is the Amdahl law operative as the problem size N becomes large? Develop your own performance model that is appropriate for the behavior of the timing data with number of processors p, sample size N and Chi-Square bin size Nb. Does your performance model account for deviations in Amdahl's law?
3. Row versus Column Oriented LU Decomposition Loops. Determine regions of array size where there are efficiency advantages on the Cray using column referencing as opposed to row referencing in reordering LU decomposition multiple loops. Is the simple Fortran column environment argument valid, and if not why not? How strong is the dependence on loop iteration size N? What about rectangular (non-square and very thin) matrices. Make sure your floating point arrays are genuine. (See Dongarra, Gustavson and Karp, SIAM Review, Vol. 26, 1984, pp. 91-122; for the CRAY-1).
4. Iteration Methods. Make a comparison of the performance of Jacobi and Gauss-Seidel methods for Elliptic Partial Differential equations. Gauss-Seidel is better for serial computers, but what about parallel and vector computers? (See Ortega, "Intro. Parallel and Vector Solution of Linear Systems," 1988, or the newer Golub and Ortega "Scientific Computing: An Introduction with Parallel Computing," 1993, and related papers.) See Class Sample Laplace-MPI C Code. See also the F90 version if interested.
5. Test whether higher or lower levels of optimization give higher performance. For instance, does the command `cc -O[n] ... [pgm].c' lead to faster executables for some values of Option Level `[n]' for matrix multiplication or some other large scale application. Similarly for F90.
6. Test F90 extensions for enhanced performance on some large scale problem. See the test problem in the Local TCS Guide.
7. Compare Performance of MPI Functions/Subroutines. For instance, compare the Collective Communication routine MPI_Bcast with the Blocking Point to Point Communication routine MPI_Send along with MPI_Recv, and with the Nonblocking Point to Point Communication routine MPI_Isend along with MPI_Irecv. Use MPI_Wtime to measure performance times. (Note shmem is the TCS native message passing library. See `man shmem'.) Compare new MPI versions of Send and Recv with the sequence Irec, Send and Wait for MPI.
8. Computation versus Communication: Take a suitable MPI application and try to find out what is the optimal ratio of computation to communication and what the optimal message, i.e., array, size would be.