For HPL input, what problem size (matrix dimension N) should I use?
In order to find out the best performance of your system, the largest problem size fitting in memory is what you should aim for. The amount of memory used by HPL is essentially the size of the coefficient matrix. So for example, if you have 4 nodes with 256 Mb of memory on each, this corresponds to 1 Gb total, i.e., 125 M double precision (8 bytes) elements. The square root of that number is 11585. One definitely needs to leave some memory for the OS as well as for other things, so a problem size of 10000 is likely to fit. As a rule of thumb, 80 % of the total amount of memory is a good guess. If the problem size you pick is too large, swapping will occur, and the performance will drop. If multiple processes are spawn on each node (say you have 2 processors per node), what counts is the available amount of memory to each process.
