Intel(R) - Computational and Systems Biology at MIT

LINPACK and MP LINPACK Benchmarks 10matrix decomposition: fractions 0.005,0.010,0.015,0.02,0.025,0.03,0.035,0.04,0.045,0.05,0.055,0.06,0.065,0.07,0.075,0.080,0.085,0.09,0.095,.10,...,.195,.295,.395,...,.895. However, this problem size is so small and theblock size so big by comparison that as soon as it printed the value for 0.045, it wasalready through 0.08 fraction of the columns. On a really big problem, the fractionalnumber will be more accurate. It never prints more than the 46 numbers above. So,smaller problems will have fewer than 46 updates, and the biggest problems will haveprecisely 46 updates.The Mflops is an estimate based on 1280 columns of LU being completed. However,with lookahead steps, sometimes that work is not actually completed when the outputis made. Nevertheless, this is a good estimate for comparing identical runs.The 3 numbers in parenthesis are intrusive ASYOUGO2 addins. The DT is the total timeprocessor 0 has spent in DGEMM. The DF is the number of billion operations that havebeen performed in DGEMM by one processor. Hence, the performance of processor 0 (inGflops) in DGEMM is always DF/DT. Using the number of DGEMM flops as a basis insteadof the number of LU flops, you get a lower bound on performance of our run by lookingat DMF, which can be compared to Mflops above (It uses the global LU time, but theDGEMM flops are computed under the assumption that the problem is evenly distributedamongst the nodes, as only HPL’s node (0,0) returns any output.)Note that when using the above performance monitoring tools to compare differentHPL.dat inputs, you should beware that the pattern of performance drop off that LUexperiences is sensitive to some of the inputs. For instance, when you try very smallproblems, the performance drop off from the initial values to end values is very rapid. Thelarger the problem, the less the drop off, and it is probably safe to use the first fewperformance values to estimate the difference between a problem size 700000 and701000, for instance. Another factor that influences the performance drop off is the griddimensions (P and Q). For big problems, the performance tends to fall off less from the firstfew steps when P and Q are roughly equal in value. You can make use of a large number ofparameters, such as broadcast types, and change them so that the final performance isdetermined very closely by the first few steps.Using these tools will greatly assist the amount of data you can test.10-11