GS510

Assignment 2-- Fall 2000

3. Let A and B be square matrices of order N defined as follows:

A = [a_ij] is the Hilbert matrix with a_ij = 1/(i + j -1). Note that A is symmetric, A = A^T.

B = [b_ij] with the lower triangular part of B given by b_ij = (N + 1 - i)*j/(N + 1). Define the remainder of B so that B is symmetric, ie. b_ij = b_ji for i,j = 1,2,...,N.

For N-values of N = 32*k, k = 2,3,...,16, calculate a megaflop rate for each version of the matrix multiply code.

For this experiment to be meaningful, all arrays must be tightly dimensioned. You can expedite the collection of the N values and corresponding megaflop rates by doing the following:

• compile your code with N = 64(for example "cc -xO3 mm.c" on stokes)
• execute and direct output to a file (mat.dat) with the command a.out > mat.dat
• edit the N value to be 64
• execute and append output to mat.dat with the command a.out >> mat.dat
• edit the N value to be 96
• continue to append output to mat.dat with the command !a (pronounced "bang a")

Once you have recorded the megaflop rates for both versions for all the above N values, use aa graph to display the results of your numerical experiment.

Comment on how cache misses vary with N and with stride.

Turn in your two matrix multiply codes and hardcopy of your plots. On your plot, specify which matrix multiply algorithm is used and which compiler flag(s) you used.

Task 2:

Set N = 513 in your standard matrix multiply code (the one that doesn't rely on the symmetry of either of the matrices) and record six matrix multply times for the six possible nestings of the loops in the matrix multiply algorithm. Comment on the results of this experiment.