HPL benchmarks (8 nodes)

Using the parameters obtained from the 9-node tests, and only testing the grid size the following initial 8-node HPL results were obtained. Top performance was 9.2 Gflops.

A more exhaustive test with variable NB, BCAST, problem size (shown below), indicated that best results were obtained for NB=120, BCAST=3, a 4x2 grid and (of course) the largest problem size :

============================================================================ HPLinpack 1.0a -- High-Performance Linpack benchmark -- January 20, 2004 Written by A. Petitet and R. Clint Whaley, Innovative Computing Labs., UTK ============================================================================ An explanation of the input/output parameters follows: T/V : Wall time / encoded variant. N : The order of the coefficient matrix A. NB : The partitioning blocking factor. P : The number of process rows. Q : The number of process columns. Time : Time in seconds to solve the linear system. Gflops : Rate of execution for solving the linear system. The following parameter values will be used: N : 10240 10752 11264 11776 12288 12800 13312 13824 14336 NB : 40 50 60 80 120 PMAP : Row-major process mapping P : 4 2 Q : 2 4 PFACT : Crout NBMIN : 8 NDIV : 2 RFACT : Right BCAST : 1ring 1ringM 2ring 2ringM Blong BlongM DEPTH : 0 SWAP : Mix (threshold = 60) L1 : transposed form U : transposed form EQUIL : yes ALIGN : 8 double precision words ---------------------------------------------------------------------------- - The matrix A is randomly generated for each test. - The following scaled residual checks will be computed: 1) ||Ax-b||_oo / ( eps * ||A||_1 * N ) 2) ||Ax-b||_oo / ( eps * ||A||_1 * ||x||_1 ) 3) ||Ax-b||_oo / ( eps * ||A||_oo * ||x||_oo ) - The relative machine precision (eps) is taken to be 1.110223e-16 - Computational tests pass if scaled residuals are less than 16.0 ============================================================================ T/V N NB P Q Time Gflops ---------------------------------------------------------------------------- WR00R2C8 10240 40 4 2 100.08 7.154e+00 WR01R2C8 10240 40 4 2 99.31 7.210e+00 WR02R2C8 10240 40 4 2 99.14 7.222e+00 WR03R2C8 10240 40 4 2 100.04 7.157e+00 WR04R2C8 10240 40 4 2 103.43 6.923e+00 WR05R2C8 10240 40 4 2 99.82 7.173e+00 WR00R2C8 10240 50 4 2 99.09 7.226e+00 WR01R2C8 10240 50 4 2 98.61 7.260e+00 WR02R2C8 10240 50 4 2 98.45 7.273e+00 WR03R2C8 10240 50 4 2 98.95 7.236e+00 WR04R2C8 10240 50 4 2 102.65 6.975e+00 WR05R2C8 10240 50 4 2 98.38 7.278e+00 WR00R2C8 10240 60 4 2 104.58 6.846e+00 WR01R2C8 10240 60 4 2 103.87 6.893e+00 WR02R2C8 10240 60 4 2 104.07 6.880e+00 WR03R2C8 10240 60 4 2 104.44 6.855e+00 WR04R2C8 10240 60 4 2 108.35 6.608e+00 WR05R2C8 10240 60 4 2 104.36 6.861e+00 WR00R2C8 10240 80 4 2 102.94 6.955e+00 WR01R2C8 10240 80 4 2 103.02 6.950e+00 WR02R2C8 10240 80 4 2 103.25 6.934e+00 WR03R2C8 10240 80 4 2 102.85 6.961e+00 WR04R2C8 10240 80 4 2 107.77 6.643e+00 WR05R2C8 10240 80 4 2 103.49 6.918e+00 WR00R2C8 10240 120 4 2 103.31 6.931e+00 WR01R2C8 10240 120 4 2 103.06 6.948e+00 WR02R2C8 10240 120 4 2 103.94 6.888e+00 WR03R2C8 10240 120 4 2 103.26 6.934e+00 WR04R2C8 10240 120 4 2 107.56 6.657e+00 WR05R2C8 10240 120 4 2 103.45 6.921e+00 WR00R2C8 10752 40 4 2 108.73 7.623e+00 WR01R2C8 10752 40 4 2 108.88 7.612e+00 WR02R2C8 10752 40 4 2 109.08 7.599e+00 WR03R2C8 10752 40 4 2 108.83 7.616e+00 WR04R2C8 10752 40 4 2 113.77 7.285e+00 WR05R2C8 10752 40 4 2 108.71 7.624e+00 WR00R2C8 10752 50 4 2 110.32 7.513e+00 WR01R2C8 10752 50 4 2 110.89 7.474e+00 WR02R2C8 10752 50 4 2 110.23 7.519e+00 WR03R2C8 10752 50 4 2 111.42 7.439e+00 WR04R2C8 10752 50 4 2 115.20 7.195e+00 WR05R2C8 10752 50 4 2 110.61 7.493e+00 WR00R2C8 10752 60 4 2 109.99 7.535e+00 WR01R2C8 10752 60 4 2 109.24 7.587e+00 WR02R2C8 10752 60 4 2 109.09 7.597e+00 WR03R2C8 10752 60 4 2 109.73 7.554e+00 WR04R2C8 10752 60 4 2 114.01 7.270e+00 WR05R2C8 10752 60 4 2 109.53 7.567e+00 WR00R2C8 10752 80 4 2 111.35 7.444e+00 WR01R2C8 10752 80 4 2 111.41 7.440e+00 WR02R2C8 10752 80 4 2 111.73 7.418e+00 WR03R2C8 10752 80 4 2 111.30 7.447e+00 WR04R2C8 10752 80 4 2 115.94 7.149e+00 WR05R2C8 10752 80 4 2 112.09 7.394e+00 WR00R2C8 10752 120 4 2 109.88 7.543e+00 WR01R2C8 10752 120 4 2 111.10 7.460e+00 WR02R2C8 10752 120 4 2 109.98 7.536e+00 WR03R2C8 10752 120 4 2 109.94 7.539e+00 WR04R2C8 10752 120 4 2 115.25 7.192e+00 WR05R2C8 10752 120 4 2 110.16 7.524e+00 WR00R2C8 11264 40 4 2 121.90 7.818e+00 WR01R2C8 11264 40 4 2 121.77 7.826e+00 WR02R2C8 11264 40 4 2 121.64 7.835e+00 WR03R2C8 11264 40 4 2 121.90 7.818e+00 WR04R2C8 11264 40 4 2 126.58 7.529e+00 WR05R2C8 11264 40 4 2 121.94 7.815e+00 WR00R2C8 11264 50 4 2 126.12 7.556e+00 WR01R2C8 11264 50 4 2 125.90 7.569e+00 WR02R2C8 11264 50 4 2 126.81 7.515e+00 WR03R2C8 11264 50 4 2 126.37 7.541e+00 WR04R2C8 11264 50 4 2 131.88 7.226e+00 WR05R2C8 11264 50 4 2 125.93 7.568e+00 WR00R2C8 11264 60 4 2 123.41 7.722e+00 WR01R2C8 11264 60 4 2 123.48 7.718e+00 WR02R2C8 11264 60 4 2 123.12 7.740e+00 WR03R2C8 11264 60 4 2 124.02 7.684e+00 WR04R2C8 11264 60 4 2 128.64 7.408e+00 WR05R2C8 11264 60 4 2 123.81 7.697e+00 WR00R2C8 11264 80 4 2 122.15 7.802e+00 WR01R2C8 11264 80 4 2 122.18 7.799e+00 WR02R2C8 11264 80 4 2 122.77 7.762e+00 WR03R2C8 11264 80 4 2 122.36 7.788e+00 WR04R2C8 11264 80 4 2 127.66 7.465e+00 WR05R2C8 11264 80 4 2 122.27 7.794e+00 WR00R2C8 11264 120 4 2 123.24 7.732e+00 WR01R2C8 11264 120 4 2 122.67 7.769e+00 WR02R2C8 11264 120 4 2 122.98 7.749e+00 WR03R2C8 11264 120 4 2 122.72 7.765e+00 WR04R2C8 11264 120 4 2 128.24 7.431e+00 WR05R2C8 11264 120 4 2 123.00 7.747e+00 WR00R2C8 11776 40 4 2 135.73 8.022e+00 WR01R2C8 11776 40 4 2 135.76 8.021e+00 WR02R2C8 11776 40 4 2 135.68 8.026e+00 WR03R2C8 11776 40 4 2 135.90 8.013e+00 WR04R2C8 11776 40 4 2 141.09 7.718e+00 WR05R2C8 11776 40 4 2 135.53 8.035e+00 WR00R2C8 11776 50 4 2 142.74 7.628e+00 WR01R2C8 11776 50 4 2 142.60 7.636e+00 WR02R2C8 11776 50 4 2 143.25 7.601e+00 WR03R2C8 11776 50 4 2 142.45 7.644e+00 WR04R2C8 11776 50 4 2 148.33 7.341e+00 WR05R2C8 11776 50 4 2 142.02 7.667e+00 WR00R2C8 11776 60 4 2 134.58 8.091e+00 WR01R2C8 11776 60 4 2 134.55 8.093e+00 WR02R2C8 11776 60 4 2 134.87 8.074e+00 WR03R2C8 11776 60 4 2 134.42 8.101e+00 WR04R2C8 11776 60 4 2 140.37 7.758e+00 WR05R2C8 11776 60 4 2 134.49 8.097e+00 WR00R2C8 11776 80 4 2 135.91 8.012e+00 WR01R2C8 11776 80 4 2 135.64 8.028e+00 WR02R2C8 11776 80 4 2 136.47 7.979e+00 WR03R2C8 11776 80 4 2 135.56 8.033e+00 WR04R2C8 11776 80 4 2 141.31 7.706e+00 WR05R2C8 11776 80 4 2 135.58 8.031e+00 WR00R2C8 11776 120 4 2 134.99 8.067e+00 WR01R2C8 11776 120 4 2 135.32 8.047e+00 WR02R2C8 11776 120 4 2 135.38 8.043e+00 WR03R2C8 11776 120 4 2 135.85 8.016e+00 WR04R2C8 11776 120 4 2 141.03 7.721e+00 WR05R2C8 11776 120 4 2 135.54 8.034e+00 WR00R2C8 12288 40 4 2 150.07 8.244e+00 WR01R2C8 12288 40 4 2 150.61 8.215e+00 WR02R2C8 12288 40 4 2 149.94 8.251e+00 WR03R2C8 12288 40 4 2 151.28 8.178e+00 WR04R2C8 12288 40 4 2 156.34 7.913e+00 WR05R2C8 12288 40 4 2 156.88 7.886e+00 WR00R2C8 12288 50 4 2 150.39 8.227e+00 WR01R2C8 12288 50 4 2 151.09 8.188e+00 WR02R2C8 12288 50 4 2 149.88 8.254e+00 WR03R2C8 12288 50 4 2 150.48 8.222e+00 WR04R2C8 12288 50 4 2 156.08 7.926e+00 WR05R2C8 12288 50 4 2 150.59 8.216e+00 WR00R2C8 12288 60 4 2 149.82 8.258e+00 WR01R2C8 12288 60 4 2 150.47 8.222e+00 WR02R2C8 12288 60 4 2 150.52 8.219e+00 WR03R2C8 12288 60 4 2 150.06 8.245e+00 WR04R2C8 12288 60 4 2 156.01 7.930e+00 WR05R2C8 12288 60 4 2 150.47 8.222e+00 WR00R2C8 12288 80 4 2 150.41 8.225e+00 WR01R2C8 12288 80 4 2 150.34 8.229e+00 WR02R2C8 12288 80 4 2 150.71 8.209e+00 WR03R2C8 12288 80 4 2 150.56 8.217e+00 WR04R2C8 12288 80 4 2 156.79 7.891e+00 WR05R2C8 12288 80 4 2 150.01 8.247e+00 WR00R2C8 12288 120 4 2 153.50 8.060e+00 WR01R2C8 12288 120 4 2 153.70 8.049e+00 WR02R2C8 12288 120 4 2 154.11 8.028e+00 WR03R2C8 12288 120 4 2 152.40 8.118e+00 WR04R2C8 12288 120 4 2 159.96 7.734e+00 WR05R2C8 12288 120 4 2 153.02 8.085e+00 WR00R2C8 12800 40 4 2 164.89 8.481e+00 WR01R2C8 12800 40 4 2 164.42 8.505e+00 WR02R2C8 12800 40 4 2 165.11 8.469e+00 WR03R2C8 12800 40 4 2 164.38 8.507e+00 WR04R2C8 12800 40 4 2 171.66 8.146e+00 WR05R2C8 12800 40 4 2 164.97 8.476e+00 WR00R2C8 12800 50 4 2 166.10 8.419e+00 WR01R2C8 12800 50 4 2 167.88 8.330e+00 WR02R2C8 12800 50 4 2 166.68 8.389e+00 WR03R2C8 12800 50 4 2 166.87 8.380e+00 WR04R2C8 12800 50 4 2 172.49 8.107e+00 WR05R2C8 12800 50 4 2 166.72 8.388e+00 WR00R2C8 12800 60 4 2 169.33 8.258e+00 WR01R2C8 12800 60 4 2 169.09 8.270e+00 WR02R2C8 12800 60 4 2 169.50 8.250e+00 WR03R2C8 12800 60 4 2 169.40 8.255e+00 WR04R2C8 12800 60 4 2 175.70 7.959e+00 WR05R2C8 12800 60 4 2 169.13 8.268e+00 WR00R2C8 12800 80 4 2 164.49 8.501e+00 WR01R2C8 12800 80 4 2 163.81 8.536e+00 WR02R2C8 12800 80 4 2 163.57 8.549e+00 WR03R2C8 12800 80 4 2 164.10 8.521e+00 WR04R2C8 12800 80 4 2 170.33 8.209e+00 WR05R2C8 12800 80 4 2 164.17 8.518e+00 WR00R2C8 12800 120 4 2 166.25 8.411e+00 WR01R2C8 12800 120 4 2 166.86 8.380e+00 WR02R2C8 12800 120 4 2 166.05 8.421e+00 WR03R2C8 12800 120 4 2 166.51 8.398e+00 WR04R2C8 12800 120 4 2 174.21 8.027e+00 WR05R2C8 12800 120 4 2 166.42 8.403e+00 WR00R2C8 13312 40 4 2 182.14 8.636e+00 WR01R2C8 13312 40 4 2 181.57 8.663e+00 WR02R2C8 13312 40 4 2 182.97 8.597e+00 WR03R2C8 13312 40 4 2 182.21 8.633e+00 WR04R2C8 13312 40 4 2 188.70 8.336e+00 WR05R2C8 13312 40 4 2 182.53 8.617e+00 WR00R2C8 13312 50 4 2 193.00 8.150e+00 WR01R2C8 13312 50 4 2 194.17 8.101e+00 WR02R2C8 13312 50 4 2 193.99 8.108e+00 WR03R2C8 13312 50 4 2 193.12 8.145e+00 WR04R2C8 13312 50 4 2 201.48 7.807e+00 WR05R2C8 13312 50 4 2 193.43 8.132e+00 WR00R2C8 13312 60 4 2 186.64 8.428e+00 WR01R2C8 13312 60 4 2 187.37 8.395e+00 WR02R2C8 13312 60 4 2 187.34 8.396e+00 WR03R2C8 13312 60 4 2 186.33 8.442e+00 WR04R2C8 13312 60 4 2 194.96 8.068e+00 WR05R2C8 13312 60 4 2 187.33 8.397e+00 WR00R2C8 13312 80 4 2 185.13 8.496e+00 WR01R2C8 13312 80 4 2 185.25 8.491e+00 WR02R2C8 13312 80 4 2 185.70 8.470e+00 WR03R2C8 13312 80 4 2 185.00 8.502e+00 WR04R2C8 13312 80 4 2 192.54 8.170e+00 WR05R2C8 13312 80 4 2 185.26 8.490e+00 WR00R2C8 13312 120 4 2 184.79 8.512e+00 WR01R2C8 13312 120 4 2 184.28 8.536e+00 WR02R2C8 13312 120 4 2 184.87 8.508e+00 WR03R2C8 13312 120 4 2 186.12 8.451e+00 WR04R2C8 13312 120 4 2 191.80 8.201e+00 WR05R2C8 13312 120 4 2 184.01 8.548e+00 WR00R2C8 13824 40 4 2 197.76 8.907e+00 WR01R2C8 13824 40 4 2 197.72 8.909e+00 WR02R2C8 13824 40 4 2 197.33 8.926e+00 WR03R2C8 13824 40 4 2 198.01 8.896e+00 WR04R2C8 13824 40 4 2 205.28 8.581e+00 WR05R2C8 13824 40 4 2 197.80 8.905e+00 WR00R2C8 13824 50 4 2 199.92 8.811e+00 WR01R2C8 13824 50 4 2 199.54 8.828e+00 WR02R2C8 13824 50 4 2 199.03 8.850e+00 WR03R2C8 13824 50 4 2 199.96 8.809e+00 WR04R2C8 13824 50 4 2 207.45 8.491e+00 WR05R2C8 13824 50 4 2 199.16 8.844e+00 WR00R2C8 13824 60 4 2 201.32 8.750e+00 WR01R2C8 13824 60 4 2 201.20 8.755e+00 WR02R2C8 13824 60 4 2 201.45 8.744e+00 WR03R2C8 13824 60 4 2 201.26 8.752e+00 WR04R2C8 13824 60 4 2 208.85 8.434e+00 WR05R2C8 13824 60 4 2 201.12 8.758e+00 WR00R2C8 13824 80 4 2 196.77 8.952e+00 WR01R2C8 13824 80 4 2 196.84 8.949e+00 WR02R2C8 13824 80 4 2 196.41 8.969e+00 WR03R2C8 13824 80 4 2 196.14 8.981e+00 WR04R2C8 13824 80 4 2 204.42 8.617e+00 WR05R2C8 13824 80 4 2 196.92 8.945e+00 WR00R2C8 13824 120 4 2 196.86 8.948e+00 WR01R2C8 13824 120 4 2 197.78 8.906e+00 WR02R2C8 13824 120 4 2 196.43 8.968e+00 WR03R2C8 13824 120 4 2 196.60 8.960e+00 WR04R2C8 13824 120 4 2 204.83 8.600e+00 WR05R2C8 13824 120 4 2 196.44 8.967e+00 WR00R2C8 14336 40 4 2 216.63 9.069e+00 WR01R2C8 14336 40 4 2 217.12 9.048e+00 WR02R2C8 14336 40 4 2 217.46 9.034e+00 WR03R2C8 14336 40 4 2 216.37 9.079e+00 WR04R2C8 14336 40 4 2 224.95 8.733e+00 WR05R2C8 14336 40 4 2 217.03 9.052e+00 WR00R2C8 14336 50 4 2 219.30 8.958e+00 WR01R2C8 14336 50 4 2 218.71 8.982e+00 WR02R2C8 14336 50 4 2 218.59 8.987e+00 WR03R2C8 14336 50 4 2 218.88 8.975e+00 WR04R2C8 14336 50 4 2 227.77 8.625e+00 WR05R2C8 14336 50 4 2 218.72 8.982e+00 WR00R2C8 14336 60 4 2 214.32 9.166e+00 WR01R2C8 14336 60 4 2 214.78 9.147e+00 WR02R2C8 14336 60 4 2 214.24 9.170e+00 WR03R2C8 14336 60 4 2 214.17 9.173e+00 WR04R2C8 14336 60 4 2 222.77 8.819e+00 WR05R2C8 14336 60 4 2 215.08 9.134e+00 WR00R2C8 14336 80 4 2 215.14 9.132e+00 WR01R2C8 14336 80 4 2 214.28 9.168e+00 WR02R2C8 14336 80 4 2 215.71 9.107e+00 WR03R2C8 14336 80 4 2 215.11 9.133e+00 WR04R2C8 14336 80 4 2 223.95 8.772e+00 WR05R2C8 14336 80 4 2 215.11 9.133e+00 WR00R2C8 14336 120 4 2 216.28 9.083e+00 WR01R2C8 14336 120 4 2 213.99 9.180e+00 WR02R2C8 14336 120 4 2 215.15 9.131e+00 WR03R2C8 14336 120 4 2 213.85 9.187e+00 WR04R2C8 14336 120 4 2 223.56 8.788e+00 WR05R2C8 14336 120 4 2 214.42 9.162e+00 WR00R2C8 10240 40 2 4 106.50 6.723e+00 WR01R2C8 10240 40 2 4 106.15 6.745e+00 WR02R2C8 10240 40 2 4 106.43 6.727e+00 WR03R2C8 10240 40 2 4 106.06 6.751e+00 WR04R2C8 10240 40 2 4 97.22 7.365e+00 WR05R2C8 10240 40 2 4 117.45 6.096e+00 WR00R2C8 10240 50 2 4 108.51 6.598e+00 WR01R2C8 10240 50 2 4 108.88 6.576e+00 WR02R2C8 10240 50 2 4 108.56 6.595e+00 WR03R2C8 10240 50 2 4 108.70 6.587e+00 WR04R2C8 10240 50 2 4 102.24 7.003e+00 WR05R2C8 10240 50 2 4 119.65 5.984e+00 WR00R2C8 10240 60 2 4 105.93 6.759e+00 WR01R2C8 10240 60 2 4 106.02 6.753e+00 WR02R2C8 10240 60 2 4 105.56 6.783e+00 WR03R2C8 10240 60 2 4 105.52 6.785e+00 WR04R2C8 10240 60 2 4 98.33 7.282e+00 WR05R2C8 10240 60 2 4 117.25 6.107e+00 WR00R2C8 10240 80 2 4 108.63 6.591e+00 WR01R2C8 10240 80 2 4 108.36 6.607e+00 WR02R2C8 10240 80 2 4 108.04 6.627e+00 WR03R2C8 10240 80 2 4 108.10 6.623e+00 WR04R2C8 10240 80 2 4 101.24 7.072e+00 WR05R2C8 10240 80 2 4 119.66 5.983e+00 WR00R2C8 10240 120 2 4 103.91 6.891e+00 WR01R2C8 10240 120 2 4 103.69 6.905e+00 WR02R2C8 10240 120 2 4 104.26 6.867e+00 WR03R2C8 10240 120 2 4 104.33 6.863e+00 WR04R2C8 10240 120 2 4 97.90 7.313e+00 WR05R2C8 10240 120 2 4 115.83 6.181e+00 WR00R2C8 10752 40 2 4 119.26 6.950e+00 WR01R2C8 10752 40 2 4 118.96 6.967e+00 WR02R2C8 10752 40 2 4 118.94 6.969e+00 WR03R2C8 10752 40 2 4 119.01 6.965e+00 WR04R2C8 10752 40 2 4 109.03 7.602e+00 WR05R2C8 10752 40 2 4 130.90 6.332e+00 WR00R2C8 10752 50 2 4 123.27 6.723e+00 WR01R2C8 10752 50 2 4 123.32 6.721e+00 WR02R2C8 10752 50 2 4 122.96 6.741e+00 WR03R2C8 10752 50 2 4 123.00 6.739e+00 WR04R2C8 10752 50 2 4 113.41 7.309e+00 WR05R2C8 10752 50 2 4 135.75 6.106e+00 WR00R2C8 10752 60 2 4 119.80 6.918e+00 WR01R2C8 10752 60 2 4 119.39 6.943e+00 WR02R2C8 10752 60 2 4 120.07 6.903e+00 WR03R2C8 10752 60 2 4 119.21 6.953e+00 WR04R2C8 10752 60 2 4 109.84 7.546e+00 WR05R2C8 10752 60 2 4 132.24 6.268e+00 WR00R2C8 10752 80 2 4 117.15 7.075e+00 WR01R2C8 10752 80 2 4 117.18 7.073e+00 WR02R2C8 10752 80 2 4 116.70 7.102e+00