# # Sparse1.3 Timing Comparisons # # # Sparse1.3 is compared to Sparse1.2, Harwell's MA28, and # Yale's YSMP. Comparisons are made based on the time # required to perform each of three tasks: factor the matrix # given an unordered matrix, factor a previously ordered # matrix, and compute the solution to a matrix equation given # a factored matrix. Times were measured on a vax8650 under # Ultrix1.2 and are given in seconds. The last digit of the # given times is uncertain. # # Sparse is configured to use diagonal pivoting with a pivot # threshold of 0.001. It is not using its modified Markowitz # pivoting algorithm. # # YSMP uses a symbolic ordering algorithm that does not take # into account the numerical values in the matrix, which # explains why it failed on the grid10 matrix. As a result, # YSMP cannot be fairly compared with the other packages on # the basis of time required to factor an unordered matrix and # so it was not included in that table. # # Most matrices were generated during the course of computing # the DC operating point or the transient solution of some # circuit using Relax, Advice, or the simulator from Zycad. # The exceptions are mat8; which was taken from a force # directed placement problem; and grid10, grid33, grid66, # karti, and karti2; which were generated when trying to solve # a system of partial differential equations. # # # _____________________________________________________________________ # Order and factor times # _____________________________________________________________________ # matrix size entries/row sp1.3 sp1.2/sp1.3 ma28/sp1.3 # _____________________________________________________________________ # digfi.dc 378 3.85 0.4 0.93 0.74 # eprom 630 4.92 1.32 1.01 0.46 # timem.dc 1957 3.42 2.55 0.93 3.05 # timem.tr 1957 5.08 3.7 0.97 0.36 # zy1137 1137 11.14 8.37 1.05 0.21 # zy3315 3315 4.82 9.07 0.9 0.34 # zy450 450 4.52 0.58 1.24 0.55 # zy1195 1195 6.73 43.18 1.07 1.79 # matrix4000 4000 3.20 29.6 0.99 0.90 # vish 2806 8.36 80.48 1 0.31 # decode06 76 11.26 0.20 1.1 0.4 # decode07 142 13.72 0.72 1.04 0.34 # decode08 272 16.12 2.9 1.08 0.32 # decode09 530 18.42 12.5 1.01 0.21 # decode10 1044 20.64 53.85 0.99 0.19 # adv2806 2806 8.36 74.55 1.01 0.29 # adv3388 3388 11.97 118.22 1 0.08 # adv3776 3776 7.31 82.92 1 0.087 # adv920 920 8.10 6.65 0.94 0.18 # joeyADC.dc 5355 4.63 34.03 1 0.54 # joeyADC.tr 5355 6.02 126.95 0.99 0.2 # mat8 300 13.33 13.73 0.97 0.69 # grid10 100 9.22 0.17 1.08 1 # grid33 1089 4.88 11.18 1.02 2.88 # grid66 4356 4.99 135.48 1.02 5.62 # karti 171 9.39 0.85 1.02 0.72 # karti2 1073 9.20 84.83 1.48 3.24 # _____________________________________________________________________ # # # # # # _______________________________________________________________________________ # Factor times # _______________________________________________________________________________ # matrix size entries/row sp1.3 sp1.2/sp1.3 ma28/sp1.3 ysmp/sp1.3 # _______________________________________________________________________________ # digfi.dc 378 3.85 0.024 1.13 3.52 2.78 # eprom 630 4.92 0.093 1.42 2.7 1.27 # timem.dc 1957 3.42 0.084 1.46 4.79 1.99 # timem.tr 1957 5.08 0.134 1.25 4.35 1.49 # zy1137 1137 11.14 0.206 1.37 7.55 2.11 # zy3315 3315 4.82 0.264 1.35 4.08 1.64 # zy450 450 4.52 0.026 1.27 5 1.92 # zy1195 1195 6.73 2.794 1.66 0.92 6.82 # matrix4000 4000 3.20 5.907 1.38 1.3 0.75 # vish 2806 8.36 4.178 4.06 1.56 0.77 # decode06 76 11.26 0.014 1.93 3.47 1.7 # decode07 142 13.72 0.031 2.26 3.4 1.67 # decode08 272 16.12 0.084 3.51 4.37 1.19 # decode09 530 18.42 0.225 6.06 3.71 0.96 # decode10 1044 20.64 0.565 11.1 3.41 0.94 # adv2806 2806 8.36 4.455 3.54 1.21 0.67 # adv3388 3388 11.97 1.355 2.07 17.2 1.49 # adv3776 3776 7.31 1.612 1.65 9.94 1.16 # adv920 920 8.10 0.150 1.35 12.4 1.35 # joeyADC.dc 5355 4.63 0.250 2.2 6.27 2.73 # joeyADC.tr 5355 6.02 4.370 4.22 1.15 0.84 # mat8 300 13.33 3.961 1.35 0.66 0.77 # grid10 100 9.22 0.012 1.5 3.06 zero pivot # grid33 1089 4.88 1.078 1.65 1.63 0.94 # grid66 4356 4.99 12.03 1.80 2.10 0.85 # karti 171 9.39 0.062 1.42 2.12 1.34 # karti2 1073 9.20 11.14 2.09 0.77 1.05 # _______________________________________________________________________________ # # # # # # _______________________________________________________________________________ # Solve times # _______________________________________________________________________________ # matrix size entries/row sp1.3 sp1.2/sp1.3 ma28/sp1.3 ysmp/sp1.3 # _______________________________________________________________________________ # digfi.dc 378 3.85 0.011 1.36 1.5 0 # eprom 630 4.92 0.019 1.05 1.3 0.94 # timem.dc 1957 3.42 0.04 0.93 2.24 0.87 # timem.tr 1957 5.08 0.04 1.08 2.05 1.68 # zy1137 1137 11.14 0.037 1.03 2 1.52 # zy3315 3315 4.82 0.072 1.11 1.79 1.39 # zy450 450 4.52 0.008 0.88 2.57 0 # zy1195 1195 6.73 0.081 1.17 1.43 3.7 # matrix4000 4000 3.20 0.16 1.13 2.14 1.04 # vish 2806 8.36 0.297 1.01 0.92 0.62 # decode06 76 11.26 0.002 0 1.33 0 # decode07 142 13.72 0.005 2 3.33 5.67 # decode08 272 16.12 0.016 0.82 1.2 1.31 # decode09 530 18.42 0.035 0.71 1.27 1.22 # decode10 1044 20.64 0.073 0.79 1.28 1.06 # adv2806 2806 8.36 0.147 1.09 1.43 0.90 # adv3388 3388 11.97 0.122 1.12 1.89 1.37 # adv3776 3776 7.31 0.138 1.12 1.41 1.33 # adv920 920 8.10 0.023 1.23 1.85 2.17 # joeyADC.dc 5355 4.63 0.1 0.83 1.67 1.5 # joeyADC.tr 5355 6.02 0.233 1.0 1.21 1.07 # mat8 300 13.33 0.108 1.04 0.6 0.62 # grid10 100 9.22 0.005 0.6 3.5 zero pivot # grid33 1089 4.88 0.057 1.28 1.95 1.75 # grid66 4356 4.99 0.34 1.29 1.70 1.27 # karti 171 9.39 0.017 1 0.77 1.31 # karti2 1073 9.20 0.173 1.92 1.04 1.65 # _______________________________________________________________________________