In this section we present experimental results on comparison of GINV with package JB and Magma (see http://arXiv.org/math.AC/0603161 for references and more details).
The below timing were obtained on the following machines:
Example | Algorithm I | Algorithm I | Algorithm II | Algorithm II | Magma | Magma |
(JB) | (GINV) | high (GINV) | low (GINV) | V2.11-8 | V2.12-17 | |
assur44 | 10.35 | 14.20 | 6.33 | 6.4 | 4.56 | 4.99 |
butcher8 | 1.06 | 1.02 | 0.38 | 0.39 | 4.68 | 5.00 |
chemequs | 0.67 | 0.61 | 0.57 | 0.6 | 12.80 | 11.99 |
chemkin | 17.83 | 16.87 | 10.95 | 9.95 | 32.34 | 29.83 |
cohn3 | 76.72 | 107.14 | 30.21 | 25.47 | 37.73 | 39.20 |
cpdm5 | 1.78 | 1.57 | 1.69 | 1.68 | 0.69 | 0.70 |
cyclic6 | 0.12 | 0.19 | 0.14 | 0.14 | 0.09 | 0.08 |
cyclic7 | 58.72 | 60.94 | 68.59 | 65.28 | 6.64 | 7.08 |
cyclic8 | 12056.24 | 14046.26 | 5826.18 | 4424.96 | 235.73 | 245.65 |
d1 | 8.77 | 12.58 | 1.99 | 2.08 | 28.49 | 8.29 |
des18_3 | 0.19 | 0.18 | 0.19 | 0.19 | 1.81 | 1.89 |
des22_24 | 0.68 | 0.62 | 0.77 | 0.79 | 1.37 | 1.46 |
discret3 | 23322.8 | 20956.31 | 12642.49 | 13521.65 | 33658.09 | 19369.53 |
dl | 270.17 | 278.89 | 80.77 | 89.52 | 14.57 | 11.95 |
eco8 | 0.40 | 0.44 | 0.44 | 0.46 | 0.20 | 0.20 |
eco9 | 3.22 | 5.60 | 4.99 | 5.08 | 1.25 | 1.20 |
eco10 | 52.56 | 56.70 | 65.71 | 68.06 | 7.07 | 6.91 |
eco11 | 765.98 | 741.74 | 718.53 | 679.3 | 62.33 | 51.08 |
extcyc5 | 1.35 | 1.53 | 1.46 | 1.37 | 0.37 | 0.38 |
extcyc6 | 324.70 | 184.49 | 276.06 | 155.64 | 45.36 | 47.96 |
extcyc7 | * | * | * | * | 8242.00 | 8492.13 |
f744 | 4.88 | 7.71 | 2.22 | 2.68 | 1.47 | 1.38 |
f855 | 132.97 | 139.79 | 37.64 | 38.45 | 48.63 | 37.06 |
fabrice24 | 108.52 | 116.77 | 8.2 | 7.7 | 9.45 | 8.70 |
filter9 | 20.97 | 5.76 | 1.13 | 1.6 | 80.04 | 56.67 |
hairer2 | 62.91 | 108.17 | 126.69 | 125.43 | 92.07 | 85.86 |
hairer3 | 1.96 | 0.92 | 0.32 | 1.4 | * | * |
hcyclic7 | 64.17 | 53.87 | 65.81 | 73.0 | 6.26 | 6.76 |
hcyclic8 | 6024.97 | 4316.59 | * | 7560.99 | 229.70 | 237.12 |
hf744 | 22.17 | 8.58 | 7.18 | 11.26 | 1.39 | 1.32 |
hf855 | 2157.88 | 534.08 | 806.51 | 988.38 | 48.15 | 36.69 |
hietarinta1 | 0.77 | 0.71 | 0.38 | 0.53 | 2.63 | 2.15 |
i1 | 98.24 | 122.36 | 58.29 | 58.21 | 55.07 | 42.35 |
ilias13 | 1167.18 | 5851.97 | 3013.1 | 2469.62 | 336.21 | 309.64 |
ilias_k_2 | 323.59 | 669.68 | 445.51 | 270.21 | 55.41 | 54.71 |
ilias_k_3 | 452.32 | 846.19 | 1162.7 | 622.14 | 90.67 | 89.97 |
jcf26 | 224.96 | 211.24 | 16.44 | 14.65 | 31.64 | 25.59 |
katsura7 | 2.15 | 1.77 | 2.08 | 1.98 | 0.72 | 0.79 |
katsura8 | 27.48 | 24.66 | 28.8 | 27.09 | 4.7 | 5.06 |
katsura9 | 337.52 | 294.59 | 340.45 | 311.98 | 33.47 | 34.87 |
katsura10 | 4790.55 | 4983.11 | 7220.29 | 6204.95 | 287.38 | 292.02 |
kin1 | 15.18 | 20.32 | 7.11 | 7.11 | 50.56 | 45.33 |
kotsireas | 6.33 | 37.94 | 4.93 | 4.27 | 3.45 | 3.67 |
noon6 | 0.97 | 1.29 | 1.27 | 1.29 | 0.60 | 0.62 |
noon7 | 28.87 | 32.58 | 37.52 | 38.52 | 4.93 | 4.77 |
noon8 | 1552.26 | 2292.84 | 3322.62 | 3152.57 | 43.65 | 42.80 |
pinchon1 | 10.37 | 0.04 | 0.01 | 0.01 | 4.09 | 3.54 |
rbpl | 210.94 | 177.51 | 173.8 | 173.98 | 38.33 | 35.79 |
rbpl24 | 108.78 | 116.78 | 8.23 | 7.7 | 9.62 | 8.74 |
redcyc6 | 0.16 | 0.17 | 0.13 | 0.14 | 0.10 | 0.10 |
redcyc7 | 913.75 | 1048.69 | 48.19 | 48.61 | 5.73 | 6.36 |
redeco10 | 18.51 | 18.66 | 23.91 | 22.4 | 2.33 | 2.40 |
redeco11 | 178.32 | 187.36 | 253.34 | 228.41 | 14.56 | 14.85 |
redeco12 | 1735.95 | 2172.75 | 4666.8 | 3385.97 | 101.51 | 103.02 |
reimer5 | 0.22 | 0.36 | 0.34 | 0.38 | 0.74 | 0.70 |
reimer6 | 9.69 | 21.60 | 24.19 | 23.96 | 42.13 | 42.40 |
reimer7 | 719.37 | 3808.91 | 4756.4 | 4314.12 | 5216.53 | 5032.73 |
virasoro | 9.69 | 8.90 | 10.96 | 10.68 | 1.72 | 1.77 |