http://www.maths.qmul.ac.uk/~ev/flagmatic/transcripts/maxs3.txtgmatic version 1.5 ============================================================================ Optimizing for density of 3:1213. Using admissible graphs of order 3. Generated 1 type of order 1, with 3 flags of order 2. Generated 7 admissible graphs. $ ./sdpa_dd -ds output/maxs3/flags.dat-s -o output/maxs3/sdpa.out SDPA-DD start at Thu Feb 23 16:27:22 2012 data is output/maxs3/flags.dat-s : sparse out is output/maxs3/sdpa.out set is DEFAULT DENSE computations mu thetaP thetaD objP objD alphaP alphaD beta 0 1.0e+08 1.0e+00 1.0e+00 -0.00e+00 -1.00e+04 8.3e-01 9.0e-01 3.00e-01 1 2.5e+07 1.7e-01 1.0e-01 +1.40e+04 -2.04e+04 8.3e-01 9.0e-01 3.00e-01 2 6.3e+06 2.8e-02 9.9e-03 +2.73e+04 -3.17e+04 8.9e-01 9.1e-01 3.00e-01 3 1.0e+06 3.0e-03 9.0e-04 +6.06e+04 -4.82e+04 9.0e-01 1.0e+00 3.00e-01 4 1.7e+05 3.1e-04 2.8e-31 +1.03e+05 -7.54e+04 9.1e-01 1.0e+00 3.00e-01 5 3.6e+04 2.8e-05 3.6e-31 +5.61e+04 -1.11e+05 9.9e-01 1.0e+00 3.00e-01 6 1.0e+04 2.2e-07 2.4e-31 +1.10e+04 -1.08e+05 1.0e+00 1.0e+00 3.00e-01 7 3.0e+03 5.0e-33 9.1e-32 +3.02e+03 -3.33e+04 1.0e+00 1.0e+00 3.00e-01 8 9.1e+02 2.5e-33 3.1e-32 +9.08e+02 -9.99e+03 1.0e+00 1.0e+00 3.00e-01 9 2.7e+02 3.2e-34 1.1e-32 +2.72e+02 -3.00e+03 1.0e+00 1.0e+00 3.00e-01 10 8.2e+01 1.6e-34 2.4e-33 +8.16e+01 -8.99e+02 1.0e+00 1.0e+00 3.00e-01 11 2.5e+01 5.9e-35 9.5e-34 +2.44e+01 -2.70e+02 1.3e+00 1.0e+00 3.00e-01 12 6.9e+00 7.9e-35 3.5e-34 +2.32e+00 -8.10e+01 6.0e+00 1.0e+00 3.00e-01 13 1.9e+00 7.8e-35 8.9e-35 +1.03e-01 -2.31e+01 1.0e+00 1.0e+00 3.00e-01 14 5.8e-01 7.8e-35 1.5e-35 +4.35e-01 -6.51e+00 1.0e+00 9.1e-01 1.00e-01 15 1.0e-01 7.7e-35 1.3e-35 -1.19e-01 -1.35e+00 9.5e-01 7.8e-01 1.00e-01 16 2.7e-02 7.7e-35 4.6e-36 -3.38e-01 -6.67e-01 9.6e-01 9.1e-01 1.00e-01 17 4.5e-03 7.7e-35 1.0e-35 -4.43e-01 -4.96e-01 9.6e-01 9.7e-01 1.00e-01 18 6.0e-04 7.7e-35 1.6e-36 -4.61e-01 -4.68e-01 9.9e-01 9.8e-01 1.00e-01 19 6.6e-05 7.8e-35 1.5e-35 -4.64e-01 -4.65e-01 1.0e+00 9.9e-01 1.00e-01 20 6.9e-06 7.7e-35 7.8e-36 -4.64e-01 -4.64e-01 1.0e+00 9.9e-01 1.00e-01 21 6.9e-07 7.8e-35 1.8e-35 -4.64e-01 -4.64e-01 1.0e+00 9.9e-01 1.00e-01 22 6.9e-08 7.8e-35 1.1e-35 -4.64e-01 -4.64e-01 1.0e+00 9.9e-01 1.00e-01 23 6.9e-09 7.8e-35 3.9e-35 -4.64e-01 -4.64e-01 1.0e+00 9.9e-01 1.00e-01 24 6.9e-10 7.8e-35 9.3e-35 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 25 1.4e-10 7.8e-35 1.1e-34 -4.64e-01 -4.64e-01 2.4e+00 1.0e+00 3.00e-01 26 2.4e-11 7.8e-35 1.1e-34 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 27 7.1e-12 7.8e-35 1.4e-33 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 28 1.4e-12 7.8e-35 3.8e-34 -4.64e-01 -4.64e-01 2.2e+00 1.0e+00 3.00e-01 29 2.5e-13 7.8e-35 9.3e-34 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 30 7.5e-14 7.8e-35 8.6e-33 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 31 1.5e-14 7.8e-35 1.2e-33 -4.64e-01 -4.64e-01 2.2e+00 1.0e+00 3.00e-01 32 2.6e-15 7.8e-35 2.0e-33 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 33 7.9e-16 7.8e-35 5.9e-33 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 34 1.6e-16 7.8e-35 3.6e-33 -4.64e-01 -4.64e-01 2.2e+00 1.0e+00 3.00e-01 35 2.8e-17 7.8e-35 5.3e-33 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 36 8.3e-18 7.8e-35 1.9e-32 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 37 1.7e-18 7.8e-35 9.1e-33 -4.64e-01 -4.64e-01 2.2e+00 1.0e+00 3.00e-01 38 2.9e-19 7.8e-35 8.5e-33 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 39 8.7e-20 7.8e-35 2.8e-32 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 40 1.7e-20 7.8e-35 1.2e-31 -4.64e-01 -4.64e-01 2.2e+00 1.0e+00 3.00e-01 41 3.0e-21 7.8e-35 5.5e-32 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 42 9.1e-22 7.8e-35 8.3e-32 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 43 1.8e-22 7.8e-35 5.6e-32 -4.64e-01 -4.64e-01 2.3e+00 1.0e+00 3.00e-01 44 3.2e-23 7.8e-35 2.0e-31 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 45 9.6e-24 7.8e-35 4.1e-31 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 46 1.9e-24 7.7e-35 1.2e-31 -4.64e-01 -4.64e-01 2.2e+00 1.0e+00 3.00e-01 47 3.3e-25 7.8e-35 1.0e-31 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 3.00e-01 48 1.0e-25 7.8e-35 7.2e-31 -4.64e-01 -4.64e-01 1.3e+00 1.0e+00 3.00e-01 49 2.0e-26 7.8e-35 1.0e-30 -4.64e-01 -4.64e-01 2.3e+00 1.0e+00 3.00e-01 50 3.5e-27 7.7e-35 6.9e-31 -4.64e-01 -4.64e-01 7.6e-01 7.6e-01 3.00e-01 51 1.5e-27 7.8e-35 8.3e-31 -4.64e-01 -4.64e-01 1.6e+00 1.0e+00 3.00e-01 52 5.5e-28 7.8e-35 3.9e-30 -4.64e-01 -4.64e-01 3.6e-01 3.6e-01 3.00e-01 53 2.4e-28 7.8e-35 3.1e-30 -4.64e-01 -4.64e-01 1.0e+00 1.0e+00 7.53e+00 54 2.3e-26 7.8e-35 5.2e-28 -4.64e-01 -4.64e-01 9.2e-01 9.2e-01 3.00e-01 55 7.9e-27 7.8e-35 4.1e-29 -4.64e-01 -4.64e-01 1.4e+00 8.6e-01 3.00e-01 56 1.7e-27 7.8e-35 4.7e-30 -4.64e-01 -4.64e-01 3.1e+01 1.0e+00 3.54e-01 57 3.6e-28 7.7e-35 3.5e-31 -4.64e-01 -4.64e-01 2.4e-02 2.4e-02 3.00e-01 58 2.9e-28 7.8e-35 1.1e-30 -4.64e-01 -4.64e-01 5.0e-05 5.0e-05 2.24e+01 Step length is too small. :: line 182 in sdpa_dataset.cpp cannot move :: line 400 in sdpa_main.cpp 58 2.9e-28 7.8e-35 1.1e-30 -4.64e-01 -4.64e-01 5.0e-05 5.0e-05 2.24e+01 phase.value = pFEAS Iteration = 58 mu = 2.9160772130272425e-28 relative gap = 9.3706475815270728e-27 gap = 3.4992926556326910e-27 digits = 2.5694843474918880e+01 objValPrimal = -4.64101615137754587054892682623968e-01 objValDual = -4.64101615137754587054892691994620e-01 p.feas.error = 7.7863149643200082e-31 d.feas.error = 2.9834727337350789e-26 relative eps = 4.9303806576313200e-32 total time = 0.010 main loop time = 0.010000 total time = 0.010000 file read time = 0.000000 $ sage -python scripts/convert_sdpa_output.py output/maxs3/sdpa.out output/maxs3/flags.out $ sage -python scripts/find_sharp_graphs.py --dir output/maxs3 Floating point bound is 0.464101615137800017. 4 members of H are sharp. 0.464101615137800017 : graph 1 (3:) 0.464101615137733403 : graph 3 (3:1213) 0.464101615137666679 : graph 5 (3:1232) 0.464101615137666679 : graph 6 (3:121323) Written sharp graphs to flags.py $ sage -python scripts/make_zero_eigenvectors.py maxs3 --dir output/maxs3 [?1034hConstructed 2 out of 2 zero eigenvectors for type 1. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/maxs3 [?1034hFloating point bound is 0.464101615137800017. Type 1: smallest eigenvalue is 7.425625842203436910 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '4*x-1' --denominator 2 --dir output/maxs3 --diagonalize [?1034hType 1: smallest eigenvalue is 7.425625842204070182 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/maxs3 [?1034h[True] Written q.py Floating point bound (non-sharp graphs) is 0.000000000000000000 Exact bound (just sharp graphs) is 4*x - 1 Bound (all graphs) is 4*x - 1 $ sage -python scripts/make_certificate.py --dir output/maxs3 Written certificate to cert.js