$ ./flagmatic --n 7 --forbid-k4- --verbose --dir output/k4-
flagmatic version 0.91
============================================================================
Using directory output/k4-
Forbidding 4.3
Using admissible graphs of order 7.
Generating types and flags...
Generated 1 type of order 1, with 5 flags of order 4.
Generated 2 types of order 3, with [95, 47] flags of order 5.
Generated 11 types of order 5, with [388, 262, 191, 173, 148, 135, 124, 94, 101, 95, 72] flags of order 6.
Generating admissible graphs...
Generated 8157 admissible graphs.
Written flags.py
Computing flag densities...
Written flags.dat-s and flags.rat
Running: ./csdp output/k4-/flags.dat-s output/k4-/flags.out
============================================================================
Iter:  0 Ap: 0.00e+00 Pobj: -5.8008979e+04 Ad: 0.00e+00 Dobj:  0.0000000e+00
Iter:  1 Ap: 9.80e-01 Pobj: -6.4829931e+04 Ad: 9.53e-01 Dobj: -2.4175925e-01
Iter:  2 Ap: 1.00e+00 Pobj: -7.3624199e+04 Ad: 8.33e-01 Dobj: -2.5090683e-01
Iter:  3 Ap: 1.00e+00 Pobj: -1.1181688e+05 Ad: 4.26e-01 Dobj: -2.5268322e-01
Iter:  4 Ap: 6.37e-01 Pobj: -1.2319041e+05 Ad: 3.44e-01 Dobj: -2.3384540e-01
Iter:  5 Ap: 1.51e-01 Pobj: -1.3305276e+05 Ad: 2.14e-01 Dobj: -2.2863918e-01
Iter:  6 Ap: 1.95e-01 Pobj: -1.4181590e+05 Ad: 5.56e-01 Dobj: -2.2211866e-01
Iter:  7 Ap: 3.90e-01 Pobj: -1.4633553e+05 Ad: 3.52e-01 Dobj: -2.1736082e-01
Iter:  8 Ap: 5.03e-01 Pobj: -1.5560272e+05 Ad: 5.05e-01 Dobj: -2.1366547e-01
Iter:  9 Ap: 4.47e-01 Pobj: -1.5772250e+05 Ad: 4.71e-01 Dobj: -2.1219746e-01
Iter: 10 Ap: 3.11e-01 Pobj: -1.5254310e+05 Ad: 5.17e-01 Dobj: -2.1104844e-01
Iter: 11 Ap: 6.23e-01 Pobj: -1.3022856e+05 Ad: 5.10e-01 Dobj: -2.1030029e-01
Iter: 12 Ap: 3.24e-01 Pobj: -1.2112364e+05 Ad: 4.43e-01 Dobj: -2.1023644e-01
Iter: 13 Ap: 3.58e-01 Pobj: -1.1243326e+05 Ad: 5.21e-01 Dobj: -2.0990518e-01
Iter: 14 Ap: 4.80e-01 Pobj: -8.7582234e+04 Ad: 5.51e-01 Dobj: -2.0979860e-01
Iter: 15 Ap: 2.38e-01 Pobj: -8.1644946e+04 Ad: 5.24e-01 Dobj: -2.0961335e-01
Iter: 16 Ap: 1.19e-01 Pobj: -7.7485998e+04 Ad: 3.89e-01 Dobj: -2.0949550e-01
Iter: 17 Ap: 3.31e-01 Pobj: -6.5953679e+04 Ad: 4.42e-01 Dobj: -2.0937660e-01
Iter: 18 Ap: 1.71e-01 Pobj: -6.2393249e+04 Ad: 3.68e-01 Dobj: -2.0936324e-01
Iter: 19 Ap: 2.28e-01 Pobj: -5.6410303e+04 Ad: 4.67e-01 Dobj: -2.0925724e-01
Iter: 20 Ap: 5.18e-01 Pobj: -4.6724039e+04 Ad: 4.37e-01 Dobj: -2.0929541e-01
Iter: 21 Ap: 4.90e-01 Pobj: -4.0302925e+04 Ad: 6.40e-01 Dobj: -2.0912547e-01
Iter: 22 Ap: 9.10e-01 Pobj: -2.2810920e+04 Ad: 1.00e+00 Dobj: -2.0913446e-01
Iter: 23 Ap: 9.51e-01 Pobj: -2.1173868e+03 Ad: 1.00e+00 Dobj: -2.0913188e-01
Iter: 24 Ap: 9.90e-01 Pobj: -1.1302091e+02 Ad: 1.00e+00 Dobj: -2.0913150e-01
Iter: 25 Ap: 1.00e+00 Pobj: -5.4376308e+00 Ad: 1.00e+00 Dobj: -2.0915615e-01
Iter: 26 Ap: 1.00e+00 Pobj: -1.0437326e+00 Ad: 1.00e+00 Dobj: -2.0972229e-01
Iter: 27 Ap: 1.00e+00 Pobj: -6.6058593e-01 Ad: 1.00e+00 Dobj: -2.1310447e-01
Iter: 28 Ap: 3.32e-01 Pobj: -6.1194949e-01 Ad: 1.00e+00 Dobj: -2.1594164e-01
Iter: 29 Ap: 1.00e+00 Pobj: -4.6305043e-01 Ad: 1.00e+00 Dobj: -2.1892001e-01
Iter: 30 Ap: 1.00e+00 Pobj: -3.7273768e-01 Ad: 1.00e+00 Dobj: -2.2390711e-01
Iter: 31 Ap: 1.00e+00 Pobj: -3.4216595e-01 Ad: 1.00e+00 Dobj: -2.3079634e-01
Iter: 32 Ap: 9.66e-01 Pobj: -3.1265503e-01 Ad: 1.00e+00 Dobj: -2.4061090e-01
Iter: 33 Ap: 4.82e-01 Pobj: -3.1197955e-01 Ad: 8.16e-01 Dobj: -2.4783525e-01
Iter: 34 Ap: 2.53e-01 Pobj: -3.1042042e-01 Ad: 8.37e-01 Dobj: -2.5222772e-01
Iter: 35 Ap: 6.45e-01 Pobj: -3.0365361e-01 Ad: 1.00e+00 Dobj: -2.5908454e-01
Iter: 36 Ap: 8.54e-01 Pobj: -2.9421193e-01 Ad: 1.00e+00 Dobj: -2.6664917e-01
Iter: 37 Ap: 4.81e-01 Pobj: -2.9201072e-01 Ad: 8.52e-01 Dobj: -2.7170330e-01
Iter: 38 Ap: 1.33e-01 Pobj: -2.9158472e-01 Ad: 5.60e-01 Dobj: -2.7463140e-01
Iter: 39 Ap: 3.98e-01 Pobj: -2.9031957e-01 Ad: 6.93e-01 Dobj: -2.7649281e-01
Iter: 40 Ap: 7.53e-01 Pobj: -2.8837540e-01 Ad: 1.00e+00 Dobj: -2.8038774e-01
Iter: 41 Ap: 9.61e-01 Pobj: -2.8726627e-01 Ad: 1.00e+00 Dobj: -2.8332346e-01
Iter: 42 Ap: 9.00e-01 Pobj: -2.8707377e-01 Ad: 1.00e+00 Dobj: -2.8514646e-01
Iter: 43 Ap: 9.22e-01 Pobj: -2.8702387e-01 Ad: 1.00e+00 Dobj: -2.8604895e-01
Iter: 44 Ap: 9.07e-01 Pobj: -2.8700180e-01 Ad: 1.00e+00 Dobj: -2.8643953e-01
Iter: 45 Ap: 7.70e-01 Pobj: -2.8698689e-01 Ad: 9.03e-01 Dobj: -2.8655948e-01
Iter: 46 Ap: 8.49e-01 Pobj: -2.8697002e-01 Ad: 1.00e+00 Dobj: -2.8674117e-01
Iter: 47 Ap: 8.21e-01 Pobj: -2.8695940e-01 Ad: 6.85e-01 Dobj: -2.8677966e-01
Iter: 48 Ap: 8.28e-01 Pobj: -2.8695130e-01 Ad: 1.00e+00 Dobj: -2.8685971e-01
Iter: 49 Ap: 8.35e-01 Pobj: -2.8694412e-01 Ad: 1.00e+00 Dobj: -2.8689466e-01
Iter: 50 Ap: 7.97e-01 Pobj: -2.8693933e-01 Ad: 1.00e+00 Dobj: -2.8691994e-01
Iter: 51 Ap: 7.45e-01 Pobj: -2.8693634e-01 Ad: 1.00e+00 Dobj: -2.8693177e-01
Iter: 52 Ap: 7.43e-01 Pobj: -2.8693304e-01 Ad: 1.00e+00 Dobj: -2.8694400e-01
Iter: 53 Ap: 8.48e-01 Pobj: -2.8693076e-01 Ad: 1.00e+00 Dobj: -2.8694982e-01
Iter: 54 Ap: 9.17e-01 Pobj: -2.8692889e-01 Ad: 1.00e+00 Dobj: -2.8695586e-01
Iter: 55 Ap: 3.93e-01 Pobj: -2.8692715e-01 Ad: 5.29e-01 Dobj: -2.8695192e-01
Iter: 56 Ap: 6.00e-02 Pobj: -2.8692648e-01 Ad: 2.60e-01 Dobj: -2.8694760e-01
Iter: 57 Ap: 2.87e-01 Pobj: -2.8692331e-01 Ad: 3.72e-01 Dobj: -2.8694330e-01
Iter: 58 Ap: 1.42e-01 Pobj: -2.8692158e-01 Ad: 3.10e-01 Dobj: -2.8693958e-01
Iter: 59 Ap: 2.64e-01 Pobj: -2.8691902e-01 Ad: 4.35e-01 Dobj: -2.8693603e-01
Iter: 60 Ap: 2.27e-01 Pobj: -2.8691722e-01 Ad: 4.58e-01 Dobj: -2.8693317e-01
Iter: 61 Ap: 2.04e-01 Pobj: -2.8691544e-01 Ad: 4.30e-01 Dobj: -2.8693029e-01
Iter: 62 Ap: 1.63e-01 Pobj: -2.8691448e-01 Ad: 5.28e-01 Dobj: -2.8692860e-01
Iter: 63 Ap: 2.22e-01 Pobj: -2.8691234e-01 Ad: 3.74e-01 Dobj: -2.8692623e-01
Iter: 64 Ap: 2.71e-01 Pobj: -2.8691059e-01 Ad: 6.04e-01 Dobj: -2.8692376e-01
Iter: 65 Ap: 3.11e-01 Pobj: -2.8690875e-01 Ad: 5.00e-01 Dobj: -2.8692219e-01
Iter: 66 Ap: 3.84e-01 Pobj: -2.8690693e-01 Ad: 5.13e-01 Dobj: -2.8692093e-01
Iter: 67 Ap: 2.40e-01 Pobj: -2.8690538e-01 Ad: 4.62e-01 Dobj: -2.8691763e-01
Iter: 68 Ap: 2.50e-01 Pobj: -2.8690418e-01 Ad: 5.04e-01 Dobj: -2.8691567e-01
Iter: 69 Ap: 3.45e-01 Pobj: -2.8690302e-01 Ad: 8.00e-01 Dobj: -2.8691433e-01
Iter: 70 Ap: 2.63e-01 Pobj: -2.8690211e-01 Ad: 5.41e-01 Dobj: -2.8691357e-01
Iter: 71 Ap: 3.37e-01 Pobj: -2.8690069e-01 Ad: 7.02e-01 Dobj: -2.8691189e-01
Iter: 72 Ap: 1.05e-01 Pobj: -2.8690004e-01 Ad: 3.42e-01 Dobj: -2.8691003e-01
Iter: 73 Ap: 2.63e-01 Pobj: -2.8689896e-01 Ad: 4.00e-01 Dobj: -2.8690872e-01
Iter: 74 Ap: 3.07e-01 Pobj: -2.8689779e-01 Ad: 5.35e-01 Dobj: -2.8690700e-01
Iter: 75 Ap: 3.76e-01 Pobj: -2.8689672e-01 Ad: 7.07e-01 Dobj: -2.8690559e-01
Iter: 76 Ap: 2.69e-01 Pobj: -2.8689593e-01 Ad: 5.70e-01 Dobj: -2.8690438e-01
Iter: 77 Ap: 3.82e-01 Pobj: -2.8689515e-01 Ad: 6.85e-01 Dobj: -2.8690366e-01
Iter: 78 Ap: 1.59e-01 Pobj: -2.8689461e-01 Ad: 4.07e-01 Dobj: -2.8690222e-01
Iter: 79 Ap: 4.46e-01 Pobj: -2.8689363e-01 Ad: 5.25e-01 Dobj: -2.8690123e-01
Iter: 80 Ap: 3.30e-01 Pobj: -2.8689301e-01 Ad: 5.27e-01 Dobj: -2.8689984e-01
Iter: 81 Ap: 2.81e-01 Pobj: -2.8689257e-01 Ad: 5.13e-01 Dobj: -2.8689864e-01
Iter: 82 Ap: 4.16e-01 Pobj: -2.8689207e-01 Ad: 6.07e-01 Dobj: -2.8689805e-01
Iter: 83 Ap: 2.41e-01 Pobj: -2.8689173e-01 Ad: 5.49e-01 Dobj: -2.8689703e-01
Iter: 84 Ap: 3.25e-01 Pobj: -2.8689126e-01 Ad: 5.77e-01 Dobj: -2.8689614e-01
Iter: 85 Ap: 3.14e-01 Pobj: -2.8689085e-01 Ad: 4.85e-01 Dobj: -2.8689538e-01
Iter: 86 Ap: 3.13e-01 Pobj: -2.8689062e-01 Ad: 5.61e-01 Dobj: -2.8689487e-01
Iter: 87 Ap: 5.12e-01 Pobj: -2.8689025e-01 Ad: 7.70e-01 Dobj: -2.8689426e-01
Iter: 88 Ap: 3.31e-01 Pobj: -2.8688992e-01 Ad: 5.23e-01 Dobj: -2.8689343e-01
Iter: 89 Ap: 4.27e-01 Pobj: -2.8688967e-01 Ad: 6.86e-01 Dobj: -2.8689278e-01
Iter: 90 Ap: 1.77e-01 Pobj: -2.8688951e-01 Ad: 3.81e-01 Dobj: -2.8689219e-01
Iter: 91 Ap: 2.20e-01 Pobj: -2.8688935e-01 Ad: 3.26e-01 Dobj: -2.8689172e-01
Iter: 92 Ap: 2.96e-01 Pobj: -2.8688917e-01 Ad: 4.03e-01 Dobj: -2.8689118e-01
Iter: 93 Ap: 3.77e-01 Pobj: -2.8688901e-01 Ad: 5.25e-01 Dobj: -2.8689067e-01
Iter: 94 Ap: 3.03e-01 Pobj: -2.8688890e-01 Ad: 3.95e-01 Dobj: -2.8689032e-01
Iter: 95 Ap: 2.65e-01 Pobj: -2.8688883e-01 Ad: 5.03e-01 Dobj: -2.8688997e-01
Iter: 96 Ap: 3.73e-01 Pobj: -2.8688874e-01 Ad: 3.65e-01 Dobj: -2.8688977e-01
Iter: 97 Ap: 1.78e-01 Pobj: -2.8688871e-01 Ad: 4.73e-01 Dobj: -2.8688949e-01
Iter: 98 Ap: 3.50e-01 Pobj: -2.8688865e-01 Ad: 5.76e-01 Dobj: -2.8688928e-01
Iter: 99 Ap: 2.17e-01 Pobj: -2.8688862e-01 Ad: 3.60e-01 Dobj: -2.8688916e-01
Iter: 100 Ap: 1.21e-01 Pobj: -2.8688861e-01 Ad: 2.19e-01 Dobj: -2.8688909e-01
Iter: 101 Ap: 3.23e-01 Pobj: -2.8688858e-01 Ad: 6.13e-01 Dobj: -2.8688893e-01
Iter: 102 Ap: 2.16e-01 Pobj: -2.8688856e-01 Ad: 2.28e-01 Dobj: -2.8688887e-01
Iter: 103 Ap: 2.59e-01 Pobj: -2.8688854e-01 Ad: 5.89e-01 Dobj: -2.8688875e-01
Iter: 104 Ap: 4.40e-01 Pobj: -2.8688852e-01 Ad: 6.37e-01 Dobj: -2.8688867e-01
Iter: 105 Ap: 3.41e-01 Pobj: -2.8688851e-01 Ad: 4.74e-01 Dobj: -2.8688862e-01
Iter: 106 Ap: 2.50e-01 Pobj: -2.8688850e-01 Ad: 5.76e-01 Dobj: -2.8688859e-01
Iter: 107 Ap: 1.30e-01 Pobj: -2.8688850e-01 Ad: 4.49e-01 Dobj: -2.8688856e-01
Iter: 108 Ap: 2.67e-01 Pobj: -2.8688850e-01 Ad: 7.09e-01 Dobj: -2.8688853e-01
Iter: 109 Ap: 3.14e-01 Pobj: -2.8688849e-01 Ad: 6.95e-01 Dobj: -2.8688851e-01
Iter: 110 Ap: 4.16e-01 Pobj: -2.8688849e-01 Ad: 5.21e-01 Dobj: -2.8688851e-01
Iter: 111 Ap: 2.89e-01 Pobj: -2.8688848e-01 Ad: 4.12e-01 Dobj: -2.8688850e-01
Success: SDP solved
Primal objective value: -2.8688848e-01
Dual objective value: -2.8688850e-01
Relative primal infeasibility: 2.71e-11
Relative dual infeasibility: 2.53e-11
Real Relative Gap: -1.27e-08
XZ Relative Gap: 7.61e-09
DIMACS error measures: 4.73e-10 0.00e+00 6.20e-11 0.00e+00 -1.27e-08 7.61e-09
Elements time: 80857.841161
Factor time: 3660.986203
Other time: 608.735255
Total time: 85127.562619
============================================================================
Return code is 0
Floating point bound is 0.28688848

$ python make_nontight_exact_qdash.py --denominator 10000000 --dir output/k4-
Written r.py
Written qdash.py
Marked bound as non-tight in flags.py

$ python verify_bound.py --verbose --dir output/k4-
Constructing Q matrices...
Type 1 done.
Type 2 done.
Type 3 done.
Type 4 done.
Type 5 done.
Type 6 done.
Type 7 done.
Type 8 done.
Type 9 done.
Type 10 done.
Type 11 done.
Type 12 done.
Type 13 done.
Type 14 done.
Written q.py
Done type 1.
Done type 2.
Done type 3.
Done type 4.
Done type 5.
Done type 6.
Done type 7.
Done type 8.
Done type 9.
Done type 10.
Done type 11.
Done type 12.
Done type 13.
Done type 14.
Bound (all graphs) is 7229590138218029/25200000000000000
(Approximately 0.286888498)
Added exact bound to flags.py

$ python make_certificate.py --dir output/k4-
Written certificate to cert.js