$ ./flagmatic --n 8 --r 2 --induced-density 4.0 --induced-density 4.6 --verbose --minimize --dir output/4046 flagmatic version 1.1 ============================================================================ Optimizing for density of 4.0. Optimizing for density of 4.6. Using directory output/4046 Using admissible graphs of order 8. Generating types and flags... Generated 1 type of order 0, with 11 flags of order 4. Generated 2 types of order 2, with [120, 120] flags of order 5. Generated 11 types of order 4, with [272, 272, 272, 272, 272, 272, 272, 272, 272, 272, 272] flags of order 6. Generated 156 types of order 6, with [64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64] flags of order 7. Generating admissible graphs... Generated 12346 admissible graphs. Written flags.py Computing flag densities... Written flags.dat-s and flags.rat Running: ./csdp output/4046/flags.dat-s output/4046/flags.out ============================================================================ Iter: 0 Ap: 0.00e+00 Pobj: 1.7328199e+05 Ad: 0.00e+00 Dobj: 0.0000000e+00 Iter: 1 Ap: 4.50e-01 Pobj: 6.8626522e+03 Ad: 8.63e-01 Dobj: 5.8920388e-01 Iter: 2 Ap: 4.11e-02 Pobj: 1.3086710e+04 Ad: 4.32e-01 Dobj: 4.0079264e+00 Iter: 3 Ap: 3.53e-03 Pobj: 1.2435110e+04 Ad: 3.36e-02 Dobj: 4.7727971e+00 Iter: 4 Ap: 3.79e-01 Pobj: 1.1868089e+04 Ad: 3.66e-01 Dobj: 1.1086740e+01 Iter: 5 Ap: 4.95e-01 Pobj: 2.2684317e+03 Ad: 5.54e-01 Dobj: 1.8629480e+01 Iter: 6 Ap: 6.02e-01 Pobj: 1.7902267e+02 Ad: 5.37e-01 Dobj: 2.6156726e+01 Iter: 7 Ap: 2.53e-01 Pobj: 1.0151934e+02 Ad: 4.07e-01 Dobj: 3.6491996e+01 Iter: 8 Ap: 1.69e-01 Pobj: 7.3364250e+01 Ad: 3.69e-01 Dobj: 4.7990505e+01 Iter: 9 Ap: 2.67e-01 Pobj: 4.3719802e+01 Ad: 5.81e-01 Dobj: 6.7350931e+01 Iter: 10 Ap: 3.08e-01 Pobj: 2.3899792e+01 Ad: 5.37e-01 Dobj: 8.9729500e+01 Iter: 11 Ap: 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2.9433984e-02 Iter: 143 Ap: 4.87e-01 Pobj: 2.9434378e-02 Ad: 4.85e-01 Dobj: 2.9434053e-02 Iter: 144 Ap: 5.02e-01 Pobj: 2.9434385e-02 Ad: 5.83e-01 Dobj: 2.9434114e-02 Iter: 145 Ap: 2.77e-01 Pobj: 2.9434392e-02 Ad: 1.54e-01 Dobj: 2.9434132e-02 Success: SDP solved Primal objective value: 2.9434392e-02 Dual objective value: 2.9434132e-02 Relative primal infeasibility: 4.09e-12 Relative dual infeasibility: 3.94e-11 Real Relative Gap: -2.45e-07 XZ Relative Gap: 9.71e-09 DIMACS error measures: 1.80e-11 0.00e+00 3.86e-10 0.00e+00 -2.45e-07 9.71e-09 Elements time: 274140.364119 Factor time: 2818.038647 Other time: 1100.217311 Total time: 278058.620078 ============================================================================ Return code is 0 Approximate floating-point bound is 0.02943439 $ python make_nontight_exact_qdash.py --denominator 10000000 --dir output/4046 Written r.py Written qdash.py Marked bound as non-tight in flags.py $ sage sage/verify_bound.sage --dir output/4046 Written q.py Bound (all graphs) is 1236244044566347/42000000000000000 (Approximately 0.029434382) Added exact bound to flags.py $ python make_certificate.py --dir output/4046 Written certificate to cert.js