$ ./flagmatic --n 4 --r 2 --oriented --induced-density 4:121314 --exclude-type 1 --dir output/maxs4 --nosolve flagmatic version 1.5 ============================================================================ Optimizing for density of 4:121314. Using admissible graphs of order 4. Generated 1 type of order 0, with 2 flags of order 2. Generated 2 types of order 2, with [9, 9] flags of order 3. 1 type removed; remaining types have [9, 9] flags. Generated 42 admissible graphs. $ ./sdpa_dd -ds output/maxs4/flags.dat-s -o output/maxs4/sdpa.out SDPA-DD start at Thu Jan 19 23:04:14 2012 data is output/maxs4/flags.dat-s : sparse out is output/maxs4/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 8.8e-01 1.0e+00 3.00e-01 1 1.9e+07 1.2e-01 1.4e-31 -4.58e+01 -1.78e+04 8.2e-01 1.0e+00 3.00e-01 2 5.4e+06 2.1e-02 1.0e-31 -2.77e+01 -2.85e+04 9.0e-01 1.0e+00 3.00e-01 3 8.7e+05 2.1e-03 1.0e-31 -2.87e+00 -4.56e+04 9.0e-01 1.0e+00 3.00e-01 4 1.4e+05 2.1e-04 2.4e-31 -3.09e-01 -7.29e+04 9.0e-01 1.0e+00 3.00e-01 5 2.4e+04 2.1e-05 3.2e-31 -5.64e-02 -1.15e+05 9.0e-01 1.0e+00 3.00e-01 6 5.9e+03 2.2e-06 9.7e-31 -3.14e-02 -1.58e+05 9.1e-01 1.0e+00 3.00e-01 7 2.0e+03 2.1e-07 8.5e-31 -3.18e-02 -1.07e+05 1.0e+00 1.0e+00 3.00e-01 8 6.3e+02 1.7e-36 4.2e-31 -3.48e-02 -3.85e+04 1.8e+01 1.0e+00 3.00e-01 9 1.9e+02 1.9e-37 8.1e-32 -4.11e-02 -1.16e+04 1.0e+00 1.0e+00 3.00e-01 10 5.7e+01 4.1e-37 2.5e-31 -3.83e-02 -3.47e+03 1.0e+00 1.0e+00 3.00e-01 11 1.7e+01 7.9e-37 1.9e-32 -3.69e-02 -1.04e+03 1.0e+00 1.0e+00 3.00e-01 12 5.1e+00 6.5e-37 2.4e-33 -3.62e-02 -3.12e+02 1.0e+00 1.0e+00 3.00e-01 13 1.5e+00 5.3e-37 8.7e-34 -3.60e-02 -9.37e+01 2.0e+01 1.0e+00 3.00e-01 14 4.6e-01 1.2e-36 1.8e-34 -3.88e-02 -2.81e+01 1.0e+00 1.0e+00 3.00e-01 15 1.4e-01 2.5e-36 4.6e-34 -3.84e-02 -8.47e+00 9.0e+00 1.0e+00 3.00e-01 16 4.1e-02 6.2e-37 2.7e-35 -6.53e-02 -2.57e+00 2.6e+00 8.2e-01 1.00e-01 17 1.0e-02 3.3e-36 5.5e-35 -1.35e-01 -7.45e-01 7.9e-01 6.3e-01 1.00e-01 18 3.9e-03 1.1e-36 1.8e-34 -2.79e-01 -5.15e-01 8.4e-01 7.0e-01 3.00e-01 19 1.7e-03 2.1e-36 9.9e-35 -3.60e-01 -4.66e-01 9.6e-01 8.0e-01 1.00e-01 20 3.4e-04 2.5e-36 7.1e-35 -4.14e-01 -4.34e-01 9.4e-01 7.1e-01 1.00e-01 21 9.3e-05 2.3e-37 9.7e-35 -4.21e-01 -4.27e-01 8.4e-01 7.7e-01 1.00e-01 22 2.7e-05 6.3e-37 2.2e-34 -4.23e-01 -4.24e-01 1.1e+00 8.3e-01 3.00e-01 23 9.6e-06 3.2e-37 5.4e-34 -4.23e-01 -4.24e-01 1.2e+00 1.0e+00 3.00e-01 24 2.2e-06 2.4e-36 1.6e-33 -4.23e-01 -4.24e-01 1.1e+00 9.5e-01 3.00e-01 25 5.5e-07 1.4e-36 1.4e-33 -4.24e-01 -4.24e-01 1.1e+00 9.6e-01 3.00e-01 26 1.5e-07 8.2e-37 9.7e-33 -4.24e-01 -4.24e-01 1.1e+00 9.9e-01 3.00e-01 27 3.7e-08 1.3e-36 1.2e-32 -4.24e-01 -4.24e-01 1.1e+00 9.9e-01 3.00e-01 28 9.7e-09 4.9e-37 1.6e-32 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 29 2.5e-09 1.5e-36 5.0e-32 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 30 6.6e-10 6.3e-37 2.7e-31 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 31 1.7e-10 2.9e-37 1.4e-31 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 32 4.6e-11 2.4e-36 3.0e-31 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 33 1.2e-11 1.1e-36 1.2e-30 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 34 3.1e-12 2.3e-36 1.4e-30 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 35 8.2e-13 6.2e-37 3.1e-30 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 36 2.2e-13 2.1e-36 3.8e-30 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 37 5.7e-14 6.9e-37 5.2e-30 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 38 1.5e-14 1.2e-36 1.8e-29 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 39 3.9e-15 5.3e-37 6.4e-29 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 40 1.0e-15 4.0e-37 6.0e-29 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 41 2.7e-16 2.7e-36 1.2e-28 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 42 7.1e-17 8.7e-37 6.4e-28 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 43 1.9e-17 7.5e-37 3.8e-28 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 44 4.9e-18 1.3e-36 1.4e-27 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 45 1.3e-18 3.1e-37 2.1e-27 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 46 3.4e-19 3.9e-37 4.9e-27 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 47 8.8e-20 2.1e-36 9.2e-27 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 48 2.3e-20 9.9e-37 1.2e-26 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 49 6.1e-21 9.2e-37 3.5e-26 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 50 1.6e-21 2.3e-36 7.0e-26 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 51 4.2e-22 2.0e-36 1.5e-25 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 52 1.1e-22 1.9e-36 2.5e-25 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 53 2.9e-23 2.0e-36 4.0e-25 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 54 7.6e-24 1.8e-36 1.2e-24 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 cholesky miss condition :: not positive definite :: info = 39 :: line 642 in sdpa_linear.cpp 55 2.0e-24 1.2e-36 4.9e-25 -4.24e-01 -4.24e-01 1.1e+00 1.0e+00 3.00e-01 phase.value = pFEAS Iteration = 55 mu = 1.9911458722626287e-24 relative gap = 1.4075841823977209e-21 gap = 1.2145989820802035e-22 digits = 2.0478450991559274e+01 objValPrimal = -4.23570172100070861323080366640725e-01 objValDual = -4.23570172100070861324487950823123e-01 p.feas.error = 1.2325951644078309e-32 d.feas.error = 4.9381756423392576e-21 relative eps = 4.9303806576313200e-32 total time = 0.080 main loop time = 0.080000 total time = 0.080000 file read time = 0.000000 $ sage -python convert_sdpa_output.py output/maxs4/sdpa.out output/maxs4/flags.out $ sage -python scripts/find_sharp_graphs.py --dir output/maxs4 Floating point bound is 0.423570172100138254. 11 members of H are sharp. 0.423570172100100006 : graph 1 (4:) 0.423570172100025011 : graph 7 (4:121314) 0.423570172100138254 : graph 16 (4:123242) 0.423570172098633180 : graph 22 (4:12132343) 0.423570172100100006 : graph 26 (4:12134243) 0.423570172100100062 : graph 29 (4:1213142324) 0.423570172100036890 : graph 31 (4:1213142343) 0.423570172097967212 : graph 34 (4:1213232443) 0.423570172100057096 : graph 37 (4:1213234243) 0.423570172100057096 : graph 39 (4:121314232434) 0.423570172095063147 : graph 42 (4:121323244143) Written sharp graphs to flags.py $ sage -python scripts/make_zero_eigenvectors.py maxs4 --dir output/maxs4 Constructed 2 out of 2 zero eigenvectors for type 1. Constructed 4 out of 4 zero eigenvectors for type 2. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/maxs4 Floating point bound is 0.423570172100138254. Type 1: smallest eigenvalue is 0.420488215661034115 Type 2: smallest eigenvalue is 1.315109759873879902 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '1-9*x^2' --denominator 2 --dir output/maxs4 --diagonalize Type 1: smallest eigenvalue is 0.547684406832853909 Type 2: smallest eigenvalue is 1.326216744330268149 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/maxs4 Written q.py Floating point bound (non-sharp graphs) is 0.327766463630751348 Exact bound (just sharp graphs) is -9*x^2 + 1 Bound (all graphs) is -9*x^2 + 1 $ sage -python scripts/make_certificate.py --dir output/maxs4 Written certificate to cert.js