reduced LP: 8548 rows, 960 potential variables
 alpha      F(alpha)        min(8a,(12-4a)/7)   difference    kappa*
 0.000   0.0000000000   0.0000000000       +0.00e+00   +24.000000   ~0
 0.025   0.2000000000   0.2000000000       +0.00e+00   +8.000000   ~1/5
 0.050   0.4000000000   0.4000000000       +0.00e+00   +8.000000   ~2/5
 0.075   0.6000000000   0.6000000000       -1.11e-16   +8.000000   ~3/5
 0.100   0.8000000000   0.8000000000       +0.00e+00   +8.000000   ~4/5
 0.125   1.0000000000   1.0000000000       +0.00e+00   +8.000000   ~1
 0.150   1.2000000000   1.2000000000       +0.00e+00   +8.000000   ~6/5
 0.175   1.4000000000   1.4000000000       +0.00e+00   +8.000000   ~7/5
 0.200   1.6000000000   1.6000000000       +2.22e-16   -0.280323   ~8/5
 0.225   1.5857142857   1.5857142857       +2.22e-16   -0.571429   ~111/70
 0.250   1.5714285714   1.5714285714       -2.22e-16   -0.571429   ~11/7
 0.275   1.5571428571   1.5571428571       +2.22e-16   -0.571429   ~109/70
 0.300   1.5428571429   1.5428571429       +2.22e-16   -0.571429   ~54/35
 0.325   1.5285714286   1.5285714286       +0.00e+00   -0.571429   ~107/70
 0.350   1.5142857143   1.5142857143       +0.00e+00   -0.571429   ~53/35
 0.375   1.5000000000   1.5000000000       +0.00e+00   -2.400000   ~3/2
 0.400   1.4400000000   1.4857142857       -4.57e-02   -2.400000   ~36/25
 0.425   1.3800000000   1.4714285714       -9.14e-02   -2.400000   ~69/50
 0.450   1.3200000000   1.4571428571       -1.37e-01   -2.400000   ~33/25
 0.475   1.2600000000   1.4428571429       -1.83e-01   -2.400000   ~63/50
 0.500   1.2000000000   1.4285714286       -2.29e-01   -2.400000   ~6/5
 0.525   1.1400000000   1.4142857143       -2.74e-01   -2.400000   ~57/50
 0.550   1.0800000000   1.4000000000       -3.20e-01   -2.400000   ~27/25
 0.575   1.0200000000   1.3857142857       -3.66e-01   -2.400000   ~51/50
 0.600   0.9600000000   1.3714285714       -4.11e-01   -2.400000   ~24/25
 0.625   0.9000000000   1.3571428571       -4.57e-01   -2.400000   ~9/10
 0.650   0.8400000000   1.3428571429       -5.03e-01   -2.400000   ~21/25
 0.675   0.7800000000   1.3285714286       -5.49e-01   -2.400000   ~39/50
 0.700   0.7200000000   1.3142857143       -5.94e-01   -2.400000   ~18/25
 0.725   0.6600000000   1.3000000000       -6.40e-01   -2.400000   ~33/50
 0.750   0.6000000000   1.2857142857       -6.86e-01   -2.400000   ~3/5
 0.775   0.5400000000   1.2714285714       -7.31e-01   -2.400000   ~27/50
 0.800   0.4800000000   1.2571428571       -7.77e-01   -2.400000   ~12/25
 0.825   0.4200000000   1.2428571429       -8.23e-01   -2.400000   ~21/50
 0.850   0.3600000000   1.2285714286       -8.69e-01   -2.400000   ~9/25
 0.875   0.3000000000   1.2142857143       -9.14e-01   -2.400000   ~3/10
 0.900   0.2400000000   1.2000000000       -9.60e-01   -2.400000   ~6/25
 0.925   0.1800000000   1.1857142857       -1.01e+00   -2.400000   ~9/50
 0.950   0.1200000000   1.1714285714       -1.05e+00   -2.400000   ~3/25
 0.975   0.0600000000   1.1571428571       -1.10e+00   -2.400000   ~3/50
 1.000   0.0000000000   1.1428571429       -1.14e+00   -5.500000   ~0
 unreduced primal (IPM) alpha=0.1: value 0.800000000  (4.8s)
 unreduced primal (IPM) alpha=0.2: value 1.600000000  (5.8s)
 unreduced primal (IPM) alpha=0.3: value 1.542857143  (7.1s)
 unreduced primal (IPM) alpha=0.375: value 1.500000000  (8.9s)
 unreduced primal (IPM) alpha=0.5: value 1.200000000  (11.9s)
nice -n 10 PYTHON $F/lp_density.py   283.82s user 0.65s system 99% cpu 4:45.26 total
