1{
  2  "ridge_sweep": [
  3    {
  4      "lambda_": 0.0001,
  5      "condition": 9999.000199974857,
  6      "sqrt_condition": 99.99500087491802,
  7      "active_cg_matvecs": 56,
  8      "pivots": 0,
  9      "active_free": 16,
 10      "pg_steps": 3239,
 11      "active_objective": -105.40781739382753,
 12      "pg_objective": -105.40781739382759,
 13      "simplex_error": 4.729550084903167e-13,
 14      "min_x": 0.0,
 15      "kkt_free": 2.461248982399411e-10,
 16      "kkt_bound_min": -2.3039348207021249e-10,
 17      "active_time": 0.0034129239993490046,
 18      "pg_time": 0.2553559389998554
 19    },
 20    {
 21      "lambda_": 0.001,
 22      "condition": 9990.010989017504,
 23      "sqrt_condition": 99.95004246631166,
 24      "active_cg_matvecs": 55,
 25      "pivots": 0,
 26      "active_free": 16,
 27      "pg_steps": 3239,
 28      "active_objective": -105.40798164382757,
 29      "pg_objective": -105.40798164382753,
 30      "simplex_error": 1.3871126469666706e-12,
 31      "min_x": 0.0,
 32      "kkt_free": 3.213749266706145e-10,
 33      "kkt_bound_min": -6.067857327707316e-10,
 34      "active_time": 0.003321640000649495,
 35      "pg_time": 0.2504232419996697
 36    },
 37    {
 38      "lambda_": 0.01,
 39      "condition": 9900.999999998474,
 40      "sqrt_condition": 99.50376877283831,
 41      "active_cg_matvecs": 55,
 42      "pivots": 0,
 43      "active_free": 16,
 44      "pg_steps": 3238,
 45      "active_objective": -105.40962414382756,
 46      "pg_objective": -105.40962414382757,
 47      "simplex_error": 1.2466694343515883e-12,
 48      "min_x": 0.0,
 49      "kkt_free": 6.832223675701243e-11,
 50      "kkt_bound_min": -1.042721464727947e-11,
 51      "active_time": 0.003294611000455916,
 52      "pg_time": 0.24821845299993583
 53    },
 54    {
 55      "lambda_": 0.1,
 56      "condition": 9090.999999994923,
 57      "sqrt_condition": 95.34673565463541,
 58      "active_cg_matvecs": 55,
 59      "pivots": 0,
 60      "active_free": 16,
 61      "pg_steps": 3233,
 62      "active_objective": -105.42604914382761,
 63      "pg_objective": -105.42604914382756,
 64      "simplex_error": 8.881784197001252e-15,
 65      "min_x": 0.0,
 66      "kkt_free": 1.866240495473903e-11,
 67      "kkt_bound_min": -1.0278000672769849e-11,
 68      "active_time": 0.0032702349999453872,
 69      "pg_time": 0.24844830499932868
 70    },
 71    {
 72      "lambda_": 1.0,
 73      "condition": 5000.5000000019445,
 74      "sqrt_condition": 70.7142135641905,
 75      "active_cg_matvecs": 53,
 76      "pivots": 0,
 77      "active_free": 16,
 78      "pg_steps": 3178,
 79      "active_objective": -105.59029914382761,
 80      "pg_objective": -105.59029914382755,
 81      "simplex_error": 8.44035952241029e-12,
 82      "min_x": 0.0,
 83      "kkt_free": 1.5955627929997718e-08,
 84      "kkt_bound_min": -1.4328826125620253e-08,
 85      "active_time": 0.003214570999261923,
 86      "pg_time": 0.2523497069996665
 87    }
 88  ],
 89  "spectrum_sweep": [
 90    {
 91      "raw_ratio": 1,
 92      "condition": 1.000000000000004,
 93      "sqrt_condition": 1.000000000000002,
 94      "cg_matvecs": 2,
 95      "pg_steps": 2,
 96      "objective_gap": 2.7755575615628914e-17
 97    },
 98    {
 99      "raw_ratio": 10,
100      "condition": 9.991008991008988,
101      "sqrt_condition": 3.160855737139705,
102      "cg_matvecs": 32,
103      "pg_steps": 94,
104      "objective_gap": -1.1102230246251565e-16
105    },
106    {
107      "raw_ratio": 100,
108      "condition": 99.9010989010994,
109      "sqrt_condition": 9.995053721771555,
110      "cg_matvecs": 39,
111      "pg_steps": 340,
112      "objective_gap": 4.440892098500626e-16
113    },
114    {
115      "raw_ratio": 1000,
116      "condition": 999.0019980020144,
117      "sqrt_condition": 31.60699286553554,
118      "cg_matvecs": 46,
119      "pg_steps": 1102,
120      "objective_gap": -1.0658141036401503e-14
121    },
122    {
123      "raw_ratio": 10000,
124      "condition": 9990.010989017504,
125      "sqrt_condition": 99.95004246631166,
126      "cg_matvecs": 55,
127      "pg_steps": 3239,
128      "objective_gap": 4.263256414560601e-14
129    }
130  ],
131  "predictions": [
132    "Increasing ridge decreases kappa(A) monotonically and should reduce CG work.",
133    "Across spectra, CG work should track sqrt(kappa) more closely than projected-gradient steps track kappa.",
134    "The active-set output should have exact simplex feasibility and nonnegative coefficients, with sparse support."
135  ]
136}