1{
 2  "math_verification": {
 3    "prediction_1_secant_exactness": "s.T ytilde / abs(s.T y) = 1 for every rho",
 4    "prediction_2_correction_scaling": "||ytilde-y||/||y|| = 2 rho for prescribed c=-rho||s||||y||",
 5    "prediction_3_positive_definiteness": "BFGS corrected update has strictly positive eigenvalues when B is SPD",
 6    "sweep": [
 7      {
 8        "rho": 0.001,
 9        "observed_secant_over_abs_c": 0.9999999999999867,
10        "predicted_secant_over_abs_c": 1.0,
11        "observed_delta_ratio": 0.0020000000000001397,
12        "predicted_delta_ratio": 0.002
13      },
14      {
15        "rho": 0.01,
16        "observed_secant_over_abs_c": 1.000000000000001,
17        "predicted_secant_over_abs_c": 1.0,
18        "observed_delta_ratio": 0.019999999999999907,
19        "predicted_delta_ratio": 0.02
20      },
21      {
22        "rho": 0.05,
23        "observed_secant_over_abs_c": 1.0000000000000004,
24        "predicted_secant_over_abs_c": 1.0,
25        "observed_delta_ratio": 0.09999999999999987,
26        "predicted_delta_ratio": 0.1
27      },
28      {
29        "rho": 0.1,
30        "observed_secant_over_abs_c": 1.0000000000000002,
31        "predicted_secant_over_abs_c": 1.0,
32        "observed_delta_ratio": 0.20000000000000018,
33        "predicted_delta_ratio": 0.2
34      },
35      {
36        "rho": 0.25,
37        "observed_secant_over_abs_c": 0.9999999999999999,
38        "predicted_secant_over_abs_c": 1.0,
39        "observed_delta_ratio": 0.5000000000000002,
40        "predicted_delta_ratio": 0.5
41      },
42      {
43        "rho": 0.5,
44        "observed_secant_over_abs_c": 1.0,
45        "predicted_secant_over_abs_c": 1.0,
46        "observed_delta_ratio": 1.0000000000000002,
47        "predicted_delta_ratio": 1.0
48      },
49      {
50        "rho": 0.9,
51        "observed_secant_over_abs_c": 0.9999999999999999,
52        "predicted_secant_over_abs_c": 1.0,
53        "observed_delta_ratio": 1.7999999999999998,
54        "predicted_delta_ratio": 1.8
55      }
56    ],
57    "spd_sweep": [
58      {
59        "dimension": 3,
60        "minimum_observed_eigenvalue": 0.03528108020571712,
61        "predicted_lower_bound": 0.0
62      },
63      {
64        "dimension": 8,
65        "minimum_observed_eigenvalue": 0.00927656923766997,
66        "predicted_lower_bound": 0.0
67      },
68      {
69        "dimension": 20,
70        "minimum_observed_eigenvalue": 0.0010288274956301389,
71        "predicted_lower_bound": 0.0
72      }
73    ]
74  },
75  "mini_experiment": {
76    "baseline_ordinary_reject": {
77      "initial_loss": -0.05734205502046099,
78      "final_loss": -0.625,
79      "best_loss": -0.625,
80      "negative_pairs": 1,
81      "corrected_pairs": 0,
82      "backtracking_halvings": 164,
83      "steps": 180,
84      "finite": true
85    },
86    "idea_euclidean_correction": {
87      "initial_loss": -0.05734205502046099,
88      "final_loss": -0.625,
89      "best_loss": -0.625,
90      "negative_pairs": 1,
91      "corrected_pairs": 1,
92      "backtracking_halvings": 1,
93      "steps": 180,
94      "finite": true
95    }
96  }
97}