{
  "point": [
    "1",
    "2"
  ],
  "direction_not_unit": [
    "1",
    "-1"
  ],
  "scalar_value": "7",
  "gradient": [
    "8",
    "5"
  ],
  "analytic_H": [
    [
      "16",
      "2"
    ],
    [
      "2",
      "2"
    ]
  ],
  "analytic_H_times_v": [
    "14",
    "0"
  ],
  "v_transpose_H_v": "14",
  "central_difference_checks": [
    {
      "h": "1/1000",
      "central_gradient_difference": [
        "3500001/250000",
        "0"
      ],
      "difference_from_analytic_Hv": [
        "1/250000",
        "0"
      ]
    },
    {
      "h": "1/2000",
      "central_gradient_difference": [
        "14000001/1000000",
        "0"
      ],
      "difference_from_analytic_Hv": [
        "1/1000000",
        "0"
      ]
    }
  ],
  "saddle_counterexample": {
    "function": "u^2-v^2",
    "origin_gradient": [
      0,
      0
    ],
    "origin_H": [
      [
        2,
        0
      ],
      [
        0,
        -2
      ]
    ],
    "curvature_along_unit_u": 2,
    "curvature_along_unit_v": -2,
    "value_at_t_zero": "1/100",
    "value_at_zero_t": "-1/100",
    "t": "1/10"
  },
  "PyTorch_SciPy_or_optimization_executed": false
}