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      "initial_energy": 2,
      "preconditioner_spd": true,
      "error_propagation_matrix_equal": true,
      "pcg_steps": 8
    }
  ],
  "smoothed_aggregation": {
    "A": [
      [
        2,
        -1,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      [
        -1,
        2,
        -1,
        0,
        0,
        0,
        0,
        0
      ],
      [
        0,
        -1,
        2,
        -1,
        0,
        0,
        0,
        0
      ],
      [
        0,
        0,
        -1,
        2,
        -1,
        0,
        0,
        0
      ],
      [
        0,
        0,
        0,
        -1,
        2,
        -1,
        0,
        0
      ],
      [
        0,
        0,
        0,
        0,
        -1,
        2,
        -1,
        0
      ],
      [
        0,
        0,
        0,
        0,
        0,
        -1,
        2,
        -1
      ],
      [
        0,
        0,
        0,
        0,
        0,
        0,
        -1,
        2
      ]
    ],
    "P0": [
      [
        1,
        0,
        0,
        0
      ],
      [
        1,
        0,
        0,
        0
      ],
      [
        0,
        1,
        0,
        0
      ],
      [
        0,
        1,
        0,
        0
      ],
      [
        0,
        0,
        1,
        0
      ],
      [
        0,
        0,
        1,
        0
      ],
      [
        0,
        0,
        0,
        1
      ],
      [
        0,
        0,
        0,
        1
      ]
    ],
    "P": [
      [
        "2/3",
        0,
        0,
        0
      ],
      [
        "2/3",
        "1/3",
        0,
        0
      ],
      [
        "1/3",
        "2/3",
        0,
        0
      ],
      [
        0,
        "2/3",
        "1/3",
        0
      ],
      [
        0,
        "1/3",
        "2/3",
        0
      ],
      [
        0,
        0,
        "2/3",
        "1/3"
      ],
      [
        0,
        0,
        "1/3",
        "2/3"
      ],
      [
        0,
        0,
        0,
        "2/3"
      ]
    ],
    "Ac": [
      [
        "2/3",
        "-1/9",
        "-1/9",
        0
      ],
      [
        "-1/9",
        "4/9",
        "-1/9",
        "-1/9"
      ],
      [
        "-1/9",
        "-1/9",
        "4/9",
        "-1/9"
      ],
      [
        0,
        "-1/9",
        "-1/9",
        "2/3"
      ]
    ],
    "constant_reproduction": [
      "2/3",
      1,
      1,
      1,
      1,
      1,
      1,
      "2/3"
    ],
    "defect": [
      "1/3",
      0,
      0,
      0,
      0,
      0,
      0,
      "1/3"
    ],
    "Aones": [
      1,
      0,
      0,
      0,
      0,
      0,
      0,
      1
    ],
    "energy_columns_before": [
      2,
      2,
      2,
      2
    ],
    "energy_columns_after": [
      "2/3",
      "4/9",
      "4/9",
      "2/3"
    ],
    "nnz_A": 22,
    "nnz_P0": 8,
    "nnz_P": 14,
    "nnz_Ac": 14,
    "constant_errors": [
      [
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ],
      [
        "1/7",
        "-1/7",
        0,
        "1/7",
        "1/7",
        0,
        "-1/7",
        "1/7"
      ]
    ],
    "constant_energies": [
      0,
      "2/7"
    ]
  }
}