{
  "provenance": {
    "version": "1.0.0",
    "implementation_sha256": "a656f7615237a80558d7b51524a964509e3ee76aeb8663da12d0b5a9c2dc87ac",
    "command": "python3 solve_node.py --grids 32,64,128,256,512,1024,2048,4096,8192,16384 --nu 0.01 --amplitude 0.2 --phase 0.07 --reconstruction first --gradient-check --continuous-adjoint --output examples/refinement_first.json",
    "python": "3.11.12",
    "numpy": "2.3.1",
    "scipy": "1.16.0",
    "platform": "macOS-26.6.2-arm64-arm-64bit",
    "generated_utc": "2026-10-03T22:54:00Z",
    "formulation": "node-centred finite volumes: point values at the nodes, dual volumes, one-sided boundary slopes, constraint rows, alpha=2, analytic source and Dirichlet data, trapezoid objective",
    "mathematical_proof": false,
    "max_cells": 65536
  },
  "results": [
    {
      "objective": 1.41197336417411,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.457075887933612,
        0.1273595826159544,
        0.09217229257661777
      ],
      "tangent_gradient": [
        -0.45707588793361187,
        0.12735958261595498,
        0.09217229257661785
      ],
      "reverse_gradient": [
        -0.4570758879336119,
        0.12735958261595481,
        0.09217229257661774
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.3130681898903752,
      "amplitude_gradient_error": 0.3130681898903752,
      "phase_gradient_error": 0.04220372430293985,
      "viscosity_gradient_error": 0.09217229257661777,
      "gradient_duality_error": 5.828670879282072e-16,
      "gradient_reverse_error": 4.163336342344337e-16,
      "reverse_state_adjoint_error": 8.049116928532385e-16,
      "transpose_relative_error": 0.0,
      "state_l1_error": 0.03820186222066729,
      "state_linf_error": 0.08133444966707282,
      "primal_residual_inf": 4.440892098500626e-16,
      "primal_residual_density_inf": 1.4210854715202004e-14,
      "newton_correction_inf": 1.6263862289123403e-16,
      "tangent_residual_inf": 4.718447854656915e-16,
      "adjoint_residual_inf": 9.228728892196614e-16,
      "jacobian_nonzeros": 95,
      "psi_0": -1.4744085861076095,
      "psi_N": -0.09267090507534234,
      "exact_nodal_residual_inf": 0.00767156680876635,
      "exact_nodal_residual_boundary_rows_inf": 0.004644199557038431,
      "exact_nodal_residual_inner_rows_inf": 0.00767156680876635,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4712910523906082,
      "objective_quadrature_error": 9.259199925559791e-05,
      "objective_quadrature_remainder": 5.951159946012297e-08,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.4188680130967625,
        "adjoint_directional_gradient": -0.41886801314882566,
        "absolute_error": 5.206313158367948e-11,
        "perturbed_primal_residuals_inf": [
          3.3306690738754696e-16,
          2.7755575615628914e-16
        ],
        "axis_central_differences": [
          -0.45707588794963167,
          0.12735958251353097,
          0.09217229155478178
        ],
        "axis_absolute_errors": [
          1.601968557807254e-11,
          1.0242343084776451e-10,
          1.021835990822062e-09
        ]
      },
      "adjoint_l1_reference_error": 0.04516903330154719,
      "adjoint_linf_reference_error": 0.6147222759063237,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.04784062071672435,
      "psi_N_boundary_flux_error": 0.07063635361802562,
      "elapsed_seconds": 0.05412462500680704,
      "cells": 32,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.00767156680876635,
          "correction_inf": 0.0781586644735905,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 0.0004559208270421,
          "correction_inf": 0.003251585624377233,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 1.0889237025968335e-06,
          "correction_inf": 5.221785040293015e-06,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 3.5410008258907055e-12,
          "correction_inf": 1.231118712072011e-11,
          "step": 1.0
        },
        {
          "iteration": 4,
          "residual_inf": 3.3306690738754696e-16,
          "correction_inf": 1.6263862289123403e-16,
          "step": 1.0
        }
      ],
      "profile": {
        "x": [
          0.0,
          0.03125,
          0.0625,
          0.09375,
          0.125,
          0.15625,
          0.1875,
          0.21875,
          0.25,
          0.28125,
          0.3125,
          0.34375,
          0.375,
          0.40625,
          0.4375,
          0.46875,
          0.5,
          0.53125,
          0.5625,
          0.59375,
          0.625,
          0.65625,
          0.6875,
          0.71875,
          0.75,
          0.78125,
          0.8125,
          0.84375,
          0.875,
          0.90625,
          0.9375,
          0.96875,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9526740550022922,
          0.990999605792731,
          1.0284568235542406,
          1.0636774634737498,
          1.0953370525311101,
          1.122205600313671,
          1.1431981229967902,
          1.1574222865876642,
          1.1642208560027232,
          1.1632071282420013,
          1.1542920142779267,
          1.1377017710062396,
          1.1139853922162015,
          1.0840101825652604,
          1.0489430672762896,
          1.010214143571974,
          0.9694588143228339,
          0.9284367984363262,
          0.8889310635535427,
          0.8526363542467442,
          0.8210527161540797,
          0.7954008785559183,
          0.7765718568112251,
          0.7651141189232938,
          0.7612520353139384,
          0.7649230843276144,
          0.7758202863501138,
          0.7934298010770615,
          0.8170591634236509,
          0.8458568087656476,
          0.8788268477859241,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9517849878333923,
          0.9905787098580715,
          1.0297344867793845,
          1.0677475840490582,
          1.1031571796570094,
          1.1346025027019546,
          1.160875127054017,
          1.180965410493204,
          1.1941012946937084,
          1.199777974992394,
          1.197777299748901,
          1.188176153790845,
          1.17134350377301,
          1.147926218995722,
          1.1188242125804078,
          1.0851558583130145,
          1.0482150121666078,
          1.0094212901419286,
          0.9702655132206155,
          0.9322524159509418,
          0.8968428203429906,
          0.8653974972980454,
          0.8391248729459831,
          0.8190345895067961,
          0.8058987053062915,
          0.800222025007606,
          0.8022227002510991,
          0.8118238462091549,
          0.82865649622699,
          0.852073781004278,
          0.8811757874195922,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4744085861076095,
          -0.8207299830677414,
          -1.1882517367957977,
          -1.3368712150013031,
          -1.383524982299344,
          -1.3843967873735166,
          -1.3654108219821322,
          -1.3380238174188805,
          -1.3070540423696795,
          -1.2743897535663395,
          -1.240668419809638,
          -1.2060053917722966,
          -1.1702982000077824,
          -1.1333497166676083,
          -1.0949173480676364,
          -1.0547337511209778,
          -1.0125180642253977,
          -0.9679857373458733,
          -0.9208606086503143,
          -0.8708908610503546,
          -0.8178691826965857,
          -0.7616561961691947,
          -0.7022048959331467,
          -0.6395826361767966,
          -0.5739864872846635,
          -0.5057478658183325,
          -0.4353234180838256,
          -0.363271127864648,
          -0.2902131880936836,
          -0.2167897808940699,
          -0.14360990736994791,
          -0.07120620989619367,
          -0.09267090507534234
        ],
        "amplitude_tangent": [
          -0.4257792915650725,
          -0.2364316626555338,
          -0.0441667972066347,
          0.14463911703116594,
          0.32337584374155365,
          0.4854428772717546,
          0.6245212399718367,
          0.7348495756088065,
          0.8114856699128679,
          0.8505408115066108,
          0.8493814657168308,
          0.8067999921182167,
          0.72316217146393,
          0.6005408174142846,
          0.44283635977872543,
          0.25586200021925276,
          0.04733457480506667,
          -0.17332137810464734,
          -0.3954492829925549,
          -0.607948145477958,
          -0.8002861894677115,
          -0.9635307894786409,
          -1.091132201147639,
          -1.1792628660639455,
          -1.226670019496075,
          -1.2341648569125765,
          -1.2039659082206917,
          -1.1391080438704955,
          -1.043048651938367,
          -0.91950152451311,
          -0.7724504934139712,
          -0.6062574341510911,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -1.435452258974065,
          -1.4786383980768152,
          -1.4487585756787476,
          -1.415764514000809,
          -1.3828790750042284,
          -1.3501356615065214,
          -1.3174075855632377,
          -1.2845406736100697,
          -1.2513618407046998,
          -1.2176815743703033,
          -1.1832951386352595,
          -1.1479830797943542,
          -1.1115114976775105,
          -1.0736325868078067,
          -1.0340860297515553,
          -0.9926019348639512,
          -0.9489061349092898,
          -0.9027287589134401,
          -0.8538169794012982,
          -0.8019526011111301,
          -0.7469745432344487,
          -0.6888051370372679,
          -0.6274774923346687,
          -0.5631592260425939,
          -0.49616624040342966,
          -0.4269599914822432,
          -0.3561237726601953,
          -0.28431817230583833,
          -0.21222186987012365,
          -0.14046885733724157,
          -0.06959452629354974,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.4415151713148686,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.30038771160162536,
        0.1201583278524538,
        0.017262223037291406
      ],
      "tangent_gradient": [
        -0.3003877116016249,
        0.12015832785245345,
        0.017262223037291444
      ],
      "reverse_gradient": [
        -0.30038771160162525,
        0.1201583278524534,
        0.017262223037291635
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.15638001355838863,
      "amplitude_gradient_error": 0.15638001355838863,
      "phase_gradient_error": 0.03500246953943925,
      "viscosity_gradient_error": 0.017262223037291406,
      "gradient_duality_error": 4.440892098500626e-16,
      "gradient_reverse_error": 4.0245584642661925e-16,
      "reverse_state_adjoint_error": 8.847089727481716e-16,
      "transpose_relative_error": 2.220446049250313e-16,
      "state_l1_error": 0.01901376187885464,
      "state_linf_error": 0.040321794193280414,
      "primal_residual_inf": 6.661338147750939e-16,
      "primal_residual_density_inf": 4.263256414560601e-14,
      "newton_correction_inf": 6.758547540637973e-14,
      "tangent_residual_inf": 9.471590178833367e-16,
      "adjoint_residual_inf": 8.777700788442644e-16,
      "jacobian_nonzeros": 191,
      "psi_0": -1.4524803220136504,
      "psi_N": -0.05707246823489607,
      "exact_nodal_residual_inf": 0.0019252739542620079,
      "exact_nodal_residual_boundary_rows_inf": 0.0009987131170852148,
      "exact_nodal_residual_inner_rows_inf": 0.0019252739542620079,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.47122159723018,
      "objective_quadrature_error": 2.3136838827486628e-05,
      "objective_quadrature_remainder": 3.7169134521803943e-09,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.26434021320742573,
        "adjoint_directional_gradient": -0.26434021324588924,
        "absolute_error": 3.8463510154684855e-11,
        "perturbed_primal_residuals_inf": [
          6.661338147750939e-16,
          5.551115123125783e-16
        ],
        "axis_central_differences": [
          -0.3003877116269926,
          0.12015832777656497,
          0.017262222340441724
        ],
        "axis_absolute_errors": [
          2.5367263845055277e-11,
          7.588882300346711e-11,
          6.968496821246895e-10
        ]
      },
      "adjoint_l1_reference_error": 0.027343705000736077,
      "adjoint_linf_reference_error": 0.48548673319604163,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.025912356622765254,
      "psi_N_boundary_flux_error": 0.03503791677757935,
      "elapsed_seconds": 0.01981845800037263,
      "cells": 64,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.0019252739542620079,
          "correction_inf": 0.03948160102428115,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 6.052236344100681e-05,
          "correction_inf": 0.0008423156315571334,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 3.931565928372294e-08,
          "correction_inf": 3.6996849899485145e-07,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 1.0436096431476471e-14,
          "correction_inf": 6.758547540637973e-14,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.0065989689209125,
      "state_linf_observed_order": 1.0123067077392476,
      "gradient_observed_order": 1.0014207890571465,
      "amplitude_gradient_observed_order": 1.0014207890571465,
      "phase_gradient_observed_order": 0.26991360384801033,
      "viscosity_gradient_observed_order": 2.4167148674957026,
      "adjoint_l1_observed_order": 0.7241253002349703,
      "psi_0_observed_order": 0.8845958794701363,
      "psi_N_observed_order": 1.011493869984404,
      "profile": {
        "x": [
          0.0,
          0.015625,
          0.03125,
          0.046875,
          0.0625,
          0.078125,
          0.09375,
          0.109375,
          0.125,
          0.140625,
          0.15625,
          0.171875,
          0.1875,
          0.203125,
          0.21875,
          0.234375,
          0.25,
          0.265625,
          0.28125,
          0.296875,
          0.3125,
          0.328125,
          0.34375,
          0.359375,
          0.375,
          0.390625,
          0.40625,
          0.421875,
          0.4375,
          0.453125,
          0.46875,
          0.484375,
          0.5,
          0.515625,
          0.53125,
          0.546875,
          0.5625,
          0.578125,
          0.59375,
          0.609375,
          0.625,
          0.640625,
          0.65625,
          0.671875,
          0.6875,
          0.703125,
          0.71875,
          0.734375,
          0.75,
          0.765625,
          0.78125,
          0.796875,
          0.8125,
          0.828125,
          0.84375,
          0.859375,
          0.875,
          0.890625,
          0.90625,
          0.921875,
          0.9375,
          0.953125,
          0.96875,
          0.984375,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9334526435792807,
          0.9525150663518128,
          0.9718579093463384,
          0.991304285813641,
          1.0106753713007617,
          1.029791927219337,
          1.0484758823544316,
          1.0665519529100123,
          1.0838492803710746,
          1.1002030658871225,
          1.115456179931471,
          1.1294607265520902,
          1.1420795424981731,
          1.1531876127910323,
          1.1626733858308542,
          1.1704399728276356,
          1.1764062181612762,
          1.1805076291659093,
          1.182697155754948,
          1.1829458122144985,
          1.1812431353490986,
          1.1775974749138591,
          1.1720361138498827,
          1.1646052171822285,
          1.155369609457076,
          1.1444123811952498,
          1.131834324934731,
          1.1177532009605435,
          1.1023028317663843,
          1.085632022744474,
          1.0679033047880369,
          1.049291492830725,
          1.0299820534619053,
          1.0101692754492468,
          0.9900542401600485,
          0.9698425953026085,
          0.9497421455827559,
          0.9299602876697499,
          0.9107013333649502,
          0.8921637822620802,
          0.8745376209404836,
          0.8580017369529184,
          0.8427215398908523,
          0.8288468768241388,
          0.816510314987412,
          0.8058258419121682,
          0.796888004963661,
          0.7897714821280313,
          0.7845310478949366,
          0.7812018757161636,
          0.77980010423162,
          0.7803235892615819,
          0.7827527670538198,
          0.787051564858943,
          0.7931683102631734,
          0.8010366082614941,
          0.8105761724136783,
          0.8216936116862554,
          0.8342831864840263,
          0.8482275553173195,
          0.8633985375174977,
          0.8796579178213723,
          0.8968583161865892,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9329919024553353,
          0.9517849878333923,
          0.9710424101356204,
          0.9905787098580715,
          1.0102057417547903,
          1.0297344867793845,
          1.0489768724417694,
          1.0677475840490582,
          1.0858658493873579,
          1.1031571796570094,
          1.1194550498951135,
          1.1346025027019546,
          1.1484536598265633,
          1.160875127054017,
          1.1717472788646501,
          1.180965410493204,
          1.188440746292952,
          1.1941012946937084,
          1.1978925415200037,
          1.199777974992394,
          1.1997394373558574,
          1.197777299748901,
          1.1939104586292928,
          1.188176153790845,
          1.1806296097238422,
          1.17134350377301,
          1.1604072662149567,
          1.147926218995722,
          1.1340205614228616,
          1.1188242125804078,
          1.1024835216148825,
          1.0851558583130145,
          1.0670080975446647,
          1.0482150121666078,
          1.0289575898643795,
          1.0094212901419286,
          0.9897942582452098,
          0.9702655132206155,
          0.9510231275582306,
          0.9322524159509418,
          0.9141341506126421,
          0.8968428203429906,
          0.8805449501048866,
          0.8653974972980454,
          0.8515463401734367,
          0.8391248729459831,
          0.82825272113535,
          0.8190345895067961,
          0.8115592537070481,
          0.8058987053062915,
          0.8021074584799963,
          0.800222025007606,
          0.8002605626441425,
          0.8022227002510991,
          0.8060895413707072,
          0.8118238462091549,
          0.8193703902761578,
          0.82865649622699,
          0.8395927337850433,
          0.852073781004278,
          0.8659794385771384,
          0.8811757874195922,
          0.8975164783851173,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4524803220136504,
          -0.6887825975020218,
          -1.0648453745410753,
          -1.2640304623548226,
          -1.3644648254892922,
          -1.410507101642754,
          -1.4270064773494182,
          -1.4276903481628471,
          -1.4200336358610444,
          -1.4080462064098285,
          -1.3938452729943374,
          -1.3785290964126837,
          -1.3626550605309327,
          -1.3464972768448678,
          -1.3301832979019264,
          -1.313765605632257,
          -1.2972584647360341,
          -1.280656666925327,
          -1.263944945361785,
          -1.247102648324798,
          -1.2301060342633938,
          -1.212929387061934,
          -1.1955455525290775,
          -1.1779261946665611,
          -1.1600419195202647,
          -1.1418623403696606,
          -1.1233561222124095,
          -1.1044910265395294,
          -1.0852339696162596,
          -1.06555110413114,
          -1.04540793281952,
          -1.024769462348995,
          -1.0036004057670052,
          -0.981865441798417,
          -0.9595295389912678,
          -0.9365583519296741,
          -0.9129186952689186,
          -0.8885790990227703,
          -0.8635104452073917,
          -0.8376866815440593,
          -0.8110856024651261,
          -0.7836896813026986,
          -0.7554869305668958,
          -0.7264717600987278,
          -0.6966457962157255,
          -0.6660186194685553,
          -0.6346083750522401,
          -0.6024422089895763,
          -0.5695564855232222,
          -0.5359967470940389,
          -0.5018173879247335,
          -0.46708102529153966,
          -0.4318575683937895,
          -0.3962230022979674,
          -0.36025792241052224,
          -0.3240458717943807,
          -0.28767154780701715,
          -0.25121895454609,
          -0.21476958229595317,
          -0.178400693911038,
          -0.1421837907937758,
          -0.10618331842619169,
          -0.07045565450896238,
          -0.03504840333394277,
          -0.05707246823489607
        ],
        "amplitude_tangent": [
          -0.4257792915650727,
          -0.3327280214896392,
          -0.23744941790330207,
          -0.14076143592420767,
          -0.04350515294567262,
          0.053461553184451685,
          0.149271136207075,
          0.24305415484595763,
          0.3339475085306629,
          0.4211029559824743,
          0.5036957438310148,
          0.5809331838830217,
          0.6520630321321292,
          0.7163815387294878,
          0.7732410549941803,
          0.8220571005423859,
          0.8623148104404198,
          0.893574698821487,
          0.9154776916570091,
          0.9277493974054064,
          0.9302036001262041,
          0.9227449753068512,
          0.9053710438811575,
          0.878173394199443,
          0.8413382140810659,
          0.7951461839948247,
          0.7399717856221595,
          0.6762820745844809,
          0.6046349484314564,
          0.5256769075244763,
          0.44014025456711114,
          0.34883960797668123,
          0.25266751900975454,
          0.15258889248343097,
          0.049633833009314274,
          -0.05511150383040028,
          -0.1605164564706773,
          -0.26542009436799374,
          -0.36864823862601304,
          -0.4690330600924428,
          -0.565434686999942,
          -0.65676388152541,
          -0.7420045299840899,
          -0.820234505129829,
          -0.8906434552248665,
          -0.9525462750623321,
          -1.0053914002363022,
          -1.048763580349374,
          -1.0823813460328249,
          -1.1060898979990357,
          -1.1198505360741036,
          -1.1237279626764936,
          -1.1178768241710646,
          -1.1025287139824167,
          -1.07798059690931,
          -1.0445852806027325,
          -1.0027442135440037,
          -0.952902575567211,
          -0.895546378709016,
          -0.831201128516954,
          -0.7604315101645531,
          -0.6838415504004306,
          -0.6020747496938709,
          -0.5158137606819293,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -1.1742693306980634,
          -1.435452258974065,
          -1.4816077253867357,
          -1.4786383980768152,
          -1.464831879429771,
          -1.4487585756787476,
          -1.4322747140810137,
          -1.415764514000809,
          -1.3992980394164103,
          -1.3828790750042284,
          -1.366496671266593,
          -1.3501356615065214,
          -1.3337788567526085,
          -1.3174075855632377,
          -1.3010018959783964,
          -1.2845406736100697,
          -1.2680017254160976,
          -1.2513618407046998,
          -1.2345968341407187,
          -1.2176815743703033,
          -1.2005900017439124,
          -1.1832951386352595,
          -1.1657690959791094,
          -1.1479830797943542,
          -1.1299074016914552,
          -1.1115114976775105,
          -1.092763959951211,
          -1.0736325868078067,
          -1.0540844562927003,
          -1.0340860297515553,
          -1.0136032919484252,
          -0.9926019348639512,
          -0.9710475926021791,
          -0.9489061349092898,
          -0.9261440265364413,
          -0.9027287589134401,
          -0.8786293591827676,
          -0.8538169794012982,
          -0.8282655654845748,
          -0.8019526011111301,
          -0.7748599162477058,
          -0.7469745432344487,
          -0.7182895956683666,
          -0.6888051370372679,
          -0.6585289978074589,
          -0.6274774923346687,
          -0.5956759816435006,
          -0.5631592260425939,
          -0.5299714738614533,
          -0.49616624040342966,
          -0.4618057447638608,
          -0.4269599914822432,
          -0.39170550769997386,
          -0.3561237726601953,
          -0.320299402115149,
          -0.28431817230583833,
          -0.2482649835604309,
          -0.21222186987012365,
          -0.1762661569175357,
          -0.14046885733724157,
          -0.10489337034717086,
          -0.06959452629354974,
          -0.034617988649380725,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.4564153402967346,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.2217668873960609,
        0.10647897186620842,
        -7.80199754903287e-05
      ],
      "tangent_gradient": [
        -0.2217668873960608,
        0.10647897186620742,
        -7.801997549033198e-05
      ],
      "reverse_gradient": [
        -0.22176688739606087,
        0.10647897186620936,
        -7.80199754908395e-05
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.07775918935282417,
      "amplitude_gradient_error": 0.07775918935282417,
      "phase_gradient_error": 0.02132311355319387,
      "viscosity_gradient_error": 7.80199754903287e-05,
      "gradient_duality_error": 9.992007221626409e-16,
      "gradient_reverse_error": 9.43689570931383e-16,
      "reverse_state_adjoint_error": 1.887379141862766e-15,
      "transpose_relative_error": 8.586170042811897e-16,
      "state_l1_error": 0.00944537953881716,
      "state_linf_error": 0.019960052915596993,
      "primal_residual_inf": 8.881784197001252e-16,
      "primal_residual_density_inf": 1.1368683772161603e-13,
      "newton_correction_inf": 3.322963240544309e-16,
      "tangent_residual_inf": 9.26342336171615e-16,
      "adjoint_residual_inf": 1.663599813461758e-15,
      "jacobian_nonzeros": 383,
      "psi_0": -1.4397800027501422,
      "psi_N": -0.03947206655954155,
      "exact_nodal_residual_inf": 0.0004817651134967349,
      "exact_nodal_residual_boundary_rows_inf": 0.00022789323739691447,
      "exact_nodal_residual_inner_rows_inf": 0.0004817651134967349,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4712042439040982,
      "objective_quadrature_error": 5.783512745605179e-06,
      "objective_quadrature_remainder": 2.322670965675404e-10,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.18982319580640447,
        "adjoint_directional_gradient": -0.1898231958361984,
        "absolute_error": 2.9793917333265085e-11,
        "perturbed_primal_residuals_inf": [
          8.881784197001252e-16,
          1.1102230246251565e-15
        ],
        "axis_central_differences": [
          -0.2217668874093803,
          0.10647897179527631,
          -7.802039014848106e-05
        ],
        "axis_absolute_errors": [
          1.3319401137579234e-11,
          7.093210740993783e-11,
          4.146581523512081e-10
        ]
      },
      "adjoint_l1_reference_error": 0.015006795156544166,
      "adjoint_linf_reference_error": 0.30482485177960694,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.013212037359257023,
      "psi_N_boundary_flux_error": 0.01743751510222483,
      "elapsed_seconds": 0.02121604199783178,
      "cells": 128,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.0004817651134967349,
          "correction_inf": 0.01974920721918413,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 7.665563096115324e-06,
          "correction_inf": 0.00021106146169189713,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 1.266467875016275e-09,
          "correction_inf": 2.3744004469917417e-08,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 8.881784197001252e-16,
          "correction_inf": 3.322963240544309e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.0093633239391515,
      "state_linf_observed_order": 1.01444429029416,
      "gradient_observed_order": 1.0079710541779383,
      "amplitude_gradient_observed_order": 1.0079710541779383,
      "phase_gradient_observed_order": 0.7150385999611846,
      "viscosity_gradient_observed_order": 7.7895590069509915,
      "adjoint_l1_observed_order": 0.8655928289634599,
      "psi_0_observed_order": 0.9717872744885548,
      "psi_N_observed_order": 1.0067225338546821,
      "profile": {
        "x": [
          0.0,
          0.0078125,
          0.015625,
          0.0234375,
          0.03125,
          0.0390625,
          0.046875,
          0.0546875,
          0.0625,
          0.0703125,
          0.078125,
          0.0859375,
          0.09375,
          0.1015625,
          0.109375,
          0.1171875,
          0.125,
          0.1328125,
          0.140625,
          0.1484375,
          0.15625,
          0.1640625,
          0.171875,
          0.1796875,
          0.1875,
          0.1953125,
          0.203125,
          0.2109375,
          0.21875,
          0.2265625,
          0.234375,
          0.2421875,
          0.25,
          0.2578125,
          0.265625,
          0.2734375,
          0.28125,
          0.2890625,
          0.296875,
          0.3046875,
          0.3125,
          0.3203125,
          0.328125,
          0.3359375,
          0.34375,
          0.3515625,
          0.359375,
          0.3671875,
          0.375,
          0.3828125,
          0.390625,
          0.3984375,
          0.40625,
          0.4140625,
          0.421875,
          0.4296875,
          0.4375,
          0.4453125,
          0.453125,
          0.4609375,
          0.46875,
          0.4765625,
          0.484375,
          0.4921875,
          0.5,
          0.5078125,
          0.515625,
          0.5234375,
          0.53125,
          0.5390625,
          0.546875,
          0.5546875,
          0.5625,
          0.5703125,
          0.578125,
          0.5859375,
          0.59375,
          0.6015625,
          0.609375,
          0.6171875,
          0.625,
          0.6328125,
          0.640625,
          0.6484375,
          0.65625,
          0.6640625,
          0.671875,
          0.6796875,
          0.6875,
          0.6953125,
          0.703125,
          0.7109375,
          0.71875,
          0.7265625,
          0.734375,
          0.7421875,
          0.75,
          0.7578125,
          0.765625,
          0.7734375,
          0.78125,
          0.7890625,
          0.796875,
          0.8046875,
          0.8125,
          0.8203125,
          0.828125,
          0.8359375,
          0.84375,
          0.8515625,
          0.859375,
          0.8671875,
          0.875,
          0.8828125,
          0.890625,
          0.8984375,
          0.90625,
          0.9140625,
          0.921875,
          0.9296875,
          0.9375,
          0.9453125,
          0.953125,
          0.9609375,
          0.96875,
          0.9765625,
          0.984375,
          0.9921875,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9239756510238804,
          0.9332653073746683,
          0.9426914208889898,
          0.9522319689847364,
          0.9618646432200062,
          0.9715668973378627,
          0.9813159963861451,
          0.9910890668030621,
          1.0008631473491532,
          1.0106152407574307,
          1.0203223659661256,
          1.0299616107924008,
          1.0395101849006303,
          1.0489454729152996,
          1.0582450875261828,
          1.0673869224321262,
          1.0763492049694272,
          1.085110548271358,
          1.093650002806765,
          1.1019471071477966,
          1.1099819378196163,
          1.1177351580883343,
          1.1251880655473272,
          1.132322638366505,
          1.1391215800739118,
          1.1455683627442206,
          1.151647268474206,
          1.1573434290310667,
          1.1626428635655126,
          1.1675325142877917,
          1.1720002800112628,
          1.1760350474747194,
          1.1796267203613893,
          1.1827662459393549,
          1.185445639255045,
          1.1876580048184087,
          1.1893975557253669,
          1.1906596301701413,
          1.19144070530704,
          1.1917384084282245,
          1.1915515254308595,
          1.1908800065538256,
          1.1897249693708392,
          1.1880886990333253,
          1.1859746457627058,
          1.1833874195978638,
          1.180332782409376,
          1.1768176371976484,
          1.1728500146972864,
          1.168439057314856,
          1.1635950004315951,
          1.158329151106583,
          1.152653864219327,
          1.1465825160936542,
          1.1401294756471871,
          1.1333100731124872,
          1.1261405663772377,
          1.1186381049915506,
          1.1108206918907306,
          1.1027071428816508,
          1.0943170439404128,
          1.085670706368319,
          1.0767891198525756,
          1.067693903477802,
          1.0584072547346473,
          1.0489518965729072,
          1.039351022548915,
          1.029628240121012,
          1.019807512153011,
          1.0099130966942107,
          0.9999694851159967,
          0.990001338699806,
          0.9800334237893755,
          0.9700905456418912,
          0.9601974811378118,
          0.9503789105374909,
          0.9406593485037609,
          0.9310630746426336,
          0.9216140638482331,
          0.9123359167717773,
          0.9032517907664902,
          0.8943843316891771,
          0.8857556069632528,
          0.8773870403256576,
          0.8692993486898754,
          0.8615124815579056,
          0.8540455634046034,
          0.8469168394377229,
          0.840143625106205,
          0.8337422596881253,
          0.8277280642391975,
          0.8221153041241765,
          0.816917156288755,
          0.8121456813607336,
          0.8078118005987401,
          0.803925277637048,
          0.8004947049085317,
          0.7975274945667838,
          0.7950298736748876,
          0.7930068833839342,
          0.7914623817902644,
          0.790399050137307,
          0.7898184020159758,
          0.7897207952165948,
          0.7901054458945481,
          0.7909704447301911,
          0.7923127747896558,
          0.7941283308254605,
          0.7964119397925772,
          0.7991573823951366,
          0.8023574155195679,
          0.8060037954501557,
          0.8100873018013668,
          0.8145977621367128,
          0.8195240772754375,
          0.8248542473152871,
          0.8305753984215921,
          0.8366738104496652,
          0.8431349454790875,
          0.8499434773450015,
          0.8570833222533563,
          0.8645376705646133,
          0.8722890198242116,
          0.8803192091086789,
          0.8886094547442521,
          0.8971403874408065,
          0.9058920908683653,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9238262674743176,
          0.9329919024553353,
          0.942318965812554,
          0.9517849878333923,
          0.9613671640416761,
          0.9710424101356204,
          0.9807874175999334,
          0.9905787098580715,
          1.000392698829369,
          1.0102057417547903,
          1.019994198154407,
          1.0297344867793845,
          1.0394031424212773,
          1.0489768724417694,
          1.0584326128866821,
          1.0677475840490582,
          1.0768993453474727,
          1.0858658493873579,
          1.0946254950751089,
          1.1031571796570094,
          1.1114403495576144,
          1.1194550498951135,
          1.1271819725543883,
          1.1346025027019546,
          1.1416987636307252,
          1.1484536598265633,
          1.1548509181528746,
          1.160875127054017,
          1.1665117736830892,
          1.1717472788646501,
          1.176569029808141,
          1.180965410493204,
          1.1849258296536906,
          1.188440746292952,
          1.1915016926689335,
          1.1941012946937084,
          1.1962332896983008,
          1.1978925415200037,
          1.1990750528758454,
          1.199777974992394,
          1.199999614468702,
          1.1997394373558574,
          1.1989980704433143,
          1.197777299748901,
          1.1960800662161468,
          1.1939104586292928,
          1.1912737037630503,
          1.188176153790845,
          1.1846252709818732,
          1.1806296097238422,
          1.1761987959147013,
          1.17134350377301,
          1.1660754301228111,
          1.1604072662149567,
          1.1543526671527733,
          1.147926218995722,
          1.1411434036203034,
          1.1340205614228616,
          1.1265748519541372,
          1.1188242125804078,
          1.1107873152708003,
          1.1024835216148825,
          1.0939328361788985,
          1.0851558583130145,
          1.0761737325256824,
          1.0670080975446647,
          1.057681034187446,
          1.0482150121666078,
          1.038632835958324,
          1.0289575898643795,
          1.0192125824000666,
          1.0094212901419286,
          0.999607301170631,
          0.9897942582452098,
          0.9800058018455932,
          0.9702655132206155,
          0.9605968575787228,
          0.9510231275582306,
          0.941567387113318,
          0.9322524159509418,
          0.9231006546525273,
          0.9141341506126421,
          0.9053745049248911,
          0.8968428203429906,
          0.8885596504423856,
          0.8805449501048866,
          0.8728180274456117,
          0.8653974972980454,
          0.8583012363692749,
          0.8515463401734367,
          0.8451490818471254,
          0.8391248729459831,
          0.8334882263169109,
          0.82825272113535,
          0.8234309701918588,
          0.8190345895067961,
          0.8150741703463094,
          0.8115592537070481,
          0.8084983073310664,
          0.8058987053062915,
          0.8037667103016992,
          0.8021074584799963,
          0.8009249471241546,
          0.800222025007606,
          0.800000385531298,
          0.8002605626441425,
          0.8010019295566856,
          0.8022227002510991,
          0.8039199337838531,
          0.8060895413707072,
          0.8087262962369496,
          0.8118238462091549,
          0.8153747290181267,
          0.8193703902761578,
          0.8238012040852987,
          0.82865649622699,
          0.8339245698771889,
          0.8395927337850433,
          0.8456473328472267,
          0.852073781004278,
          0.8588565963796965,
          0.8659794385771384,
          0.8734251480458627,
          0.8811757874195922,
          0.8892126847291997,
          0.8975164783851173,
          0.9060671638211015,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4397800027501422,
          -0.524535024409919,
          -0.8694444789184564,
          -1.0942699469688668,
          -1.2391575705810767,
          -1.3310636547514074,
          -1.3880109360977675,
          -1.421996620643202,
          -1.4409712709818012,
          -1.4501797837496313,
          -1.4530661565864167,
          -1.4518812146934048,
          -1.4480889452928256,
          -1.442636904216654,
          -1.4361353053373744,
          -1.4289750552070573,
          -1.4214051654828967,
          -1.4135832720440635,
          -1.4056084395816417,
          -1.397542357183678,
          -1.3894229651781151,
          -1.381273172820503,
          -1.3731064082863134,
          -1.3649301351755327,
          -1.356748070288419,
          -1.3485615761197842,
          -1.3403705315187973,
          -1.3321738739766396,
          -1.3239699362406154,
          -1.3157566546740642,
          -1.3075316979664144,
          -1.2992925465588279,
          -1.291036541667416,
          -1.282760915593389,
          -1.274462810527347,
          -1.2661392902756605,
          -1.2577873476218615,
          -1.2494039089826174,
          -1.2409858373738512,
          -1.2325299343105889,
          -1.2240329410265967,
          -1.2154915392565988,
          -1.206902351737909,
          -1.1982619425370478,
          -1.1895668172766392,
          -1.1808134233202525,
          -1.1719981499628722,
          -1.1631173286692977,
          -1.1541672334002375,
          -1.1451440810650395,
          -1.1360440321402807,
          -1.1268631914944194,
          -1.1175976094601656,
          -1.1082432831979916,
          -1.0987961583961943,
          -1.0892521313550534,
          -1.0796070515048486,
          -1.0698567244097401,
          -1.0599969153117272,
          -1.0500233532710024,
          -1.0399317359609457,
          -1.0297177351776743,
          -1.019377003125353,
          -1.008905179539311,
          -0.998297899709238,
          -0.9875508034642373,
          -0.9766595451801221,
          -0.9656198048669253,
          -0.954427300390942,
          -0.9430778008805852,
          -0.9315671413587292,
          -0.919891238635839,
          -0.9080461084878935,
          -0.8960278841307228,
          -0.8838328359877894,
          -0.8714573927315119,
          -0.8588981635589364,
          -0.8461519616408782,
          -0.833215828659645,
          -0.8200870603242674,
          -0.8067632327239966,
          -0.7932422293510383,
          -0.7795222685924498,
          -0.7656019314594084,
          -0.7514801892902547,
          -0.7371564311325791,
          -0.7226304904799843,
          -0.7079026710119181,
          -0.6929737709611159,
          -0.6778451057137219,
          -0.6625185282331044,
          -0.6469964468907375,
          -0.631281840287227,
          -0.6153782686544561,
          -0.5992898814466151,
          -0.5830214207540694,
          -0.5665782202099207,
          -0.549966199104758,
          -0.5331918514802388,
          -0.5162622300362398,
          -0.49918492475850246,
          -0.4819680362527797,
          -0.4646201438559763,
          -0.4471502686828886,
          -0.4295678318568633,
          -0.4118826082617971,
          -0.39410467623904355,
          -0.3762443637335883,
          -0.3583121914669293,
          -0.34031881377721,
          -0.3222749578182763,
          -0.30419136184670803,
          -0.2860787133481758,
          -0.267947587760764,
          -0.2498083885427747,
          -0.23167128930609593,
          -0.21354617869412781,
          -0.19544260862668617,
          -0.1773697464648951,
          -0.15933633156891103,
          -0.14135063663279404,
          -0.12342043408660616,
          -0.105552967758639,
          -0.08775492989333852,
          -0.07003244352569155,
          -0.05239105012304451,
          -0.034835702322730346,
          -0.017370761520300898,
          -0.03947206655954155
        ],
        "amplitude_tangent": [
          -0.4257792915650729,
          -0.3801052667912043,
          -0.33365493653416306,
          -0.2865329907436338,
          -0.23884590728611235,
          -0.19070175161959238,
          -0.14220996517866608,
          -0.09348114321856678,
          -0.044626802985377,
          0.004240856825406738,
          0.05300920428682319,
          0.10156542904694245,
          0.1497968026011194,
          0.19759094288827964,
          0.24483608206436608,
          0.2914213363126967,
          0.33723697656749285,
          0.3821746990514992,
          0.42612789455987393,
          0.4689919154590121,
          0.5106643394094724,
          0.5510452288657003,
          0.5900373854509197,
          0.6275465983527018,
          0.6634818859327525,
          0.6977557297929453,
          0.7302843005882353,
          0.7609876749255654,
          0.7897900427360676,
          0.8166199045556369,
          0.8414102581962873,
          0.8640987743375345,
          0.8846279606134266,
          0.9029453138167554,
          0.9190034598874993,
          0.9327602813976743,
          0.9441790322895655,
          0.9532284396687797,
          0.9598827924977282,
          0.964122017078963,
          0.9659317392612512,
          0.9653033333442488,
          0.9622339577000336,
          0.9567265771713745,
          0.9487899723472112,
          0.9384387358551015,
          0.9256932558479286,
          0.9105796868974811,
          0.8931299085400426,
          0.8733814717480971,
          0.8513775336268834,
          0.8271667806538204,
          0.8008033407916687,
          0.7723466848115004,
          0.7418615171577212,
          0.7094176566731606,
          0.675089907476124,
          0.6389579202418847,
          0.6011060440870779,
          0.5616231691857972,
          0.520602560160264,
          0.4781416801866417,
          0.43434200563867414,
          0.38930883096003427,
          0.3431510633135947,
          0.2959810064066957,
          0.24791413274196053,
          0.1990688434011151,
          0.14956621434416711,
          0.09952972810934817,
          0.04908498974293542,
          -0.0016405742142701683,
          -0.052518034791993386,
          -0.10341729867019467,
          -0.15420746600076204,
          -0.2047572083642179,
          -0.2549351668183121,
          -0.3046103694593742,
          -0.35365266728991024,
          -0.4019331864826537,
          -0.449324794374824,
          -0.495702575746277,
          -0.540944315166986,
          -0.584930980482528,
          -0.627547201882748,
          -0.6686817405097126,
          -0.7082279402442393,
          -0.7460841561971364,
          -0.7821541535442026,
          -0.8163474706942541,
          -0.8485797413653963,
          -0.8787729709516856,
          -0.9068557635624166,
          -0.9327634972702495,
          -0.9564384463635911,
          -0.9778298507080397,
          -0.9968939336233652,
          -1.0135938709191235,
          -1.0278997148504996,
          -1.0397882777105003,
          -1.049242980529162,
          -1.056253672880423,
          -1.060816430090576,
          -1.062933334198898,
          -1.0626122448528201,
          -1.0598665659485265,
          -1.0547150132828733,
          -1.0471813877994331,
          -1.0372943582289957,
          -1.0250872560826272,
          -1.0105978850918642,
          -0.9938683463411084,
          -0.9749448795327659,
          -0.953877720091573,
          -0.9307209711703791,
          -0.9055324890787795,
          -0.8783737802258638,
          -0.8493099073509806,
          -0.8184094026091376,
          -0.7857441849738165,
          -0.7513894794099806,
          -0.7154237353420964,
          -0.6779285420830445,
          -0.6389885390862392,
          -0.5986913191216401,
          -0.5571273227437439,
          -0.5143897227042923,
          -0.47057429725379984,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.7931120078566245,
          -1.1742693306980634,
          -1.3538335289342776,
          -1.435452258974065,
          -1.469833852307646,
          -1.4816077253867357,
          -1.482648499900719,
          -1.4786383980768152,
          -1.4722757335080559,
          -1.464831879429771,
          -1.4569010507123703,
          -1.4487585756787476,
          -1.4405307479617266,
          -1.4322747140810137,
          -1.4240157494076802,
          -1.415764514000809,
          -1.4075249787955346,
          -1.3992980394164103,
          -1.3910831528669891,
          -1.3828790750042284,
          -1.3746841922120292,
          -1.366496671266593,
          -1.3583145282436164,
          -1.3501356615065214,
          -1.341957868732299,
          -1.3337788567526085,
          -1.3255962480475916,
          -1.3174075855632377,
          -1.3092103365831076,
          -1.3010018959783964,
          -1.292779588988537,
          -1.2845406736100697,
          -1.2762823426410626,
          -1.2680017254160976,
          -1.2596958892624928,
          -1.2513618407046998,
          -1.2429965264440392,
          -1.2345968341407187,
          -1.226159593026162,
          -1.2176815743703033,
          -1.2091594918367101,
          -1.2005900017439124,
          -1.191969703271647,
          -1.1832951386352595,
          -1.1745627932590055,
          -1.1657690959791094,
          -1.1569104193080115,
          -1.1479830797943542,
          -1.138983338507517,
          -1.1299074016914552,
          -1.1207514216173566,
          -1.1115114976775105,
          -1.102183677760575,
          -1.092763959951211,
          -1.0832482945996913,
          -1.0736325868078067,
          -1.0639126993802408,
          -1.0540844562927003,
          -1.0441436467304397,
          -1.0340860297515553,
          -1.0239073396317244,
          -1.0136032919484252,
          -1.0031695904636784,
          -0.9926019348639512,
          -0.9818960294168146,
          -0.9710475926021791,
          -0.9600523677744659,
          -0.9489061349092898,
          -0.9376047234840642,
          -0.9261440265364413,
          -0.9145200159383187,
          -0.9027287589134401,
          -0.8907664358168657,
          -0.8786293591827676,
          -0.8663139940300429,
          -0.8538169794012982,
          -0.8411351510895689,
          -0.8282655654845748,
          -0.8152055244498968,
          -0.8019526011111301,
          -0.7885046664097182,
          -0.7748599162477058,
          -0.7610168990111564,
          -0.7469745432344487,
          -0.7327321851293124,
          -0.7182895956683666,
          -0.7036470068881545,
          -0.6888051370372679,
          -0.6737652141753118,
          -0.6585289978074589,
          -0.643098798113265,
          -0.6274774923346687,
          -0.6116685378696545,
          -0.5956759816435006,
          -0.5795044653306175,
          -0.5631592260425939,
          -0.5466460921385233,
          -0.5299714738614533,
          -0.5131423485672851,
          -0.49616624040342966,
          -0.47905119436564964,
          -0.4618057447638608,
          -0.44443887822697925,
          -0.4269599914822432,
          -0.409378844250141,
          -0.39170550769997386,
          -0.37395030900931486,
          -0.3561237726601953,
          -0.3382365591821996,
          -0.320299402115149,
          -0.302323044009176,
          -0.28431817230583833,
          -0.2662953559492223,
          -0.2482649835604309,
          -0.23023720397284939,
          -0.21222186987012365,
          -0.1942284851959933,
          -0.1762661569175357,
          -0.15834355162418218,
          -0.14046885733724157,
          -0.12264975079268342,
          -0.10489337034717086,
          -0.08720629454651528,
          -0.06959452629354974,
          -0.05206348245349239,
          -0.034617988649380725,
          -0.017262278942452004,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.4638327152068433,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.18271646348109213,
        0.09682318617547421,
        -0.0024453524800723803
      ],
      "tangent_gradient": [
        -0.18271646348109435,
        0.09682318617547643,
        -0.002445352480072404
      ],
      "reverse_gradient": [
        -0.1827164634810925,
        0.0968231861754758,
        -0.0024453524800722715
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.0387087654378554,
      "amplitude_gradient_error": 0.0387087654378554,
      "phase_gradient_error": 0.011667327862459664,
      "viscosity_gradient_error": 0.0024453524800723803,
      "gradient_duality_error": 2.220446049250313e-15,
      "gradient_reverse_error": 1.5959455978986625e-15,
      "reverse_state_adjoint_error": 1.942890293094024e-15,
      "transpose_relative_error": 4.254308691087148e-15,
      "state_l1_error": 0.0047015827745343,
      "state_linf_error": 0.009913011720305787,
      "primal_residual_inf": 1.4432899320127035e-15,
      "primal_residual_density_inf": 3.694822225952521e-13,
      "newton_correction_inf": 2.0586765095475052e-16,
      "tangent_residual_inf": 2.1909557501587074e-15,
      "adjoint_residual_inf": 1.7147741560030738e-15,
      "jacobian_nonzeros": 767,
      "psi_0": -1.4331979112130924,
      "psi_N": -0.030732101262739422,
      "exact_nodal_residual_inf": 0.00012046585441882751,
      "exact_nodal_residual_boundary_rows_inf": 5.416303049865512e-05,
      "exact_nodal_residual_inner_rows_inf": 0.00012046585441882751,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4711999062259884,
      "objective_quadrature_error": 1.4458346357937302e-06,
      "objective_quadrature_remainder": 1.4516166577216547e-11,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.1536695075965433,
        "adjoint_directional_gradient": -0.1536695076284499,
        "absolute_error": 3.190658848239991e-11,
        "perturbed_primal_residuals_inf": [
          1.4432899320127035e-15,
          1.4432899320127035e-15
        ],
        "axis_central_differences": [
          -0.1827164634815581,
          0.09682318610204631,
          -0.0024453526981105256
        ],
        "axis_absolute_errors": [
          4.659606034351782e-13,
          7.342790264708299e-11,
          2.1803814526447085e-10
        ]
      },
      "adjoint_l1_reference_error": 0.007850885558030464,
      "adjoint_linf_reference_error": 0.1786429855256082,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.006629945822207217,
      "psi_N_boundary_flux_error": 0.0086975498054227,
      "elapsed_seconds": 0.020133541998802684,
      "cells": 256,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.00012046585441882751,
          "correction_inf": 0.009860523277868155,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 9.601783784174422e-07,
          "correction_inf": 5.256689223070986e-05,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 3.960004546499363e-11,
          "correction_inf": 1.4863547773908167e-09,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 1.3322676295501878e-15,
          "correction_inf": 2.0586765095475052e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.0064622510873522,
      "state_linf_observed_order": 1.0097202040548354,
      "gradient_observed_order": 1.0063528831691888,
      "amplitude_gradient_observed_order": 1.0063528831691888,
      "phase_gradient_observed_order": 0.8699439303608368,
      "viscosity_gradient_observed_order": -4.970055078968604,
      "adjoint_l1_observed_order": 0.9346886083629786,
      "psi_0_observed_order": 0.9947839679475502,
      "psi_N_observed_order": 1.0035135260341,
      "profile": {
        "x": [
          0.0,
          0.00390625,
          0.01171875,
          0.015625,
          0.0234375,
          0.03125,
          0.03515625,
          0.04296875,
          0.046875,
          0.0546875,
          0.0625,
          0.06640625,
          0.07421875,
          0.078125,
          0.0859375,
          0.09375,
          0.09765625,
          0.10546875,
          0.109375,
          0.1171875,
          0.125,
          0.12890625,
          0.13671875,
          0.140625,
          0.1484375,
          0.15625,
          0.16015625,
          0.16796875,
          0.171875,
          0.1796875,
          0.1875,
          0.19140625,
          0.19921875,
          0.203125,
          0.2109375,
          0.21875,
          0.22265625,
          0.23046875,
          0.234375,
          0.2421875,
          0.25,
          0.25390625,
          0.26171875,
          0.265625,
          0.2734375,
          0.28125,
          0.28515625,
          0.29296875,
          0.296875,
          0.3046875,
          0.3125,
          0.31640625,
          0.32421875,
          0.328125,
          0.3359375,
          0.34375,
          0.34765625,
          0.35546875,
          0.359375,
          0.3671875,
          0.375,
          0.37890625,
          0.38671875,
          0.390625,
          0.3984375,
          0.40625,
          0.41015625,
          0.41796875,
          0.421875,
          0.4296875,
          0.4375,
          0.44140625,
          0.44921875,
          0.453125,
          0.4609375,
          0.46875,
          0.47265625,
          0.48046875,
          0.484375,
          0.4921875,
          0.5,
          0.50390625,
          0.51171875,
          0.515625,
          0.5234375,
          0.53125,
          0.53515625,
          0.54296875,
          0.546875,
          0.5546875,
          0.5625,
          0.56640625,
          0.57421875,
          0.578125,
          0.5859375,
          0.59375,
          0.59765625,
          0.60546875,
          0.609375,
          0.6171875,
          0.625,
          0.62890625,
          0.63671875,
          0.640625,
          0.6484375,
          0.65625,
          0.66015625,
          0.66796875,
          0.671875,
          0.6796875,
          0.6875,
          0.69140625,
          0.69921875,
          0.703125,
          0.7109375,
          0.71875,
          0.72265625,
          0.73046875,
          0.734375,
          0.7421875,
          0.75,
          0.75390625,
          0.76171875,
          0.765625,
          0.7734375,
          0.78125,
          0.78515625,
          0.79296875,
          0.796875,
          0.8046875,
          0.8125,
          0.81640625,
          0.82421875,
          0.828125,
          0.8359375,
          0.84375,
          0.84765625,
          0.85546875,
          0.859375,
          0.8671875,
          0.875,
          0.87890625,
          0.88671875,
          0.890625,
          0.8984375,
          0.90625,
          0.91015625,
          0.91796875,
          0.921875,
          0.9296875,
          0.9375,
          0.94140625,
          0.94921875,
          0.953125,
          0.9609375,
          0.96875,
          0.97265625,
          0.98046875,
          0.984375,
          0.9921875,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.919352834946248,
          0.9285035635088558,
          0.9331401742556904,
          0.9425221457576802,
          0.952030539855743,
          0.956825106788262,
          0.9664807574628568,
          0.9713361098097524,
          0.98108745418036,
          0.9908736630651497,
          0.9957725731119301,
          1.0055674373053103,
          1.010457562483192,
          1.020208641702442,
          1.029901471740142,
          1.034718813502322,
          1.044280980271657,
          1.049020096007818,
          1.0584002364316265,
          1.0676309285972825,
          1.072183312888096,
          1.0811485277545438,
          1.0855559852133385,
          1.0942073841517193,
          1.1026235073377366,
          1.106736997455533,
          1.1147624672759735,
          1.118669616486187,
          1.1262609761629676,
          1.1335399016176853,
          1.1370566794582817,
          1.1438342401297321,
          1.1470909227664132,
          1.153330232046169,
          1.159191614973656,
          1.1619760988618526,
          1.1672441847388113,
          1.1697245777827232,
          1.1743704981020253,
          1.1785872368920178,
          1.1805313921578338,
          1.1840853017915398,
          1.1856928660131592,
          1.188564243540562,
          1.1909714585289193,
          1.1919990795924682,
          1.1936991116064244,
          1.1943704401686426,
          1.1953535521179501,
          1.1958552155972622,
          1.195925004578942,
          1.1957021324473636,
          1.1954095435289278,
          1.1944627858089263,
          1.1930357367085398,
          1.1921430552432315,
          1.1900019144863836,
          1.1887546848341612,
          1.1859105152988696,
          1.1826057001994097,
          1.1807829255955171,
          1.1768019963121428,
          1.174646187495062,
          1.1700102489103414,
          1.164951140799576,
          1.162266612409131,
          1.1565955890127262,
          1.1536124722843744,
          1.147359926494768,
          1.1407381785368182,
          1.1372937724564252,
          1.1301482153962827,
          1.1264513516387609,
          1.1188205555277937,
          1.1108890432126683,
          1.1068164602336912,
          1.0984699153493724,
          1.0942009905503352,
          1.0854847292235061,
          1.0765482146753236,
          1.0720041048603597,
          1.0627779492961373,
          1.0581015007850887,
          1.0486360591507893,
          1.0390397720275952,
          1.0341998477287826,
          1.024451174553249,
          1.0195483680818487,
          1.009700768505235,
          0.9998172406629575,
          0.994869550009643,
          0.9849774424329791,
          0.9800390790237521,
          0.9701928502263553,
          0.9604073799529707,
          0.9555449331565659,
          0.9458955231717479,
          0.9411144788261965,
          0.9316543753930122,
          0.9223495610227532,
          0.9177625382829743,
          0.9087333277531349,
          0.9042966764104624,
          0.8955928754554606,
          0.8871327833548313,
          0.8830006227854471,
          0.8749446984873039,
          0.871025852344838,
          0.8634183344029509,
          0.8561330621723316,
          0.8526168287284279,
          0.84584781424915,
          0.842599122899012,
          0.8363831577362477,
          0.8305547589124593,
          0.827790292154763,
          0.8225690554401786,
          0.8201153817917246,
          0.8155291635748287,
          0.8113799764754234,
          0.8094723324503175,
          0.8059964559602767,
          0.8044302158473517,
          0.8016455762210536,
          0.7993298092683908,
          0.7983493883784302,
          0.7967461065083852,
          0.7961240810070049,
          0.7952408035160619,
          0.794839766198272,
          0.7948202691585265,
          0.7951430502094224,
          0.7954850059032547,
          0.7965287076371401,
          0.7980495196236798,
          0.7989876009964207,
          0.8012160276498729,
          0.8025049333084647,
          0.8054280248901803,
          0.8088052430437338,
          0.8106615618776051,
          0.8147038816538541,
          0.8168873984785089,
          0.8215724721229599,
          0.8266719946836705,
          0.8293733508636529,
          0.835071101102174,
          0.8380640656883035,
          0.8443291899570441,
          0.8509539766831635,
          0.8543963265654414,
          0.8615306709258435,
          0.8652184143845951,
          0.8728240711309292,
          0.8807214761459908,
          0.8847737469760154,
          0.8930734000094525,
          0.8973158581541948,
          0.9059734588751832,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9193109025330743,
          0.9283875166237151,
          0.9329919024553353,
          0.942318965812554,
          0.9517849878333923,
          0.9565629935232906,
          0.9661946055358682,
          0.9710424101356204,
          0.9807874175999334,
          0.9905787098580715,
          0.9954843443126529,
          1.0053008167989943,
          1.0102057417547903,
          1.019994198154407,
          1.0297344867793845,
          1.034579229217671,
          1.0442033206452674,
          1.0489768724417694,
          1.0584326128866821,
          1.0677475840490582,
          1.0723452537361091,
          1.0814071156686507,
          1.0858658493873579,
          1.0946254950751089,
          1.1031571796570094,
          1.1073310907251543,
          1.1154824808905242,
          1.1194550498951135,
          1.1271819725543883,
          1.1346025027019546,
          1.138192254089601,
          1.145119919135096,
          1.1484536598265633,
          1.1548509181528746,
          1.160875127054017,
          1.1637427666284934,
          1.1691804802714947,
          1.1717472788646501,
          1.176569029808141,
          1.180965410493204,
          1.1830007364738542,
          1.186739530428566,
          1.188440746292952,
          1.1915016926689335,
          1.1941012946937084,
          1.1952260906445198,
          1.1971222851560026,
          1.1978925415200037,
          1.1990750528758454,
          1.199777974992394,
          1.1999490156357697,
          1.1999297410123453,
          1.1997394373558574,
          1.1989980704433143,
          1.197777299748901,
          1.196988012088837,
          1.195054009043474,
          1.1939104586292928,
          1.1912737037630503,
          1.188176153790845,
          1.18645686970948,
          1.1826824608946107,
          1.1806296097238422,
          1.1761987959147013,
          1.17134350377301,
          1.1687602943934048,
          1.1632905282230717,
          1.1604072662149567,
          1.1543526671527733,
          1.147926218995722,
          1.1445783556056548,
          1.1376234321263032,
          1.1340205614228616,
          1.1265748519541372,
          1.1188242125804078,
          1.114840351692455,
          1.1066675447130307,
          1.1024835216148825,
          1.0939328361788985,
          1.0851558583130145,
          1.0806890974669257,
          1.0716124833762848,
          1.0670080975446647,
          1.057681034187446,
          1.0482150121666078,
          1.0434370064767093,
          1.0338053944641319,
          1.0289575898643795,
          1.0192125824000666,
          1.0094212901419286,
          1.0045156556873471,
          0.9946991832010057,
          0.9897942582452098,
          0.9800058018455932,
          0.9702655132206155,
          0.9654207707823291,
          0.9557966793547326,
          0.9510231275582306,
          0.941567387113318,
          0.9322524159509418,
          0.9276547462638909,
          0.9185928843313493,
          0.9141341506126421,
          0.9053745049248911,
          0.8968428203429906,
          0.8926689092748457,
          0.884517519109476,
          0.8805449501048866,
          0.8728180274456117,
          0.8653974972980454,
          0.861807745910399,
          0.854880080864904,
          0.8515463401734367,
          0.8451490818471254,
          0.8391248729459831,
          0.8362572333715067,
          0.8308195197285054,
          0.82825272113535,
          0.8234309701918588,
          0.8190345895067961,
          0.8169992635261459,
          0.813260469571434,
          0.8115592537070481,
          0.8084983073310664,
          0.8058987053062915,
          0.8047739093554801,
          0.8028777148439973,
          0.8021074584799963,
          0.8009249471241546,
          0.800222025007606,
          0.8000509843642302,
          0.8000702589876546,
          0.8002605626441425,
          0.8010019295566856,
          0.8022227002510991,
          0.803011987911163,
          0.8049459909565259,
          0.8060895413707072,
          0.8087262962369496,
          0.8118238462091549,
          0.8135431302905201,
          0.8173175391053893,
          0.8193703902761578,
          0.8238012040852987,
          0.82865649622699,
          0.8312397056065951,
          0.8367094717769283,
          0.8395927337850433,
          0.8456473328472267,
          0.852073781004278,
          0.8554216443943452,
          0.8623765678736969,
          0.8659794385771384,
          0.8734251480458627,
          0.8811757874195922,
          0.8851596483075448,
          0.893332455286969,
          0.8975164783851173,
          0.9060671638211015,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4331979112130924,
          -0.3562595019827205,
          -0.8399892204546284,
          -1.0004983597422537,
          -1.2156888825059602,
          -1.3385381684396749,
          -1.3778005397433906,
          -1.4278216891704907,
          -1.4428418809128585,
          -1.460125489657215,
          -1.4664778881966913,
          -1.4670833784014063,
          -1.4650547760093848,
          -1.462924093048459,
          -1.45726915566428,
          -1.4504480397660688,
          -1.4467711097881313,
          -1.439092617858845,
          -1.4351450661191587,
          -1.4271216103393232,
          -1.4189979072577945,
          -1.4149155221150038,
          -1.4067296533376394,
          -1.4026311179618338,
          -1.3944304277681443,
          -1.3862302909764423,
          -1.3821314942253229,
          -1.3739371632841213,
          -1.3698416136399392,
          -1.3616532235563334,
          -1.3534672575006896,
          -1.34937463369306,
          -1.3411888382970774,
          -1.3370951198753447,
          -1.3289045992111392,
          -1.3207079510758895,
          -1.3166065487350005,
          -1.308395976828476,
          -1.3042861477005199,
          -1.296055718872583,
          -1.2878086318264343,
          -1.2836779640030755,
          -1.275400588924336,
          -1.2712531533646174,
          -1.2629389361604804,
          -1.2545964126903202,
          -1.2504135801166645,
          -1.2420228286059292,
          -1.2378141206856212,
          -1.2293680404918668,
          -1.2208810318324377,
          -1.2166211496902046,
          -1.2080665387902272,
          -1.2037709627929116,
          -1.1951411245570718,
          -1.186456802481281,
          -1.182093108215023,
          -1.1733204182962034,
          -1.1689105179539796,
          -1.1600413180893587,
          -1.1511031601284754,
          -1.1466070489782338,
          -1.1375583860660463,
          -1.1330048734498726,
          -1.1238370582524497,
          -1.1145849139050075,
          -1.1099259775738215,
          -1.100539867221748,
          -1.0958116801672744,
          -1.0862824873583754,
          -1.0766527631165257,
          -1.0717989016486138,
          -1.0620105577860357,
          -1.0570750194965417,
          -1.0471185546015707,
          -1.0370446760200804,
          -1.0319623646396099,
          -1.0217043024895365,
          -1.016527470767422,
          -1.0060754992519263,
          -0.9954888391906986,
          -0.990143647780036,
          -0.9793468424090865,
          -0.9738941523545289,
          -0.9628775210947397,
          -0.9517090151110857,
          -0.9460664933504885,
          -0.9346623143099045,
          -0.9288996315970696,
          -0.9172505566712755,
          -0.9054332445992199,
          -0.8994602923341107,
          -0.8873834519035354,
          -0.8812786537934513,
          -0.8689341034857845,
          -0.8564068154429442,
          -0.8500736419769629,
          -0.8372663503526837,
          -0.8307915226779082,
          -0.8176978514602442,
          -0.8044101608514855,
          -0.797692879755578,
          -0.7841102661559759,
          -0.7772445266296831,
          -0.763363337264435,
          -0.7492816925106767,
          -0.7421654804740091,
          -0.7277820768644022,
          -0.7205148906341873,
          -0.7058297858632893,
          -0.6909443814995072,
          -0.6834269412925493,
          -0.6682436240444363,
          -0.6605782652566792,
          -0.6451017059031198,
          -0.6294331864839153,
          -0.6215280141096235,
          -0.605578311171189,
          -0.5975348788929317,
          -0.5813138778499674,
          -0.5649184953449217,
          -0.5566572246301033,
          -0.5400114701431052,
          -0.5316286719429757,
          -0.5147477088260427,
          -0.4977192835243835,
          -0.4891522789427561,
          -0.47191796812417447,
          -0.46325286184057585,
          -0.4458324502053974,
          -0.4282996666423301,
          -0.41949417977726583,
          -0.4018112791902404,
          -0.39293642257271255,
          -0.3751263976884104,
          -0.3572447592533383,
          -0.34828041738639737,
          -0.3303113999857909,
          -0.3213094156981861,
          -0.3032772167921644,
          -0.2852162904104625,
          -0.27617836957316383,
          -0.2580941526182055,
          -0.24905043258223436,
          -0.23096608821081344,
          -0.21289407571468943,
          -0.20386568978834876,
          -0.18582994068824452,
          -0.17682481171400383,
          -0.1588454184030719,
          -0.14091399134531005,
          -0.1319687011475944,
          -0.11412354930053208,
          -0.10522541734520165,
          -0.08748210068205119,
          -0.06981437200714781,
          -0.06101058776520904,
          -0.04346632552439508,
          -0.034726994734500624,
          -0.01731652423087315,
          -0.030732101262739422
        ],
        "amplitude_tangent": [
          -0.42577929156507277,
          -0.4032281269378106,
          -0.35746627757896476,
          -0.3342822156628491,
          -0.2873752994218569,
          -0.23984127705336453,
          -0.21587370941482592,
          -0.16760745328504711,
          -0.1433369909046261,
          -0.09459244246533395,
          -0.04567171999661653,
          -0.021181183628152193,
          0.02778823922723791,
          0.05223829018196923,
          0.10099699452807863,
          0.1494712438872527,
          0.17356583422572414,
          0.22139859082773142,
          0.24510838361288312,
          0.2920443888674072,
          0.33824271634018577,
          0.361030776240681,
          0.4059167071353155,
          0.4279877576471192,
          0.4713200066551104,
          0.5134861760577876,
          0.534100238482821,
          0.5743283706631536,
          0.5939182250786033,
          0.6319904723813097,
          0.6685098573103386,
          0.6861594707646834,
          0.7201850783991236,
          0.7365404231628023,
          0.7678864863761123,
          0.7973498655475291,
          0.8113528859848048,
          0.837858747949958,
          0.8503453311664455,
          0.873747412683888,
          0.8950071284595886,
          0.9048169388856431,
          0.9227659668516562,
          0.9308939718190122,
          0.9454314419417642,
          0.957647461270754,
          0.962874944782195,
          0.971551946443619,
          0.9749957564528937,
          0.9800823903813449,
          0.9827564133653206,
          0.983185809674478,
          0.982226762360335,
          0.9808383620192075,
          0.976246636654089,
          0.9692430127366746,
          0.9648410959864293,
          0.9542489218826673,
          0.9480644883794541,
          0.9339361612649277,
          0.9174889891159702,
          0.9084073125231861,
          0.8885537611457308,
          0.8777933053140399,
          0.85463610874478,
          0.8293425025522709,
          0.8159127567264255,
          0.7875265976877899,
          0.7725868102802745,
          0.7412576768064659,
          0.7080577519401655,
          0.6907805629510004,
          0.6549228363419194,
          0.6363635589110457,
          0.5980393032094211,
          0.5581839128981129,
          0.537711632430492,
          0.49573912654959534,
          0.47426406077243083,
          0.43040079364335093,
          0.38540834186050077,
          0.36252250458620994,
          0.31604082317846344,
          0.29247316001355683,
          0.24475578292823602,
          0.19635942168725926,
          0.1719435006928499,
          0.12275091816107155,
          0.09800444780008424,
          0.048287257168130225,
          -0.0016266464418242194,
          -0.02661880424953236,
          -0.07659606835843134,
          -0.10155011960876309,
          -0.1513113695477068,
          -0.20077333736377928,
          -0.22535338404841082,
          -0.27413456891522836,
          -0.2983050756096405,
          -0.3461299269371075,
          -0.39316636569921826,
          -0.4163517860355736,
          -0.46198390154740676,
          -0.4844017991202328,
          -0.5283705502976295,
          -0.5710911333176412,
          -0.5919495917746115,
          -0.6325972568661316,
          -0.6523609513099413,
          -0.6907062149742934,
          -0.7273960395717126,
          -0.7450915196857114,
          -0.7791289889033911,
          -0.7954500800246147,
          -0.8266472069720993,
          -0.8558552223398523,
          -0.869691244259951,
          -0.8957863386593564,
          -0.9080301269231696,
          -0.9308747909748627,
          -0.9514861520167814,
          -0.9609397530619375,
          -0.9781170001640468,
          -0.9858314926725088,
          -0.9994922448355941,
          -1.0107732450579863,
          -1.015514492941621,
          -1.0231881404093561,
          -1.0261175387485213,
          -1.0301567888079946,
          -1.03176802310869,
          -1.031663765458716,
          -1.02963989247371,
          -1.0277230881552053,
          -1.0220893583505022,
          -1.0140722330723968,
          -1.0091774279135852,
          -0.9976332369429888,
          -0.9909919675404044,
          -0.9759937090075472,
          -0.9587415544450866,
          -0.9492840350399737,
          -0.9287362078894651,
          -0.9176587968823926,
          -0.8939313216166765,
          -0.8681559592239576,
          -0.8545196934556394,
          -0.825791028563422,
          -0.8107158102936879,
          -0.7791884237308006,
          -0.745887699564872,
          -0.7285966955462788,
          -0.6927841317421699,
          -0.6742835309599908,
          -0.6361477040133315,
          -0.5965734832264662,
          -0.5762756395208994,
          -0.5347174905418581,
          -0.513481336230881,
          -0.4701565503166881,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.4677512621321874,
          -1.0186322059802366,
          -1.1742693306980634,
          -1.3538335289342776,
          -1.435452258974065,
          -1.4565980108661793,
          -1.4776048006101377,
          -1.4816077253867357,
          -1.482648499900719,
          -1.4786383980768152,
          -1.475649636798774,
          -1.4686414083466506,
          -1.464831879429771,
          -1.4569010507123703,
          -1.4487585756787476,
          -1.4446507109317552,
          -1.4364041956449138,
          -1.4322747140810137,
          -1.4240157494076802,
          -1.415764514000809,
          -1.4116431811554562,
          -1.4034099462754484,
          -1.3992980394164103,
          -1.3910831528669891,
          -1.3828790750042284,
          -1.3787805947090075,
          -1.3705896324681344,
          -1.366496671266593,
          -1.3583145282436164,
          -1.3501356615065214,
          -1.3460467721548313,
          -1.3378686618233568,
          -1.3337788567526085,
          -1.3255962480475916,
          -1.3174075855632377,
          -1.3133101955431665,
          -1.3051076808041397,
          -1.3010018959783964,
          -1.292779588988537,
          -1.2845406736100697,
          -1.2804141130219069,
          -1.2721450016645992,
          -1.2680017254160976,
          -1.2596958892624928,
          -1.2513618407046998,
          -1.2471832849326279,
          -1.2388011743574574,
          -1.2345968341407187,
          -1.226159593026162,
          -1.2176815743703033,
          -1.2134262487283665,
          -1.2048808839499838,
          -1.2005900017439124,
          -1.191969703271647,
          -1.1832951386352595,
          -1.1789364104123803,
          -1.170173839007986,
          -1.1657690959791094,
          -1.1569104193080115,
          -1.1479830797943542,
          -1.14349249520627,
          -1.1344551337702502,
          -1.1299074016914552,
          -1.1207514216173566,
          -1.1115114976775105,
          -1.106858823690943,
          -1.0974855581037608,
          -1.092763959951211,
          -1.0832482945996913,
          -1.0736325868078067,
          -1.0687859256843593,
          -1.0590123847059487,
          -1.0540844562927003,
          -1.0441436467304397,
          -1.0340860297515553,
          -1.0290120862490417,
          -1.0187712538098328,
          -1.0136032919484252,
          -1.0031695904636784,
          -0.9926019348639512,
          -0.9872665314191958,
          -0.9764898941860143,
          -0.9710475926021791,
          -0.9600523677744659,
          -0.9489061349092898,
          -0.9432750848645061,
          -0.9318945394936521,
          -0.9261440265364413,
          -0.9145200159383187,
          -0.9027287589134401,
          -0.8967692144205164,
          -0.8847199664487087,
          -0.8786293591827676,
          -0.8663139940300429,
          -0.8538169794012982,
          -0.847499356388463,
          -0.8347240026335662,
          -0.8282655654845748,
          -0.8152055244498968,
          -0.8019526011111301,
          -0.7952531308743377,
          -0.7817069925727447,
          -0.7748599162477058,
          -0.7610168990111564,
          -0.7469745432344487,
          -0.7398783892898276,
          -0.7255359159233802,
          -0.7182895956683666,
          -0.7036470068881545,
          -0.6888051370372679,
          -0.6813098349574449,
          -0.6661715114069415,
          -0.6585289978074589,
          -0.643098798113265,
          -0.6274774923346687,
          -0.6195962321546423,
          -0.6036949338425823,
          -0.5956759816435006,
          -0.5795044653306175,
          -0.5631592260425939,
          -0.5549232587690293,
          -0.5383285455429686,
          -0.5299714738614533,
          -0.5131423485672851,
          -0.49616624040342966,
          -0.4876255622853691,
          -0.47044421847720397,
          -0.4618057447638608,
          -0.44443887822697925,
          -0.4269599914822432,
          -0.41818157764648384,
          -0.4005530595177546,
          -0.39170550769997386,
          -0.37395030900931486,
          -0.3561237726601953,
          -0.34718708067990306,
          -0.3292735516462113,
          -0.320299402115149,
          -0.302323044009176,
          -0.28431817230583833,
          -0.2753083529837943,
          -0.25728047365937107,
          -0.2482649835604309,
          -0.23023720397284939,
          -0.21222186987012365,
          -0.2032218548316568,
          -0.18524288655035923,
          -0.1762661569175357,
          -0.15834355162418218,
          -0.14046885733724157,
          -0.13155189655287364,
          -0.11376329531524125,
          -0.10489337034717086,
          -0.08720629454651528,
          -0.06959452629354974,
          -0.060818598336400916,
          -0.04332976333180994,
          -0.034617988649380725,
          -0.017262278942452004,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.4675235623723086,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.16331031068965585,
        0.09124757021792662,
        -0.0018550938581521571
      ],
      "tangent_gradient": [
        -0.16331031068966073,
        0.09124757021792433,
        -0.0018550938581521252
      ],
      "reverse_gradient": [
        -0.16331031068965685,
        0.0912475702179274,
        -0.0018550938581520793
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.01930261264641911,
      "amplitude_gradient_error": 0.01930261264641911,
      "phase_gradient_error": 0.0060917119049120755,
      "viscosity_gradient_error": 0.0018550938581521571,
      "gradient_duality_error": 4.884981308350689e-15,
      "gradient_reverse_error": 9.992007221626409e-16,
      "reverse_state_adjoint_error": 2.7044338990478423e-15,
      "transpose_relative_error": 2.956068869261468e-15,
      "state_l1_error": 0.0023447618127647304,
      "state_linf_error": 0.004938051685799638,
      "primal_residual_inf": 2.3314683517128287e-15,
      "primal_residual_density_inf": 1.1937117960769683e-12,
      "newton_correction_inf": 1.5242467600761631e-16,
      "tangent_residual_inf": 1.1674688993323912e-14,
      "adjoint_residual_inf": 3.1411505341250034e-15,
      "jacobian_nonzeros": 1535,
      "psi_0": -1.4298830777035012,
      "psi_N": -0.026377961508792337,
      "exact_nodal_residual_inf": 3.0118401911138903e-05,
      "exact_nodal_residual_boundary_rows_inf": 1.3184240003794034e-05,
      "exact_nodal_residual_inner_rows_inf": 3.0118401911138903e-05,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.47119882184729,
      "objective_quadrature_error": 3.6145593740322113e-07,
      "objective_quadrature_remainder": 9.074964328892592e-13,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.13593603960249112,
        "adjoint_directional_gradient": -0.13593603962427786,
        "absolute_error": 2.1786739079487916e-11,
        "perturbed_primal_residuals_inf": [
          2.55351295663786e-15,
          2.3314683517128287e-15
        ],
        "axis_central_differences": [
          -0.16331031069682922,
          0.09124757015532835,
          -0.0018550939562267386
        ],
        "axis_absolute_errors": [
          7.1733730067080614e-12,
          6.259827378674032e-11,
          9.807458144217573e-11
        ]
      },
      "adjoint_l1_reference_error": 0.0040122475315121,
      "adjoint_linf_reference_error": 0.0979305034314717,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.003315112312616053,
      "psi_N_boundary_flux_error": 0.004343410051475614,
      "elapsed_seconds": 0.02268254199589137,
      "cells": 512,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 3.0118401911138903e-05,
          "correction_inf": 0.004925000234957675,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 1.2001481797252467e-07,
          "correction_inf": 1.3100593718296523e-05,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 1.2330692022999301e-12,
          "correction_inf": 9.266515995070191e-11,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 2.220446049250313e-15,
          "correction_inf": 1.5242467600761631e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.003705140435631,
      "state_linf_observed_order": 1.0053814991868228,
      "gradient_observed_order": 1.0038641633070546,
      "amplitude_gradient_observed_order": 1.0038641633070546,
      "phase_gradient_observed_order": 0.9375545629781229,
      "viscosity_gradient_observed_order": 0.3985502527412368,
      "adjoint_l1_observed_order": 0.9684447808740052,
      "psi_0_observed_order": 0.9999393329455235,
      "psi_N_observed_order": 1.00178087449738,
      "profile": {
        "x": [
          0.0,
          0.005859375,
          0.01171875,
          0.017578125,
          0.0234375,
          0.03125,
          0.037109375,
          0.04296875,
          0.048828125,
          0.0546875,
          0.0625,
          0.068359375,
          0.07421875,
          0.080078125,
          0.0859375,
          0.09375,
          0.099609375,
          0.10546875,
          0.111328125,
          0.1171875,
          0.125,
          0.130859375,
          0.13671875,
          0.142578125,
          0.1484375,
          0.15625,
          0.162109375,
          0.16796875,
          0.173828125,
          0.1796875,
          0.1875,
          0.193359375,
          0.19921875,
          0.205078125,
          0.2109375,
          0.21875,
          0.224609375,
          0.23046875,
          0.236328125,
          0.2421875,
          0.25,
          0.255859375,
          0.26171875,
          0.267578125,
          0.2734375,
          0.28125,
          0.287109375,
          0.29296875,
          0.298828125,
          0.3046875,
          0.3125,
          0.318359375,
          0.32421875,
          0.330078125,
          0.3359375,
          0.34375,
          0.349609375,
          0.35546875,
          0.361328125,
          0.3671875,
          0.375,
          0.380859375,
          0.38671875,
          0.392578125,
          0.3984375,
          0.40625,
          0.412109375,
          0.41796875,
          0.423828125,
          0.4296875,
          0.4375,
          0.443359375,
          0.44921875,
          0.455078125,
          0.4609375,
          0.46875,
          0.474609375,
          0.48046875,
          0.486328125,
          0.4921875,
          0.5,
          0.505859375,
          0.51171875,
          0.517578125,
          0.5234375,
          0.53125,
          0.537109375,
          0.54296875,
          0.548828125,
          0.5546875,
          0.5625,
          0.568359375,
          0.57421875,
          0.580078125,
          0.5859375,
          0.59375,
          0.599609375,
          0.60546875,
          0.611328125,
          0.6171875,
          0.625,
          0.630859375,
          0.63671875,
          0.642578125,
          0.6484375,
          0.65625,
          0.662109375,
          0.66796875,
          0.673828125,
          0.6796875,
          0.6875,
          0.693359375,
          0.69921875,
          0.705078125,
          0.7109375,
          0.71875,
          0.724609375,
          0.73046875,
          0.736328125,
          0.7421875,
          0.75,
          0.755859375,
          0.76171875,
          0.767578125,
          0.7734375,
          0.78125,
          0.787109375,
          0.79296875,
          0.798828125,
          0.8046875,
          0.8125,
          0.818359375,
          0.82421875,
          0.830078125,
          0.8359375,
          0.84375,
          0.849609375,
          0.85546875,
          0.861328125,
          0.8671875,
          0.875,
          0.880859375,
          0.88671875,
          0.892578125,
          0.8984375,
          0.90625,
          0.912109375,
          0.91796875,
          0.923828125,
          0.9296875,
          0.9375,
          0.943359375,
          0.94921875,
          0.955078125,
          0.9609375,
          0.96875,
          0.974609375,
          0.98046875,
          0.986328125,
          0.9921875,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9215946726585516,
          0.9284478149581072,
          0.9353943552593721,
          0.9424249542794058,
          0.9519134909120849,
          0.9591032918028963,
          0.9663452688868892,
          0.9736296803432467,
          0.9809467253600554,
          0.9907365244708309,
          0.9980913660981895,
          1.0054459129467606,
          1.012790259382389,
          1.0201145107080187,
          1.0298318650266438,
          1.0370709088451149,
          1.0442571239020606,
          1.0513808154432427,
          1.0584323698290203,
          1.067705790570332,
          1.0745521910154814,
          1.0812951601691754,
          1.0879255840688542,
          1.0944344974705253,
          1.1029088395943432,
          1.1091002897445146,
          1.1151415739270556,
          1.1210245091353186,
          1.1267411233629414,
          1.13409119213583,
          1.139389987943862,
          1.1444975507209658,
          1.149406944599456,
          1.154111499145195,
          1.1600545856679807,
          1.1642567999921853,
          1.1682339719085413,
          1.1719806821042704,
          1.1754918210954517,
          1.1797986586242362,
          1.1827420536440192,
          1.1854351708770947,
          1.1878743194206807,
          1.1900561507909344,
          1.1925598510806916,
          1.1941302114402104,
          1.1954346226586416,
          1.1964712681384297,
          1.1972386932022656,
          1.1978413069166958,
          1.1979769419025217,
          1.1978411450643793,
          1.1974340483213284,
          1.1967561511650446,
          1.1954325937040164,
          1.1941268313451152,
          1.1925545779975297,
          1.1907179137401886,
          1.188619277809189,
          1.1854184672364574,
          1.1827200430937543,
          1.179770328238678,
          1.1765732759868524,
          1.173133176645126,
          1.1681763393186484,
          1.1641876645564622,
          1.1599726019505512,
          1.1555368313720753,
          1.1508863345911253,
          1.1443625419585388,
          1.1392359155311471,
          1.1339165778230584,
          1.1284117222267482,
          1.1227287972920823,
          1.1148878992235578,
          1.1088198039757378,
          1.102600180650649,
          1.09623746444109,
          1.0897402889619536,
          1.0808835000971948,
          1.0741071886959848,
          1.0672264789103239,
          1.0602507268291932,
          1.0531894221853852,
          1.0436578940868708,
          1.0364345252718015,
          1.0291580349227085,
          1.0218383408586311,
          1.0144854239016463,
          1.0046471959538668,
          0.9972558242563803,
          0.9898647773457534,
          0.9824841494369848,
          0.9751240236462115,
          0.9653597935060144,
          0.958086550393766,
          0.9508671589951186,
          0.9437114918226039,
          0.9366293354275184,
          0.9273175367019155,
          0.9204443776859472,
          0.9136765531326726,
          0.9070233182774178,
          0.9004937699054254,
          0.891995506738028,
          0.8857889492890341,
          0.8797350909537113,
          0.8738421944168732,
          0.8681182974078783,
          0.8607627711324602,
          0.8554631152296867,
          0.8503574818890112,
          0.8454528061802198,
          0.8407557415127107,
          0.8348268930371642,
          0.830638478009661,
          0.8266777027090447,
          0.8229498994422992,
          0.8194600753055996,
          0.8151851985900389,
          0.8122682567050462,
          0.8096035561196405,
          0.8071946265808823,
          0.8050446443068621,
          0.8025856288904127,
          0.8010501974428964,
          0.7997817058164318,
          0.7987817641615322,
          0.798051616377718,
          0.7974992281430877,
          0.7974013750501916,
          0.7975748115017668,
          0.7980191923412985,
          0.7987338079667795,
          0.8001050888358879,
          0.801445460042648,
          0.8030510952205112,
          0.8049197320901392,
          0.8070487585717024,
          0.8102873494921283,
          0.8130118597791841,
          0.8159855812208215,
          0.8192044375916547,
          0.8226640288260363,
          0.8276430942664923,
          0.831645515621772,
          0.8358717462425739,
          0.840316057012117,
          0.8449724311980794,
          0.8514998844678521,
          0.8566261188885033,
          0.8619423872602415,
          0.8674415216751196,
          0.8731161123327079,
          0.8809419242896137,
          0.8869958104046353,
          0.8931988314364333,
          0.8995426436563932,
          0.9060187157763061,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9215626788176685,
          0.9283875166237151,
          0.9353094058745663,
          0.942318965812554,
          0.9517849878333923,
          0.958961988695707,
          0.9661946055358682,
          0.9734730364886012,
          0.9807874175999334,
          0.9905787098580715,
          0.9979383663337875,
          1.0053008167989943,
          1.0126560834338865,
          1.019994198154407,
          1.0297344867793845,
          1.0369939713974832,
          1.0442033206452674,
          1.051352764190421,
          1.0584326128866821,
          1.0677475840490582,
          1.0746279188868315,
          1.0814071156686507,
          1.0880759870180796,
          1.0946254950751089,
          1.1031571796570094,
          1.1093939573051783,
          1.1154824808905242,
          1.121414499058216,
          1.1271819725543883,
          1.1346025027019546,
          1.139956047293125,
          1.145119919135096,
          1.1500871199895806,
          1.1548509181528746,
          1.160875127054017,
          1.1651397048718524,
          1.1691804802714947,
          1.172991977069572,
          1.176569029808141,
          1.180965410493204,
          1.1839771362037679,
          1.186739530428566,
          1.1892488494857985,
          1.1915016926689335,
          1.1941012946937084,
          1.1957444293669393,
          1.1971222851560026,
          1.198232994748263,
          1.1990750528758454,
          1.199777974992394,
          1.19998937388428,
          1.1999297410123453,
          1.1995991571928963,
          1.1989980704433143,
          1.197777299748901,
          1.1965488389185808,
          1.195054009043474,
          1.1932948359631033,
          1.1912737037630503,
          1.188176153790845,
          1.1855550422990992,
          1.1826824608946107,
          1.1795623025882411,
          1.1761987959147013,
          1.17134350377301,
          1.1674304694645299,
          1.1632905282230717,
          1.1589292906246123,
          1.1543526671527733,
          1.147926218995722,
          1.1428716375845276,
          1.1376234321263032,
          1.1321887151508527,
          1.1265748519541372,
          1.1188242125804078,
          1.1128223287954895,
          1.1066675447130307,
          1.1003682014861313,
          1.0939328361788985,
          1.0851558583130145,
          1.0784373211823315,
          1.0716124833762848,
          1.0646905941254337,
          1.057681034187446,
          1.0482150121666078,
          1.041038011304293,
          1.0338053944641319,
          1.0265269635113987,
          1.0192125824000666,
          1.0094212901419286,
          1.0020616336662125,
          0.9946991832010057,
          0.9873439165661135,
          0.9800058018455932,
          0.9702655132206155,
          0.963006028602517,
          0.9557966793547326,
          0.948647235809579,
          0.941567387113318,
          0.9322524159509418,
          0.9253720811131685,
          0.9185928843313493,
          0.9119240129819205,
          0.9053745049248911,
          0.8968428203429906,
          0.8906060426948219,
          0.884517519109476,
          0.8785855009417841,
          0.8728180274456117,
          0.8653974972980454,
          0.8600439527068752,
          0.854880080864904,
          0.8499128800104195,
          0.8451490818471254,
          0.8391248729459831,
          0.8348602951281476,
          0.8308195197285054,
          0.827008022930428,
          0.8234309701918588,
          0.8190345895067961,
          0.8160228637962321,
          0.813260469571434,
          0.8107511505142015,
          0.8084983073310664,
          0.8058987053062915,
          0.8042555706330606,
          0.8028777148439973,
          0.8017670052517369,
          0.8009249471241546,
          0.800222025007606,
          0.8000106261157199,
          0.8000702589876546,
          0.8004008428071038,
          0.8010019295566856,
          0.8022227002510991,
          0.8034511610814192,
          0.8049459909565259,
          0.8067051640368967,
          0.8087262962369496,
          0.8118238462091549,
          0.8144449577009008,
          0.8173175391053893,
          0.8204376974117589,
          0.8238012040852987,
          0.82865649622699,
          0.8325695305354701,
          0.8367094717769283,
          0.8410707093753875,
          0.8456473328472267,
          0.852073781004278,
          0.8571283624154724,
          0.8623765678736969,
          0.8678112848491473,
          0.8734251480458627,
          0.8811757874195922,
          0.8871776712045105,
          0.893332455286969,
          0.8996317985138687,
          0.9060671638211015,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4298830777035012,
          -0.5641886334671439,
          -0.9207017025487649,
          -1.1443528474084337,
          -1.2832904661471032,
          -1.3884558363972852,
          -1.4311842356684414,
          -1.4554833604965074,
          -1.4682119299557361,
          -1.4737038833953637,
          -1.4743312943753706,
          -1.4718487460456526,
          -1.4678979667360454,
          -1.4630473268996662,
          -1.4576489163881807,
          -1.4499616661445518,
          -1.4439900046666232,
          -1.4379222633292237,
          -1.431800442831114,
          -1.4256498483061946,
          -1.4174294241295438,
          -1.4112599639541146,
          -1.405091849422512,
          -1.3989272828775245,
          -1.3927672764010073,
          -1.384561452394216,
          -1.3784124466284522,
          -1.3722674909526789,
          -1.3661259206813277,
          -1.3599869678097805,
          -1.3518043081314906,
          -1.3456681026749528,
          -1.339531522742468,
          -1.333393585599134,
          -1.327253278811242,
          -1.3190607165886483,
          -1.312910794493716,
          -1.3067549415382753,
          -1.300592038509554,
          -1.2944209442748593,
          -1.2861780646136851,
          -1.2799833011693889,
          -1.2737763917438596,
          -1.2675561063102578,
          -1.261321195337423,
          -1.2529830341964097,
          -1.2467090300476078,
          -1.2404160975432275,
          -1.2341029052445203,
          -1.227768103222105,
          -1.2192857177590364,
          -1.2128951401481738,
          -1.206478320619514,
          -1.2000338300212519,
          -1.193560221052558,
          -1.1848809117676282,
          -1.1783336298711669,
          -1.1717522746783229,
          -1.1651353207103903,
          -1.1584812246009888,
          -1.1495486189356878,
          -1.1428017561032615,
          -1.1360124787529817,
          -1.1291791674125724,
          -1.1223001855558599,
          -1.1130543067905747,
          -1.1060623025329948,
          -1.0990190535031852,
          -1.0919228532256895,
          -1.0847719803450293,
          -1.0751494351205813,
          -1.0678642199691009,
          -1.0605184956267049,
          -1.0531104846786226,
          -1.0456383992661356,
          -1.0355728399945423,
          -1.027944245056288,
          -1.020245556661677,
          -1.0124749568715832,
          -1.0046306250859054,
          -0.9940536739935687,
          -0.9860302206018567,
          -0.9779269733549638,
          -0.9697421246110015,
          -0.9614738763852133,
          -0.9503167291778841,
          -0.941846966447061,
          -0.9332879196070579,
          -0.9246378688281376,
          -0.915895121905358,
          -0.9040910670796214,
          -0.8951256344411032,
          -0.8860621183965077,
          -0.876898996351511,
          -0.8676347976418148,
          -0.8551228682076737,
          -0.8456174362319474,
          -0.8360064695408131,
          -0.8262887859209341,
          -0.8164632854328032,
          -0.803193168376034,
          -0.793112326758033,
          -0.7829206769636766,
          -0.7726175490629524,
          -0.7622023897799725,
          -0.7481405149917598,
          -0.7374625020308274,
          -0.7266715400794181,
          -0.7157676565831047,
          -0.7047510297000216,
          -0.6898874169885365,
          -0.6786093046800286,
          -0.6672202037851925,
          -0.6557210085985722,
          -0.6441127909891428,
          -0.6284677692100248,
          -0.6166103571884812,
          -0.604648819032532,
          -0.5925850288649426,
          -0.5804210495377531,
          -0.5640504786582043,
          -0.5516618026542969,
          -0.5391811656497354,
          -0.526611432790148,
          -0.5139556455126715,
          -0.49695297608762273,
          -0.4841091709709541,
          -0.47119064626233276,
          -0.4582011324722036,
          -0.4451444963969741,
          -0.42763815339386835,
          -0.41444062169624823,
          -0.4011897007834669,
          -0.3878897167858001,
          -0.3745450674553354,
          -0.35669042918236615,
          -0.3432589588457707,
          -0.32979781540034897,
          -0.31631153922429656,
          -0.3028046635519665,
          -0.28477124401569165,
          -0.2712337791565916,
          -0.25769058145382223,
          -0.24414598150742153,
          -0.23060422544773174,
          -0.21256012938805433,
          -0.19904095103220987,
          -0.18553799816109717,
          -0.1720550095660085,
          -0.15859557885919912,
          -0.1406922390656055,
          -0.12730087370349477,
          -0.11394389290838917,
          -0.10062417404041725,
          -0.08734441464623928,
          -0.06970454710726277,
          -0.05652748363920988,
          -0.043398036802501386,
          -0.030318098180559708,
          -0.017289372226233876,
          -0.026377961508792337
        ],
        "amplitude_tangent": [
          -0.425779291565073,
          -0.3920201689203613,
          -0.357750899706374,
          -0.3230171200354518,
          -0.2878651006810217,
          -0.24042619266069143,
          -0.20448134952764566,
          -0.1682763305658368,
          -0.13185946994378536,
          -0.09527941371992375,
          -0.04633668244741806,
          -0.00956629121090761,
          0.0272037087712324,
          0.06392406077000842,
          0.10054554095019434,
          0.149135495445954,
          0.18533552676378307,
          0.22127369028388869,
          0.2569016660716179,
          0.29217151807456704,
          0.33855890241400594,
          0.37280935772612983,
          0.40654550779583176,
          0.43972182622264677,
          0.4722935112641549,
          0.5147059282640288,
          0.545697102107379,
          0.5759403186817338,
          0.6053946132338061,
          0.6340200607585315,
          0.6708310570362649,
          0.6973735143683059,
          0.7229622465803721,
          0.7475624511951426,
          0.7711406412279541,
          0.8009331042844227,
          0.8220040994413633,
          0.8419515386804935,
          0.8607481468635524,
          0.878368189350253,
          0.8999898420889899,
          0.9147734025250456,
          0.9283061840914029,
          0.9405695130961894,
          0.9515464217377172,
          0.9641551160021087,
          0.9720741474565494,
          0.978662807781577,
          0.9839117663111058,
          0.98781349785776,
          0.9909105160476941,
          0.9916496729082634,
          0.9910296815640773,
          0.9890509364268786,
          0.9857156677747267,
          0.9791657830810682,
          0.9726842581657307,
          0.9648668577377546,
          0.9557237118403005,
          0.9452667470097083,
          0.9293043562192678,
          0.9158381691183648,
          0.9011106825247799,
          0.8851414042534096,
          0.8679515316944996,
          0.8431727458607967,
          0.8232265368945412,
          0.8021422284447588,
          0.7799479973067033,
          0.7566735401511981,
          0.7240146757953031,
          0.6983434253552186,
          0.6717014089098482,
          0.6441244426634974,
          0.615649637044252,
          0.5763530595154219,
          0.5459345217731927,
          0.5147505662721661,
          0.48284333784901534,
          0.45025600204805266,
          0.40582468262040844,
          0.37182360761216576,
          0.33729295405120235,
          0.3022796473762231,
          0.26683132057717324,
          0.21897371535275137,
          0.182699085104899,
          0.14615251066637772,
          0.10938395493631574,
          0.072443742827652,
          0.02301062913276435,
          -0.014132883239211766,
          -0.05127856596959577,
          -0.08837532100561427,
          -0.125372060074501,
          -0.17445732680890727,
          -0.21102261499953456,
          -0.2473185941426297,
          -0.2832950592419956,
          -0.31890220600620356,
          -0.36571872416527285,
          -0.4002732540647023,
          -0.4342963027880265,
          -0.46774066405660525,
          -0.5005599291992984,
          -0.5432680048984594,
          -0.5744532619649511,
          -0.6048654222960894,
          -0.6344623681026444,
          -0.6632031574443882,
          -0.7001239804420059,
          -0.7267149479535208,
          -0.7523226090417509,
          -0.7769118501429709,
          -0.8004490571367786,
          -0.830140313764354,
          -0.8511008540252493,
          -0.8709087765069147,
          -0.8895375132216359,
          -0.9069622277726869,
          -0.9282826342691896,
          -0.9428113305286882,
          -0.9560660933393362,
          -0.9680298988777436,
          -0.9786875749334275,
          -0.9908433158527971,
          -0.9984048226243483,
          -1.0046231009951314,
          -1.0094910732906575,
          -1.0130035273535702,
          -1.0155726852714717,
          -1.0159124142258287,
          -1.0148926133365945,
          -1.012516040154388,
          -1.0087872526700448,
          -1.0017233039118478,
          -0.9948670483250093,
          -0.9866865282790837,
          -0.9771938734392958,
          -0.9664029005416459,
          -0.9500223207801922,
          -0.9362649596256927,
          -0.9212671946012445,
          -0.9050498540794898,
          -0.887635310371502,
          -0.862595102297618,
          -0.8424825359900512,
          -0.821258102352182,
          -0.7989505076353244,
          -0.7755898315670903,
          -0.742858627226556,
          -0.7171651846570626,
          -0.6905283803183067,
          -0.6629838184642166,
          -0.634568272016586,
          -0.5953916724243706,
          -0.5650930750631428,
          -0.5340539482233739,
          -0.5023156143495686,
          -0.46992031848470217,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.6452236866184494,
          -1.0186322059802366,
          -1.2327318371863474,
          -1.3538335289342776,
          -1.435452258974065,
          -1.4640310887728583,
          -1.4776048006101377,
          -1.482579164708046,
          -1.482648499900719,
          -1.4786383980768152,
          -1.474001928983762,
          -1.4686414083466506,
          -1.4628803761714422,
          -1.4569010507123703,
          -1.4487585756787476,
          -1.4425918454368094,
          -1.4364041956449138,
          -1.4302096642277466,
          -1.4240157494076802,
          -1.415764514000809,
          -1.4095836838753655,
          -1.4034099462754484,
          -1.397243227923015,
          -1.3910831528669891,
          -1.3828790750042284,
          -1.3767321481951589,
          -1.3705896324681344,
          -1.3644507115814777,
          -1.3583145282436164,
          -1.3501356615065214,
          -1.3440023401656065,
          -1.3378686618233568,
          -1.3317336364211718,
          -1.3255962480475916,
          -1.3174075855632377,
          -1.3112605950702376,
          -1.3051076808041397,
          -1.2989477251816484,
          -1.292779588988537,
          -1.2845406736100697,
          -1.27834890151452,
          -1.2721450016645992,
          -1.2659277465539713,
          -1.2596958892624928,
          -1.2513618407046998,
          -1.2450909553722673,
          -1.2388011743574574,
          -1.2324911691993437,
          -1.226159593026162,
          -1.2176815743703033,
          -1.2112943253394006,
          -1.2048808839499838,
          -1.1984398245079146,
          -1.191969703271647,
          -1.1832951386352595,
          -1.1767514908795726,
          -1.170173839007986,
          -1.1635606615617526,
          -1.1569104193080115,
          -1.1479830797943542,
          -1.1412402680367975,
          -1.1344551337702502,
          -1.1276260622016019,
          -1.1207514216173566,
          -1.1115114976775105,
          -1.1045240910093577,
          -1.0974855581037608,
          -1.0903941978999847,
          -1.0832482945996913,
          -1.0736325868078067,
          -1.066352665826596,
          -1.0590123847059487,
          -1.051609972194627,
          -1.0441436467304397,
          -1.0340860297515553,
          -1.0264635968152303,
          -1.0187712538098328,
          -1.0110071895957198,
          -1.0031695904636784,
          -0.9926019348639512,
          -0.9845857011867907,
          -0.9764898941860143,
          -0.9683127133370129,
          -0.9600523677744659,
          -0.9489061349092898,
          -0.9404448501553189,
          -0.9318945394936521,
          -0.9232534899275233,
          -0.9145200159383187,
          -0.9027287589134401,
          -0.8937732581389305,
          -0.8847199664487087,
          -0.8755673668753448,
          -0.8663139940300429,
          -0.8538169794012982,
          -0.8443230994292844,
          -0.8347240026335662,
          -0.8250185100598021,
          -0.8152055244498968,
          -0.8019526011111301,
          -0.7918850368733198,
          -0.7817069925727447,
          -0.7714177980403099,
          -0.7610168990111564,
          -0.7469745432344487,
          -0.7363115450793944,
          -0.7255359159233802,
          -0.7146476788497784,
          -0.7036470068881545,
          -0.6888051370372679,
          -0.6775436754101372,
          -0.6661715114069415,
          -0.6546895312325135,
          -0.643098798113265,
          -0.6274774923346687,
          -0.6156381573730669,
          -0.6036949338425823,
          -0.5916496856610944,
          -0.5795044653306175,
          -0.5631592260425939,
          -0.5507897749995923,
          -0.5383285455429686,
          -0.5257783928237234,
          -0.5131423485672851,
          -0.49616624040342966,
          -0.48334252261415894,
          -0.47044421847720397,
          -0.457475050570477,
          -0.44443887822697925,
          -0.4269599914822432,
          -0.4137831720258928,
          -0.4005530595177546,
          -0.38727397439899025,
          -0.37395030900931486,
          -0.3561237726601953,
          -0.3427134646900551,
          -0.3292735516462113,
          -0.3158085687746268,
          -0.302323044009176,
          -0.28431817230583833,
          -0.2708021705715057,
          -0.25728047365937107,
          -0.24375740523805084,
          -0.23023720397284939,
          -0.21222186987012365,
          -0.1987242683582797,
          -0.18524288655035923,
          -0.17178145326986788,
          -0.15834355162418218,
          -0.14046885733724157,
          -0.12709891627692108,
          -0.11376329531524125,
          -0.1004648596616528,
          -0.08720629454651528,
          -0.06959452629354974,
          -0.056438401475047084,
          -0.04332976333180994,
          -0.030270491526990632,
          -0.017262278942452004,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.4693632033225419,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.15364484524337646,
        0.088267062882754,
        -0.0010896030286097812
      ],
      "tangent_gradient": [
        -0.1536448452433791,
        0.08826706288274418,
        -0.0010896030286097055
      ],
      "reverse_gradient": [
        -0.15364484524337696,
        0.08826706288275354,
        -0.0010896030286096092
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.009637147200139723,
      "amplitude_gradient_error": 0.009637147200139723,
      "phase_gradient_error": 0.0031112045697394564,
      "viscosity_gradient_error": 0.0010896030286097812,
      "gradient_duality_error": 9.825473767932635e-15,
      "gradient_reverse_error": 4.996003610813204e-16,
      "reverse_state_adjoint_error": 6.2727600891321345e-15,
      "transpose_relative_error": 4.666355836666283e-15,
      "state_l1_error": 0.0011707783427565024,
      "state_linf_error": 0.002464166147156721,
      "primal_residual_inf": 4.3298697960381105e-15,
      "primal_residual_density_inf": 4.433786671143025e-12,
      "newton_correction_inf": 1.4760484642411424e-16,
      "tangent_residual_inf": 4.959140736948697e-15,
      "adjoint_residual_inf": 5.990433843416909e-15,
      "jacobian_nonzeros": 3071,
      "psi_0": -1.4282247654609472,
      "psi_N": -0.024204910190884985,
      "exact_nodal_residual_inf": 7.529771899550397e-06,
      "exact_nodal_residual_boundary_rows_inf": 3.251175292207087e-06,
      "exact_nodal_residual_inner_rows_inf": 7.529771899550397e-06,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4711985507551668,
      "objective_quadrature_error": 9.036381420912676e-08,
      "objective_quadrature_remainder": 5.673242969850956e-14,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.12716472636009613,
        "adjoint_directional_gradient": -0.12716472637855025,
        "absolute_error": 1.8454127115319352e-11,
        "perturbed_primal_residuals_inf": [
          4.440892098500626e-15,
          4.551914400963142e-15
        ],
        "axis_central_differences": [
          -0.15364484524660327,
          0.08826706282549777,
          -0.0010896030855356287
        ],
        "axis_absolute_errors": [
          3.2268077099217862e-12,
          5.7256227536939264e-11,
          5.692584749937557e-11
        ]
      },
      "adjoint_l1_reference_error": 0.002027696015646395,
      "adjoint_linf_reference_error": 0.05145946037096505,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.001656800070062081,
      "psi_N_boundary_flux_error": 0.0021703587335682624,
      "elapsed_seconds": 0.026944457997160498,
      "cells": 1024,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 7.529771899550397e-06,
          "correction_inf": 0.002460911911699481,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 1.499497764845259e-08,
          "correction_inf": 3.268985168359974e-06,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 4.007905118896815e-14,
          "correction_inf": 5.7793972654184465e-12,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 4.3298697960381105e-15,
          "correction_inf": 1.4760484642411424e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.0019734134221419,
      "state_linf_observed_order": 1.0028424035516286,
      "gradient_observed_order": 1.002118085856974,
      "amplitude_gradient_observed_order": 1.002118085856974,
      "phase_gradient_observed_order": 0.9693744552017602,
      "viscosity_gradient_observed_order": 0.7676895630820909,
      "adjoint_l1_observed_order": 0.9845692290078311,
      "psi_0_observed_order": 1.000658228519767,
      "psi_N_observed_order": 1.0008946386817412,
      "profile": {
        "x": [
          0.0,
          0.005859375,
          0.01171875,
          0.0185546875,
          0.0244140625,
          0.03125,
          0.037109375,
          0.04296875,
          0.0498046875,
          0.0556640625,
          0.0625,
          0.068359375,
          0.07421875,
          0.0810546875,
          0.0869140625,
          0.09375,
          0.099609375,
          0.10546875,
          0.1123046875,
          0.1181640625,
          0.125,
          0.130859375,
          0.13671875,
          0.1435546875,
          0.1494140625,
          0.15625,
          0.162109375,
          0.16796875,
          0.1748046875,
          0.1806640625,
          0.1875,
          0.193359375,
          0.19921875,
          0.2060546875,
          0.2119140625,
          0.21875,
          0.224609375,
          0.23046875,
          0.2373046875,
          0.2431640625,
          0.25,
          0.255859375,
          0.26171875,
          0.2685546875,
          0.2744140625,
          0.28125,
          0.287109375,
          0.29296875,
          0.2998046875,
          0.3056640625,
          0.3125,
          0.318359375,
          0.32421875,
          0.3310546875,
          0.3369140625,
          0.34375,
          0.349609375,
          0.35546875,
          0.3623046875,
          0.3681640625,
          0.375,
          0.380859375,
          0.38671875,
          0.3935546875,
          0.3994140625,
          0.40625,
          0.412109375,
          0.41796875,
          0.4248046875,
          0.4306640625,
          0.4375,
          0.443359375,
          0.44921875,
          0.4560546875,
          0.4619140625,
          0.46875,
          0.474609375,
          0.48046875,
          0.4873046875,
          0.4931640625,
          0.5,
          0.505859375,
          0.51171875,
          0.5185546875,
          0.5244140625,
          0.53125,
          0.537109375,
          0.54296875,
          0.5498046875,
          0.5556640625,
          0.5625,
          0.568359375,
          0.57421875,
          0.5810546875,
          0.5869140625,
          0.59375,
          0.599609375,
          0.60546875,
          0.6123046875,
          0.6181640625,
          0.625,
          0.630859375,
          0.63671875,
          0.6435546875,
          0.6494140625,
          0.65625,
          0.662109375,
          0.66796875,
          0.6748046875,
          0.6806640625,
          0.6875,
          0.693359375,
          0.69921875,
          0.7060546875,
          0.7119140625,
          0.71875,
          0.724609375,
          0.73046875,
          0.7373046875,
          0.7431640625,
          0.75,
          0.755859375,
          0.76171875,
          0.7685546875,
          0.7744140625,
          0.78125,
          0.787109375,
          0.79296875,
          0.7998046875,
          0.8056640625,
          0.8125,
          0.818359375,
          0.82421875,
          0.8310546875,
          0.8369140625,
          0.84375,
          0.849609375,
          0.85546875,
          0.8623046875,
          0.8681640625,
          0.875,
          0.880859375,
          0.88671875,
          0.8935546875,
          0.8994140625,
          0.90625,
          0.912109375,
          0.91796875,
          0.9248046875,
          0.9306640625,
          0.9375,
          0.943359375,
          0.94921875,
          0.9560546875,
          0.9619140625,
          0.96875,
          0.974609375,
          0.98046875,
          0.9873046875,
          0.9931640625,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9215789698247038,
          0.9284182448140899,
          0.936517084975289,
          0.9435508209537921,
          0.9518506983760562,
          0.9590343416379975,
          0.9662718708923532,
          0.9747707208163731,
          0.9820914003271938,
          0.9906602529731695,
          0.9980176915113415,
          1.005376370237623,
          1.0139498003534908,
          1.0212770759253846,
          1.0297867168598596,
          1.0370361235221335,
          1.0442340402898826,
          1.0525535529725916,
          1.0596066304810439,
          1.0677309020893089,
          1.074594374592345,
          1.0813555565479496,
          1.089102118998785,
          1.0956104804573856,
          1.103037720589466,
          1.1092519123194633,
          1.1153168901180015,
          1.122193157259997,
          1.1279069327330074,
          1.1343519326288856,
          1.1396781636782107,
          1.144813939668297,
          1.150555684601674,
          1.1552552634554705,
          1.160470244721083,
          1.1647036933140142,
          1.1687127187503312,
          1.1730990187738761,
          1.1766035203313543,
          1.1803876972511402,
          1.1833653086164388,
          1.1860931156523162,
          1.1889548922279893,
          1.1911291621331688,
          1.1933365129766607,
          1.1949433147063149,
          1.1962845033749163,
          1.19751108092844,
          1.198270938976291,
          1.1988158820030401,
          1.198989458876831,
          1.1988918051164799,
          1.1984352326579062,
          1.1977507674623487,
          1.196611520532284,
          1.195344474682404,
          1.1938109997005841,
          1.1916879674174627,
          1.1895847500744314,
          1.1868042436118744,
          1.1841445447199783,
          1.1812334655725336,
          1.1775247422099153,
          1.1740829119637737,
          1.1697672198545221,
          1.1658164316579838,
          1.1616389946590093,
          1.1564864069014988,
          1.1518376634935836,
          1.1461520114910904,
          1.1410614619196537,
          1.135777741063778,
          1.1293788093646862,
          1.1237014258625233,
          1.1168639282952577,
          1.1108289676750787,
          1.1046417862595936,
          1.0972422186799153,
          1.0907542617964845,
          1.0830276209235983,
          1.076280182592604,
          1.0694273844486508,
          1.061311707405985,
          1.0542627165759904,
          1.0459441914256722,
          1.0387439290323206,
          1.0314892836076206,
          1.0229699532001006,
          1.0156313828374492,
          1.0070413936104203,
          0.9996657177823388,
          0.9922887895676691,
          0.9836941784161722,
          0.976348949504518,
          0.9678187298310874,
          0.9605521045058357,
          0.9533374531938785,
          0.9449991476646181,
          0.937930687560879,
          0.9297894336045642,
          0.9229123227317314,
          0.9161384301614054,
          0.90837830675343,
          0.901859484788426,
          0.8944214834804873,
          0.888199367328698,
          0.8821277158841413,
          0.8752452991221064,
          0.8695276944620219,
          0.8630799468320264,
          0.8577528557661015,
          0.8526176109982486,
          0.846878246736628,
          0.842182210393242,
          0.8369730928348644,
          0.8327461262310277,
          0.8287448924111965,
          0.8243692829561717,
          0.820875260210785,
          0.8171047628257814,
          0.8141400489316817,
          0.8114261453387991,
          0.8085817557765612,
          0.8064232918391809,
          0.8042353077766383,
          0.8026457914610099,
          0.8013224161650171,
          0.8001171514136488,
          0.7993758961851909,
          0.7988528970462807,
          0.7986982123225518,
          0.7988147211737722,
          0.799293101537571,
          0.7999959758108907,
          0.8011562241620122,
          0.8024407485744202,
          0.8039911174535691,
          0.8061329969445611,
          0.8082515295705802,
          0.811048809004184,
          0.8137218590870252,
          0.8166452687080535,
          0.8203670031115206,
          0.8238187429519988,
          0.828144477420454,
          0.8321025239369743,
          0.836285937523964,
          0.841443842688628,
          0.8460957033441864,
          0.8517832957304863,
          0.8568740503592996,
          0.8621566342431709,
          0.8685525581852326,
          0.8742259432347422,
          0.8810571541764316,
          0.8870853727271605,
          0.8932646030287777,
          0.9006534255728472,
          0.9071309709283544,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9215626788176685,
          0.9283875166237151,
          0.9364718327671492,
          0.9434950839380563,
          0.9517849878333923,
          0.958961988695707,
          0.9661946055358682,
          0.9746898706406245,
          0.9820092808323381,
          0.9905787098580715,
          0.9979383663337875,
          1.0053008167989943,
          1.0138805625912966,
          1.0212148509749215,
          1.0297344867793845,
          1.0369939713974832,
          1.0442033206452674,
          1.0525378323058943,
          1.0596051462919642,
          1.0677475840490582,
          1.0746279188868315,
          1.0814071156686507,
          1.0891761025885325,
          1.0957048492639578,
          1.1031571796570094,
          1.1093939573051783,
          1.1154824808905242,
          1.1223873852592277,
          1.1281266685506355,
          1.1346025027019546,
          1.139956047293125,
          1.145119919135096,
          1.150895389350047,
          1.1556246518191757,
          1.160875127054017,
          1.1651397048718524,
          1.1691804802714947,
          1.1736045682512535,
          1.1771420669936152,
          1.180965410493204,
          1.1839771362037679,
          1.186739530428566,
          1.1896422209531279,
          1.1918520118759057,
          1.1941012946937084,
          1.1957444293669393,
          1.1971222851560026,
          1.1983920294563561,
          1.199189191533653,
          1.199777974992394,
          1.19998937388428,
          1.1999297410123453,
          1.1995177435271087,
          1.1988716422673475,
          1.197777299748901,
          1.1965488389185808,
          1.195054009043474,
          1.192976102604954,
          1.19091156731721,
          1.188176153790845,
          1.1855550422990992,
          1.1826824608946107,
          1.179018498281936,
          1.1756148678995122,
          1.17134350377301,
          1.1674304694645299,
          1.1632905282230717,
          1.158181313464674,
          1.1535693875943887,
          1.147926218995722,
          1.1428716375845276,
          1.1376234321263032,
          1.1312653094800666,
          1.1256223218467176,
          1.1188242125804078,
          1.1128223287954895,
          1.1066675447130307,
          1.0993048532665743,
          1.092847660720287,
          1.0851558583130145,
          1.0784373211823315,
          1.0716124833762848,
          1.063528167232851,
          1.0565049160619437,
          1.0482150121666078,
          1.041038011304293,
          1.0338053944641319,
          1.0253101293593756,
          1.017990719167662,
          1.0094212901419286,
          1.0020616336662125,
          0.9946991832010057,
          0.9861194374087034,
          0.9787851490250786,
          0.9702655132206155,
          0.963006028602517,
          0.9557966793547326,
          0.9474621676941057,
          0.9403948537080358,
          0.9322524159509418,
          0.9253720811131685,
          0.9185928843313493,
          0.9108238974114677,
          0.9042951507360422,
          0.8968428203429906,
          0.8906060426948219,
          0.884517519109476,
          0.8776126147407726,
          0.8718733314493645,
          0.8653974972980454,
          0.8600439527068752,
          0.854880080864904,
          0.849104610649953,
          0.8443753481808243,
          0.8391248729459831,
          0.8348602951281476,
          0.8308195197285054,
          0.8263954317487465,
          0.8228579330063848,
          0.8190345895067961,
          0.8160228637962321,
          0.813260469571434,
          0.8103577790468722,
          0.8081479881240943,
          0.8058987053062915,
          0.8042555706330606,
          0.8028777148439973,
          0.8016079705436439,
          0.800810808466347,
          0.800222025007606,
          0.8000106261157199,
          0.8000702589876546,
          0.8004822564728913,
          0.8011283577326525,
          0.8022227002510991,
          0.8034511610814192,
          0.8049459909565259,
          0.807023897395046,
          0.8090884326827901,
          0.8118238462091549,
          0.8144449577009008,
          0.8173175391053893,
          0.8209815017180638,
          0.8243851321004878,
          0.82865649622699,
          0.8325695305354701,
          0.8367094717769283,
          0.8418186865353261,
          0.8464306124056112,
          0.852073781004278,
          0.8571283624154724,
          0.8623765678736969,
          0.8687346905199331,
          0.8743776781532822,
          0.8811757874195922,
          0.8871776712045105,
          0.893332455286969,
          0.9006951467334254,
          0.907152339279713,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4282247654609472,
          -0.6017892472315747,
          -0.9672089992330241,
          -1.2141743756944237,
          -1.3342121978791117,
          -1.4125377621544037,
          -1.448408044334935,
          -1.4673637668527777,
          -1.476914388279347,
          -1.478821346450369,
          -1.476919104883398,
          -1.4732482867331194,
          -1.4685029394906086,
          -1.4621918132494487,
          -1.4564086303622934,
          -1.4494277737547439,
          -1.4433359962228036,
          -1.4371928864531829,
          -1.429994958703415,
          -1.42381503566056,
          -1.4166038585162577,
          -1.4104262326932564,
          -1.404253733681221,
          -1.397059920196701,
          -1.3909002491550833,
          -1.3837210522476797,
          -1.3775729041083205,
          -1.3714290665297268,
          -1.3642656718572204,
          -1.3581284484642853,
          -1.3509704123745576,
          -1.344835658830911,
          -1.3387005451827039,
          -1.3315411369590668,
          -1.3254018156250573,
          -1.3182346731665036,
          -1.312086239717073,
          -1.3059318792812356,
          -1.2987428075956802,
          -1.2925717392136835,
          -1.2853600154776685,
          -1.2791667713201715,
          -1.2729613903357802,
          -1.2657047992023782,
          -1.2594688804766725,
          -1.2521732102842682,
          -1.2459007894504672,
          -1.2396094566887959,
          -1.2322438905918212,
          -1.2259069949654118,
          -1.2184845476588537,
          -1.2120956589196354,
          -1.205680553226148,
          -1.1981612226205032,
          -1.1916843925944358,
          -1.184089060271808,
          -1.1775436212376449,
          -1.170964143789537,
          -1.163243032563873,
          -1.1565845551690805,
          -1.1487670256549922,
          -1.1420222159672226,
          -1.1352350381769052,
          -1.1272609571723589,
          -1.1203764115914305,
          -1.1122842307941525,
          -1.1052945553834808,
          -1.098253694993916,
          -1.0899723919389843,
          -1.082814766235453,
          -1.074392506128964,
          -1.067109971137302,
          -1.0597670021001242,
          -1.051121455254907,
          -1.0436414450986997,
          -1.0348311137474506,
          -1.0272056363114168,
          -1.0195101577743364,
          -1.0104412049165215,
          -1.0025878290554135,
          -0.9933296855754263,
          -0.9853098820033235,
          -0.9772103954468631,
          -0.9676578776641495,
          -0.9593795685784055,
          -0.949613532924988,
          -0.9411480519805959,
          -0.9325934164123971,
          -0.9224980382420974,
          -0.913744382813179,
          -0.9034122456658122,
          -0.8944518229295804,
          -0.8853934629562668,
          -0.8746995696573205,
          -0.8654238675560004,
          -0.854472488488838,
          -0.8449728745580889,
          -0.8353678840152066,
          -0.8240273066226129,
          -0.8141900591168664,
          -0.8025756615278132,
          -0.7925014939301157,
          -0.78231668028881,
          -0.7702936655787573,
          -0.7598669748910467,
          -0.7475604690682681,
          -0.7368899858262379,
          -0.7261067093719649,
          -0.7133837037647645,
          -0.7023563287270379,
          -0.6893492956731865,
          -0.6780795110730349,
          -0.6666988765306203,
          -0.6532825647987756,
          -0.6416650455182089,
          -0.6279756081161001,
          -0.6161272111732051,
          -0.6041748016110567,
          -0.5901013672621938,
          -0.5779302602935834,
          -0.5636076431250583,
          -0.5512285277018243,
          -0.5387575373389739,
          -0.5240957546263849,
          -0.511435749360317,
          -0.4965620636375527,
          -0.4837282243077229,
          -0.47081972788253296,
          -0.4556704368336239,
          -0.44261315020491765,
          -0.427301069237375,
          -0.4141137979501673,
          -0.4008731834898946,
          -0.3853641525717694,
          -0.37202288909144626,
          -0.35640856983063957,
          -0.34298757967978843,
          -0.32953695102535974,
          -0.31381314547847633,
          -0.30031385850640097,
          -0.28454565157919,
          -0.2710188260786543,
          -0.2574862896806803,
          -0.24169688141836446,
          -0.22816670347043222,
          -0.2123914923031598,
          -0.1988830311063679,
          -0.18539079743013828,
          -0.16967534151172922,
          -0.15623088268971785,
          -0.1405807203366746,
          -0.12720002423766746,
          -0.11385368614453664,
          -0.09833020371955462,
          -0.08506791788870842,
          -0.06964954559753121,
          -0.056482938558658005,
          -0.043363888539166465,
          -0.02812094198351052,
          -0.015111151001400402,
          -0.024204910190884985
        ],
        "amplitude_tangent": [
          -0.4257792915650726,
          -0.39210159128038224,
          -0.3579031791769539,
          -0.3174082358306251,
          -0.28224007412166385,
          -0.24074234217936238,
          -0.20482621010665367,
          -0.16864105251889303,
          -0.12614996311721272,
          -0.08954928636335434,
          -0.04670796997816999,
          -0.009922923788656467,
          0.026868832393237715,
          0.06973490129073054,
          0.1063712080162153,
          0.14892049038760508,
          0.18516956032433915,
          0.22116230466668657,
          0.26276508180249325,
          0.2980363244379957,
          0.3386662097727742,
          0.37299238680289887,
          0.4068085368748155,
          0.44555512953450405,
          0.47811033555373406,
          0.515264024458491,
          0.5463515572923204,
          0.5766944671375301,
          0.611098624030568,
          0.639688566323879,
          0.6719398404540815,
          0.6985949190879858,
          0.7242989597814222,
          0.7530385214380949,
          0.7765640418623315,
          0.8026724698272489,
          0.823869462442774,
          0.8439451895285323,
          0.8659133458217606,
          0.8834679862666546,
          0.9024270538006993,
          0.9173483180860228,
          0.9310208917842947,
          0.945369175883972,
          0.9562744034688667,
          0.9673506432525306,
          0.9754183281661529,
          0.9821576647245505,
          0.9883289891075873,
          0.9921606341385925,
          0.994922228359499,
          0.9958208316107569,
          0.9953623207048737,
          0.9931127854548393,
          0.989717681703392,
          0.9840514508078673,
          0.9777402808671161,
          0.9700952927085733,
          0.959503955955932,
          0.9490061715237038,
          0.9351223327191772,
          0.9218374308755565,
          0.9072932463803954,
          0.888759527859814,
          0.8715559894205032,
          0.8499805538584322,
          0.8302260487522042,
          0.8093352632334229,
          0.7835641380084599,
          0.7603098666446965,
          0.7318650265253014,
          0.7063943041623822,
          0.6799541621922635,
          0.6479297713005941,
          0.6195133452355601,
          0.5852866576821196,
          0.5550741128613921,
          0.524096606862633,
          0.48704533759841817,
          0.4545555512669862,
          0.4158591247184177,
          0.3820635882581748,
          0.3477374682640684,
          0.30708190555993536,
          0.2717668761960874,
          0.23008807222166616,
          0.19400925205671576,
          0.15765531872296493,
          0.11496070605989538,
          0.07818085984291391,
          0.0351262077507752,
          -0.0018443828389096064,
          -0.03882321569582779,
          -0.08190826001366044,
          -0.11873181916121485,
          -0.16149773708397006,
          -0.1979298558842068,
          -0.23410222071919343,
          -0.27590897178337265,
          -0.31134920074709516,
          -0.3521681270480898,
          -0.386648361884199,
          -0.4206102840080517,
          -0.45951534761798357,
          -0.49219552359427254,
          -0.5294812671052574,
          -0.5606693953417221,
          -0.5911005823192746,
          -0.6255913706814202,
          -0.6542409483400285,
          -0.6865441138906218,
          -0.7132280993404275,
          -0.7389463807348944,
          -0.7676837757694255,
          -0.7911912393777168,
          -0.8172597182111425,
          -0.8384064153146638,
          -0.8584172563010445,
          -0.880291699091369,
          -0.897751054685272,
          -0.9165822373954199,
          -0.931380264505355,
          -0.9449177768129832,
          -0.9590946095464076,
          -0.969841983912142,
          -0.9807226848274161,
          -0.9886141741622947,
          -0.995170513307774,
          -1.001121231357552,
          -1.0047590059076819,
          -1.0072904918202792,
          -1.0079898544601842,
          -1.0073315121256408,
          -1.004849677484501,
          -1.0012575173820626,
          -0.9953653965578868,
          -0.9888653130748659,
          -0.981036883941394,
          -0.9702398071990922,
          -0.9595738667167631,
          -0.9455046650408336,
          -0.9320711024348395,
          -0.9173884934423345,
          -0.8987071272202589,
          -0.8813895960561723,
          -0.8596965630478883,
          -0.8398549625862644,
          -0.8188901156315713,
          -0.7930494375769334,
          -0.7697502306117309,
          -0.7412702733312788,
          -0.7157843443198644,
          -0.6893427223477255,
          -0.6573338308086623,
          -0.6289452738204858,
          -0.5947677994520786,
          -0.5646114222613824,
          -0.5337026288147881,
          -0.4967468435472015,
          -0.46435151304253663,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.6452236866184494,
          -1.0186322059802366,
          -1.2580584378964412,
          -1.3679903307589019,
          -1.435452258974065,
          -1.4640310887728583,
          -1.4776048006101377,
          -1.482859069398939,
          -1.4823480399941174,
          -1.4786383980768152,
          -1.474001928983762,
          -1.4686414083466506,
          -1.4618954696565736,
          -1.455891239421422,
          -1.4487585756787476,
          -1.4425918454368094,
          -1.4364041956449138,
          -1.4291771640992195,
          -1.4229837969559833,
          -1.415764514000809,
          -1.4095836838753655,
          -1.4034099462754484,
          -1.3962161006604692,
          -1.390057082419985,
          -1.3828790750042284,
          -1.3767321481951589,
          -1.3705896324681344,
          -1.3634278479427417,
          -1.3572920349760977,
          -1.3501356615065214,
          -1.3440023401656065,
          -1.3378686618233568,
          -1.3307109302581637,
          -1.3245730475305442,
          -1.3174075855632377,
          -1.3112605950702376,
          -1.3051076808041397,
          -1.2979203016551337,
          -1.2917506897880204,
          -1.2845406736100697,
          -1.27834890151452,
          -1.2721450016645992,
          -1.2648901516683984,
          -1.2586557381036292,
          -1.2513618407046998,
          -1.2450909553722673,
          -1.2388011743574574,
          -1.231437441131548,
          -1.2251021375596687,
          -1.2176815743703033,
          -1.2112943253394006,
          -1.2048808839499838,
          -1.1973635284038,
          -1.1908884219034122,
          -1.1832951386352595,
          -1.1767514908795726,
          -1.170173839007986,
          -1.1624549036243028,
          -1.1557983330143715,
          -1.1479830797943542,
          -1.1412402680367975,
          -1.1344551337702502,
          -1.126483497597273,
          -1.1196011023654024,
          -1.1115114976775105,
          -1.1045240910093577,
          -1.0974855581037608,
          -1.089207048278804,
          -1.0820518866480346,
          -1.0736325868078067,
          -1.066352665826596,
          -1.0590123847059487,
          -1.0503700712703463,
          -1.0428929197794958,
          -1.0340860297515553,
          -1.0264635968152303,
          -1.0187712538098328,
          -1.0097060786668848,
          -1.0018560473068798,
          -0.9926019348639512,
          -0.9845857011867907,
          -0.9764898941860143,
          -0.9669418126008665,
          -0.9586674329776274,
          -0.9489061349092898,
          -0.9404448501553189,
          -0.9318945394936521,
          -0.9218043743727847,
          -0.9130553345946228,
          -0.9027287589134401,
          -0.8937732581389305,
          -0.8847199664487087,
          -0.8740321749839263,
          -0.8647618680347754,
          -0.8538169794012982,
          -0.8443230994292844,
          -0.8347240026335662,
          -0.8233905056330193,
          -0.8135595039187548,
          -0.8019526011111301,
          -0.7918850368733198,
          -0.7817069925727447,
          -0.7696920853376245,
          -0.7592725235090926,
          -0.7469745432344487,
          -0.7363115450793944,
          -0.7255359159233802,
          -0.7128220345799463,
          -0.7018026511490357,
          -0.6888051370372679,
          -0.6775436754101372,
          -0.6661715114069415,
          -0.6527652633287384,
          -0.6411565207243236,
          -0.6274774923346687,
          -0.6156381573730669,
          -0.6036949338425823,
          -0.589632366593696,
          -0.5774706970231887,
          -0.5631592260425939,
          -0.5507897749995923,
          -0.5383285455429686,
          -0.5236782657258161,
          -0.5110282130762174,
          -0.49616624040342966,
          -0.48334252261415894,
          -0.47044421847720397,
          -0.45530690213400904,
          -0.44225994662561985,
          -0.4269599914822432,
          -0.4137831720258928,
          -0.4005530595177546,
          -0.38505633981100806,
          -0.37172567567280373,
          -0.3561237726601953,
          -0.3427134646900551,
          -0.3292735516462113,
          -0.31356228580002554,
          -0.3000737762422044,
          -0.28431817230583833,
          -0.2708021705715057,
          -0.25728047365937107,
          -0.24150372614877288,
          -0.22798440813395202,
          -0.21222186987012365,
          -0.1987242683582797,
          -0.18524288655035923,
          -0.16954007430216594,
          -0.156106432235307,
          -0.14046885733724157,
          -0.12709891627692108,
          -0.11376329531524125,
          -0.09825226016981832,
          -0.08500058838050999,
          -0.06959452629354974,
          -0.056438401475047084,
          -0.04332976333180994,
          -0.028098867320587858,
          -0.01509931614584829,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.4702814051531203,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.14882257421713402,
        0.08672790259798008,
        -0.0005858135393340949
      ],
      "tangent_gradient": [
        -0.14882257421713355,
        0.08672790259797426,
        -0.0005858135393340526
      ],
      "reverse_gradient": [
        -0.1488225742171323,
        0.08672790259797858,
        -0.000585813539333957
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.004814876173897281,
      "amplitude_gradient_error": 0.004814876173897281,
      "phase_gradient_error": 0.001572044284965532,
      "viscosity_gradient_error": 0.0005858135393340949,
      "gradient_duality_error": 5.814793091474257e-15,
      "gradient_reverse_error": 1.7208456881689926e-15,
      "reverse_state_adjoint_error": 8.867906409193438e-15,
      "transpose_relative_error": 8.498145241035116e-15,
      "state_l1_error": 0.0005849757396747554,
      "state_linf_error": 0.0012308446545907792,
      "primal_residual_inf": 8.992806499463768e-15,
      "primal_residual_density_inf": 1.8417267710901797e-11,
      "newton_correction_inf": 1.3233715678992543e-16,
      "tangent_residual_inf": 1.1102230246251565e-14,
      "adjoint_residual_inf": 1.1179533861149782e-14,
      "jacobian_nonzeros": 6143,
      "psi_0": -1.4273960734787123,
      "psi_N": -0.023119393790603703,
      "exact_nodal_residual_inf": 1.882459976343398e-06,
      "exact_nodal_residual_boundary_rows_inf": 8.071634566841901e-07,
      "exact_nodal_residual_inner_rows_inf": 1.882459976343398e-06,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4711984829822955,
      "objective_quadrature_error": 2.2590942894140653e-08,
      "objective_quadrature_remainder": 3.5249663882258873e-15,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.12280420340626817,
        "adjoint_directional_gradient": -0.12280420343774,
        "absolute_error": 3.14718251459567e-11,
        "perturbed_primal_residuals_inf": [
          8.548717289613705e-15,
          8.659739592076221e-15
        ],
        "axis_central_differences": [
          -0.14882257421966472,
          0.08672790254848904,
          -0.0005858135532221809
        ],
        "axis_absolute_errors": [
          2.530697873481813e-12,
          4.9491036269166955e-11,
          1.3888085993729593e-11
        ]
      },
      "adjoint_l1_reference_error": 0.0010192138437541231,
      "adjoint_linf_reference_error": 0.026439737255553375,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.000828108087827184,
      "psi_N_boundary_flux_error": 0.0010848423332869804,
      "elapsed_seconds": 0.036075040996365715,
      "cells": 2048,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 1.882459976343398e-06,
          "correction_inf": 0.001230031969771759,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 1.873799559959366e-09,
          "correction_inf": 8.164133549363784e-07,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 9.43689570931383e-15,
          "correction_inf": 3.607993599317658e-13,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 8.770761894538737e-15,
          "correction_inf": 1.3233715678992543e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.0010192648251095,
      "state_linf_observed_order": 1.0014508432887144,
      "gradient_observed_order": 1.0011074451604203,
      "amplitude_gradient_observed_order": 1.0011074451604203,
      "phase_gradient_observed_order": 0.984831399590843,
      "viscosity_gradient_observed_order": 0.895289176204542,
      "adjoint_l1_observed_order": 0.9923846066398347,
      "psi_0_observed_order": 1.000508528490448,
      "psi_N_observed_order": 1.0004481398124696,
      "profile": {
        "x": [
          0.0,
          0.005859375,
          0.01220703125,
          0.0185546875,
          0.02490234375,
          0.03125,
          0.037109375,
          0.04345703125,
          0.0498046875,
          0.05615234375,
          0.0625,
          0.068359375,
          0.07470703125,
          0.0810546875,
          0.08740234375,
          0.09375,
          0.099609375,
          0.10595703125,
          0.1123046875,
          0.11865234375,
          0.125,
          0.130859375,
          0.13720703125,
          0.1435546875,
          0.14990234375,
          0.15625,
          0.162109375,
          0.16845703125,
          0.1748046875,
          0.18115234375,
          0.1875,
          0.193359375,
          0.19970703125,
          0.2060546875,
          0.21240234375,
          0.21875,
          0.224609375,
          0.23095703125,
          0.2373046875,
          0.24365234375,
          0.25,
          0.255859375,
          0.26220703125,
          0.2685546875,
          0.27490234375,
          0.28125,
          0.287109375,
          0.29345703125,
          0.2998046875,
          0.30615234375,
          0.3125,
          0.318359375,
          0.32470703125,
          0.3310546875,
          0.33740234375,
          0.34375,
          0.349609375,
          0.35595703125,
          0.3623046875,
          0.36865234375,
          0.375,
          0.380859375,
          0.38720703125,
          0.3935546875,
          0.39990234375,
          0.40625,
          0.412109375,
          0.41845703125,
          0.4248046875,
          0.43115234375,
          0.4375,
          0.443359375,
          0.44970703125,
          0.4560546875,
          0.46240234375,
          0.46875,
          0.474609375,
          0.48095703125,
          0.4873046875,
          0.49365234375,
          0.5,
          0.505859375,
          0.51220703125,
          0.5185546875,
          0.52490234375,
          0.53125,
          0.537109375,
          0.54345703125,
          0.5498046875,
          0.55615234375,
          0.5625,
          0.568359375,
          0.57470703125,
          0.5810546875,
          0.58740234375,
          0.59375,
          0.599609375,
          0.60595703125,
          0.6123046875,
          0.61865234375,
          0.625,
          0.630859375,
          0.63720703125,
          0.6435546875,
          0.64990234375,
          0.65625,
          0.662109375,
          0.66845703125,
          0.6748046875,
          0.68115234375,
          0.6875,
          0.693359375,
          0.69970703125,
          0.7060546875,
          0.71240234375,
          0.71875,
          0.724609375,
          0.73095703125,
          0.7373046875,
          0.74365234375,
          0.75,
          0.755859375,
          0.76220703125,
          0.7685546875,
          0.77490234375,
          0.78125,
          0.787109375,
          0.79345703125,
          0.7998046875,
          0.80615234375,
          0.8125,
          0.818359375,
          0.82470703125,
          0.8310546875,
          0.83740234375,
          0.84375,
          0.849609375,
          0.85595703125,
          0.8623046875,
          0.86865234375,
          0.875,
          0.880859375,
          0.88720703125,
          0.8935546875,
          0.89990234375,
          0.90625,
          0.912109375,
          0.91845703125,
          0.9248046875,
          0.93115234375,
          0.9375,
          0.943359375,
          0.94970703125,
          0.9560546875,
          0.96240234375,
          0.96875,
          0.974609375,
          0.98095703125,
          0.9873046875,
          0.99365234375,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9215708984873716,
          0.9289768384570743,
          0.936494685787623,
          0.9441125073986437,
          0.9518182113009562,
          0.9589985945813375,
          0.9668388189282465,
          0.9747308490735578,
          0.9826621558203074,
          0.9906201468997695,
          0.9979787422818409,
          1.0059525152535451,
          1.0139159904716462,
          1.021856521152171,
          1.0297614959481236,
          1.0370159775490182,
          1.0448173501857758,
          1.0525466939465158,
          1.0601917287137308,
          1.067740307184453,
          1.0746122372687192,
          1.0819417562963487,
          1.0891402535512242,
          1.096196286792546,
          1.1030986390502635,
          1.1093241432655525,
          1.1159003365874711,
          1.1222915187049292,
          1.1284875250578519,
          1.1344785002852358,
          1.139818403283918,
          1.1453885949714127,
          1.1507268658441268,
          1.155824720268313,
          1.1606740439390442,
          1.1649230701654594,
          1.1692731032144807,
          1.1733531921971299,
          1.1771568378592419,
          1.180677979802335,
          1.1836726609296486,
          1.1866351490615545,
          1.189300022677487,
          1.1916630298460398,
          1.1937203981850446,
          1.1953453797497464,
          1.1968061675745618,
          1.1979530926897535,
          1.1987843152002031,
          1.199298497046806,
          1.1994909997152918,
          1.199393580868727,
          1.1989781044576358,
          1.1982452147439857,
          1.1971960608461305,
          1.1959483237603357,
          1.1942960462116419,
          1.192333737933309,
          1.1900645040918507,
          1.1874919383473541,
          1.1848515502525108,
          1.1817075236956507,
          1.17827341405398,
          1.1745546696603009,
          1.1705571922207862,
          1.1666252975094409,
          1.1621100062354326,
          1.1573357417211634,
          1.1523100877379775,
          1.1470410288913884,
          1.1419684770941958,
          1.13625518950097,
          1.1303240132913615,
          1.1241843778578517,
          1.117846045460988,
          1.111827630818533,
          1.1051357802233541,
          1.098275529240305,
          1.0912577919370445,
          1.0840937344173935,
          1.0773607438255046,
          1.0699475311382312,
          1.0624219142345137,
          1.0547958733470324,
          1.0470815500732444,
          1.0398929001115156,
          1.0320434342971387,
          1.0241419192906445,
          1.0162009410519321,
          1.00823314977521,
          1.000865444668109,
          0.9928817897937905,
          0.9849084772806053,
          0.9769582136225585,
          0.9690436695905829,
          0.9617805510668731,
          0.9539700886215532,
          0.9462319878655585,
          0.9385785841226605,
          0.9310220780123541,
          0.9241432660496793,
          0.9168068094873694,
          0.9096019578719772,
          0.9025401960953314,
          0.8956327802463888,
          0.8894032227059442,
          0.8828233400878458,
          0.8764292248206846,
          0.8702310638376145,
          0.8642387299624377,
          0.8588982900831383,
          0.8533283006007434,
          0.8479910489953535,
          0.8428950274130456,
          0.8380483410873656,
          0.8338024507975318,
          0.8294565561804569,
          0.8253813517043292,
          0.821583305986404,
          0.8180684436188409,
          0.8150801270883526,
          0.8121251069644823,
          0.8094682490788568,
          0.8071137519552989,
          0.8050653309788568,
          0.8034489446996166,
          0.8019977738522532,
          0.8008607201068553,
          0.8000395567770113,
          0.7995355541490234,
          0.7993524950471015,
          0.7994601314939213,
          0.7998857456042715,
          0.8006286257803215,
          0.8016875569445407,
          0.8029440744984433,
          0.8046055411436259,
          0.8065766448113291,
          0.8088542241560451,
          0.8114346327984229,
          0.8140817720033714,
          0.8172325408748112,
          0.8206727588147168,
          0.824396941084958,
          0.8283991542382189,
          0.8323347737689528,
          0.8368533789185564,
          0.8416301901367337,
          0.8466576110913149,
          0.8519276495582903,
          0.8570004043575462,
          0.8627131539776671,
          0.8686430104209205,
          0.8747805554179012,
          0.8811160423257646,
          0.8871311773879983,
          0.8938187901739044,
          0.9006741181935007,
          0.907686278995109,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9215626788176685,
          0.92896076245099,
          0.9364718327671492,
          0.9440839435382744,
          0.9517849878333923,
          0.958961988695707,
          0.9667995272783676,
          0.9746898706406245,
          0.9826204693273637,
          0.9905787098580715,
          0.9979383663337875,
          1.005914167653398,
          1.0138805625912966,
          1.0218248807336492,
          1.0297344867793845,
          1.0369939713974832,
          1.0448015298822118,
          1.0525378323058943,
          1.0601905742128748,
          1.0677475840490582,
          1.0746279188868315,
          1.0819671944426394,
          1.0891761025885325,
          1.0962431776803625,
          1.1031571796570094,
          1.1093939573051783,
          1.1159829056883688,
          1.1223873852592277,
          1.1285972098033896,
          1.1346025027019546,
          1.139956047293125,
          1.1455414589124568,
          1.150895389350047,
          1.1560093232718187,
          1.160875127054017,
          1.1651397048718524,
          1.1695069354911298,
          1.1736045682512535,
          1.1774260859379484,
          1.180965410493204,
          1.1839771362037679,
          1.1869583555994632,
          1.1896422209531279,
          1.1920244636231778,
          1.1941012946937084,
          1.1957444293669393,
          1.197225070949563,
          1.1983920294563561,
          1.1992434488599284,
          1.199777974992394,
          1.19998937388428,
          1.1999125374281652,
          1.1995177435271087,
          1.1988056200940054,
          1.197777299748901,
          1.1965488389185808,
          1.1949174772056455,
          1.192976102604954,
          1.190727802839346,
          1.188176153790845,
          1.1855550422990992,
          1.1824318476450935,
          1.179018498281936,
          1.1753204230829546,
          1.17134350377301,
          1.1674304694645299,
          1.1629354644884993,
          1.158181313464674,
          1.1531755777883113,
          1.147926218995722,
          1.1428716375845276,
          1.1371775628068732,
          1.1312653094800666,
          1.1251442809411167,
          1.1188242125804078,
          1.1128223287954895,
          1.1061480043166425,
          1.0993048532665743,
          1.0923037595590763,
          1.0851558583130145,
          1.0784373211823315,
          1.07103923754901,
          1.063528167232851,
          1.0559160564617256,
          1.0482150121666078,
          1.041038011304293,
          1.0332004727216324,
          1.0253101293593756,
          1.0173795306726363,
          1.0094212901419286,
          1.0020616336662125,
          0.9940858323466022,
          0.9861194374087034,
          0.9781751192663508,
          0.9702655132206155,
          0.963006028602517,
          0.9551984701177884,
          0.9474621676941057,
          0.9398094257871252,
          0.9322524159509418,
          0.9253720811131685,
          0.9180328055573608,
          0.9108238974114677,
          0.9037568223196376,
          0.8968428203429906,
          0.8906060426948219,
          0.8840170943116313,
          0.8776126147407726,
          0.8714027901966104,
          0.8653974972980454,
          0.8600439527068752,
          0.8544585410875432,
          0.849104610649953,
          0.8439906767281813,
          0.8391248729459831,
          0.8348602951281476,
          0.8304930645088703,
          0.8263954317487465,
          0.8225739140620518,
          0.8190345895067961,
          0.8160228637962321,
          0.8130416444005368,
          0.8103577790468722,
          0.8079755363768223,
          0.8058987053062915,
          0.8042555706330606,
          0.802774929050437,
          0.8016079705436439,
          0.8007565511400716,
          0.800222025007606,
          0.8000106261157199,
          0.8000874625718349,
          0.8004822564728913,
          0.8011943799059946,
          0.8022227002510991,
          0.8034511610814192,
          0.8050825227943545,
          0.807023897395046,
          0.809272197160654,
          0.8118238462091549,
          0.8144449577009008,
          0.8175681523549067,
          0.8209815017180638,
          0.8246795769170454,
          0.82865649622699,
          0.8325695305354701,
          0.8370645355115007,
          0.8418186865353261,
          0.8468244222116887,
          0.852073781004278,
          0.8571283624154724,
          0.8628224371931267,
          0.8687346905199331,
          0.8748557190588833,
          0.8811757874195922,
          0.8871776712045105,
          0.8938519956833574,
          0.9006951467334254,
          0.9076962404409235,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4273960734787123,
          -0.6226908433158692,
          -1.015141081983295,
          -1.2358651036633352,
          -1.3581214740921532,
          -1.424174391903221,
          -1.4564453193139002,
          -1.4735670569423183,
          -1.4800716450758122,
          -1.48063231041397,
          -1.477884128644871,
          -1.4737013214507562,
          -1.4681758813602044,
          -1.4620780682145462,
          -1.455673252619631,
          -1.4491073285822782,
          -1.4429730827596627,
          -1.436289467034128,
          -1.4295894818962744,
          -1.4228859446807849,
          -1.4161854085520718,
          -1.4100057134281918,
          -1.4033181541944795,
          -1.3966382843575398,
          -1.3899658307877945,
          -1.3833001828122626,
          -1.3771526183703022,
          -1.3704976684712615,
          -1.3638468327438327,
          -1.3571990267044107,
          -1.350553112667352,
          -1.3444190793454804,
          -1.3377734420280998,
          -1.331126124667387,
          -1.324475831584084,
          -1.3178212328577945,
          -1.311673526765736,
          -1.305006790357077,
          -1.2983316768396236,
          -1.2916467337530417,
          -1.2849504796543032,
          -1.2787579774894158,
          -1.272035704174778,
          -1.265297629449691,
          -1.2585421640856285,
          -1.251767692505124,
          -1.2454960454472381,
          -1.2386803872075924,
          -1.2318408520332076,
          -1.224975723626682,
          -1.2180832604671483,
          -1.211695197772661,
          -1.2047451807583542,
          -1.197762594731827,
          -1.190745600119233,
          -1.1836923325139277,
          -1.1771477956113594,
          -1.170019441067598,
          -1.162849221970273,
          -1.1556351772119828,
          -1.1483753213229908,
          -1.1416315175453426,
          -1.1342778942025016,
          -1.126872518335556,
          -1.1194133111928826,
          -1.111898171132706,
          -1.1049096376500458,
          -1.097280945586615,
          -1.0895900513942778,
          -1.0818347695618125,
          -1.074012895253754,
          -1.0667316755820773,
          -1.0587754758458805,
          -1.050746138916586,
          -1.0426413961930836,
          -1.0344589667184456,
          -1.0268350207092158,
          -1.018496746317371,
          -1.010074066393522,
          -1.0015646725792444,
          -0.9929662560526489,
          -0.9849482474810226,
          -0.976172156984335,
          -0.9673003233200794,
          -0.9583304691347108,
          -0.949260335053685,
          -0.9407969629854881,
          -0.9315277201971246,
          -0.9221517419086138,
          -0.9126668877745977,
          -0.903071061868973,
          -0.8941131112186507,
          -0.8842981798205141,
          -0.8743664669869432,
          -0.8643161166215485,
          -0.8541453522208381,
          -0.8446486159386242,
          -0.8342416227621801,
          -0.8237095574425726,
          -0.8130510376069346,
          -0.8022648035906371,
          -0.7921939467243753,
          -0.7811590620961946,
          -0.7699935747083272,
          -0.7586967991675873,
          -0.7472682205305778,
          -0.7366014856985083,
          -0.7249186626124173,
          -0.7131035993306826,
          -0.7011565417937559,
          -0.6890779520853237,
          -0.6778123299133243,
          -0.6654829234033693,
          -0.6530246489153427,
          -0.6404388894152336,
          -0.6277272775878445,
          -0.6158834061608403,
          -0.602935295758491,
          -0.5898675724224206,
          -0.576682878953243,
          -0.5633841173931107,
          -0.5510098215751679,
          -0.5375007974037062,
          -0.523887648674442,
          -0.510174260654653,
          -0.49636475301254956,
          -0.4835359553454303,
          -0.4695539972442167,
          -0.45548920651471597,
          -0.4413465131877456,
          -0.42713101854990077,
          -0.4139489495752738,
          -0.3996083411939242,
          -0.3852106580286902,
          -0.37076149650603357,
          -0.3562665291422257,
          -0.3428508551385047,
          -0.3282839233275174,
          -0.3136879952218886,
          -0.29906882691354225,
          -0.28443214011355605,
          -0.2709107037637575,
          -0.25625618238479425,
          -0.2416004627938604,
          -0.22694892178194562,
          -0.21230679833779653,
          -0.19880374951892704,
          -0.18419387391430625,
          -0.16960777417452066,
          -0.15504998525206543,
          -0.14052482789279683,
          -0.12714949896920805,
          -0.11269840276386787,
          -0.09829124312165091,
          -0.08393140896332699,
          -0.06962203622026206,
          -0.056460667444359056,
          -0.04225620688719613,
          -0.028109900447086604,
          -0.014023874421857783,
          -0.023119393790603703
        ],
        "amplitude_tangent": [
          -0.4257792915650747,
          -0.39214364191448664,
          -0.35511279585207806,
          -0.31752318756716275,
          -0.2794343449366638,
          -0.24090659287845514,
          -0.20500571667185413,
          -0.1658059619640083,
          -0.12634730888106652,
          -0.08669228681556072,
          -0.04690374685847467,
          -0.010111901508770275,
          0.029756017566488997,
          0.06957282617763004,
          0.10927537226569607,
          0.1488006732373943,
          0.18507400715169234,
          0.2240825046658936,
          0.26273156433576067,
          0.3009598294512234,
          0.3387065999048311,
          0.3730705537669115,
          0.4097236158039568,
          0.44572242114465,
          0.48100976760143627,
          0.5155295729443692,
          0.5466652830519065,
          0.5795559399256982,
          0.6115223780600209,
          0.6425137547578049,
          0.6724807682424336,
          0.699192164589204,
          0.7270566966045727,
          0.7537623173378866,
          0.7792665062428878,
          0.8035286455836838,
          0.8247885970303152,
          0.8465553022407247,
          0.8669727363648397,
          0.8860083439944485,
          0.9036317611985838,
          0.9186217476956925,
          0.9334523433771262,
          0.9467949992219488,
          0.9586283843397886,
          0.9689335636151588,
          0.9770753232014143,
          0.9843973650969515,
          0.9901498578671994,
          0.9943235225252257,
          0.9969115880108285,
          0.9978895157561395,
          0.9974185855677257,
          0.995356729808952,
          0.9917070855359049,
          0.9864753135854302,
          0.98024875932747,
          0.9719995784014305,
          0.9621991881303286,
          0.9508630294056784,
          0.9380089860578654,
          0.924813995337654,
          0.9091000573827311,
          0.8919342370619713,
          0.8733436959579833,
          0.8533578643947994,
          0.8336983185497447,
          0.8111200810877787,
          0.7872451378248825,
          0.7621113404818473,
          0.7357585488646866,
          0.7103870698010034,
          0.681809185080498,
          0.6521397298692923,
          0.621425808452064,
          0.5897161961657961,
          0.5596055705474511,
          0.5261240514388669,
          0.4917982639898325,
          0.45668277547415315,
          0.4208334235010311,
          0.3871396492227848,
          0.350040231273852,
          0.31237661573382774,
          0.2742087577441674,
          0.23559743293293184,
          0.19961577591409327,
          0.16032502977084626,
          0.12077226436891607,
          0.0810205360708865,
          0.041133238364552294,
          0.004248891871175434,
          -0.03572015681032545,
          -0.07563848916012583,
          -0.11544236769199344,
          -0.15506821849342456,
          -0.19143315863001195,
          -0.23053902833070208,
          -0.26928293885702476,
          -0.3076029442664858,
          -0.3454377632719143,
          -0.37987922317771466,
          -0.41661164646254106,
          -0.4526845027311461,
          -0.4880400761699362,
          -0.5226217982163964,
          -0.5538086675518985,
          -0.5867478590554578,
          -0.6187552974254417,
          -0.649779802725041,
          -0.6797717843834181,
          -0.7064987798761797,
          -0.7343719706036185,
          -0.7610775582771808,
          -0.7865729577811265,
          -0.8108175505752498,
          -0.8320535873109095,
          -0.8537861440063801,
          -0.8741610475349451,
          -0.8931460006055791,
          -0.9107109621090567,
          -0.9256403977767389,
          -0.940398670864901,
          -0.9536624950017696,
          -0.9654110892339628,
          -0.9756261160068435,
          -0.9836804517417338,
          -0.9909038600984327,
          -0.9965543245991862,
          -1.000623294368489,
          -1.0031047436803768,
          -1.003983204659752,
          -1.0034040906114354,
          -1.0012343425699146,
          -0.9974778446165388,
          -0.9921409889625117,
          -0.9858196196119002,
          -0.9774707303841891,
          -0.9675743960118491,
          -0.9561466742854142,
          -0.9432060256639871,
          -0.9299359536427219,
          -0.9141464023219539,
          -0.8969113516876412,
          -0.8782583546634493,
          -0.8582171815059992,
          -0.8385131154384555,
          -0.8158939817641138,
          -0.7919859516021571,
          -0.766827013035597,
          -0.7404571118562331,
          -0.7150770007279414,
          -0.6864975143738552,
          -0.6568344646049911,
          -0.6261348582900461,
          -0.5944473310644918,
          -0.564363833061141,
          -0.5309188022687286,
          -0.4966366412739256,
          -0.461571631302892,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.6452236866184494,
          -1.041403686551528,
          -1.2580584378964412,
          -1.3745589282297428,
          -1.435452258974065,
          -1.4640310887728583,
          -1.4782828726774226,
          -1.482859069398939,
          -1.4821717113779327,
          -1.4786383980768152,
          -1.474001928983762,
          -1.4681733876554215,
          -1.4618954696565736,
          -1.4553852621255448,
          -1.4487585756787476,
          -1.4425918454368094,
          -1.435888111187398,
          -1.4291771640992195,
          -1.422467872517196,
          -1.415764514000809,
          -1.4095836838753655,
          -1.402895788605188,
          -1.3962161006604692,
          -1.3895441097823995,
          -1.3828790750042284,
          -1.3767321481951589,
          -1.3700779299972594,
          -1.3634278479427417,
          -1.3567808062691529,
          -1.3501356615065214,
          -1.3440023401656065,
          -1.3373574750008534,
          -1.3307109302581637,
          -1.3240614103115422,
          -1.3174075855632377,
          -1.3112605950702376,
          -1.3045946356807305,
          -1.2979203016551337,
          -1.2912361412085478,
          -1.2845406736100697,
          -1.27834890151452,
          -1.2716274242393255,
          -1.2648901516683984,
          -1.2581354953985968,
          -1.2513618407046998,
          -1.2450909553722673,
          -1.238276131499349,
          -1.231437441131548,
          -1.2245731689335362,
          -1.2176815743703033,
          -1.2112943253394006,
          -1.2043452036454092,
          -1.1973635284038,
          -1.1903474611508602,
          -1.1832951386352595,
          -1.1767514908795726,
          -1.169624118880319,
          -1.1624549036243028,
          -1.1552418853059692,
          -1.1479830797943542,
          -1.1412402680367975,
          -1.1338877450278733,
          -1.126483497597273,
          -1.1190254485073488,
          -1.1115114976775105,
          -1.1045240910093577,
          -1.0968966526986597,
          -1.089207048278804,
          -1.081453093992384,
          -1.0736325868078067,
          -1.066352665826596,
          -1.0583979145775928,
          -1.0503700712703463,
          -1.042266869299878,
          -1.0340860297515553,
          -1.0264635968152303,
          -1.018127012813923,
          -1.0097060786668848,
          -1.0011984882143903,
          -0.9926019348639512,
          -0.9845857011867907,
          -0.9758115952494365,
          -0.9669418126008665,
          -0.9579740781815531,
          -0.9489061349092898,
          -0.9404448501553189,
          -0.9311779411916862,
          -0.9218043743727847,
          -0.912322011543518,
          -0.9027287589134401,
          -0.8937732581389305,
          -0.8839610633932263,
          -0.8740321749839263,
          -0.863984738601081,
          -0.8538169794012982,
          -0.8443230994292844,
          -0.8339192910041043,
          -0.8233905056330193,
          -0.8127353619543484,
          -0.8019526011111301,
          -0.7918850368733198,
          -0.7808538134450653,
          -0.7696920853376245,
          -0.758399167040905,
          -0.7469745432344487,
          -0.7363115450793944,
          -0.7246328624518171,
          -0.7128220345799463,
          -0.7008793059767929,
          -0.6888051370372679,
          -0.6775436754101372,
          -0.6652188606094007,
          -0.6527652633287384,
          -0.6401842639365873,
          -0.6274774923346687,
          -0.6156381573730669,
          -0.6026950328737527,
          -0.589632366593696,
          -0.5764527980729037,
          -0.5631592260425939,
          -0.5507897749995923,
          -0.5372860551962608,
          -0.5236782657258161,
          -0.5099702886228165,
          -0.49616624040342966,
          -0.48334252261415894,
          -0.46936610873381934,
          -0.45530690213400904,
          -0.441169830145739,
          -0.4269599914822432,
          -0.4137831720258928,
          -0.3994482794284921,
          -0.38505633981100806,
          -0.3706129474234196,
          -0.3561237726601953,
          -0.3427134646900551,
          -0.32815236472683984,
          -0.31356228580002554,
          -0.29894898183693497,
          -0.28431817230583833,
          -0.2708021705715057,
          -0.2561535446147869,
          -0.24150372614877288,
          -0.2268580892099719,
          -0.21222186987012365,
          -0.1987242683582797,
          -0.1841202881129827,
          -0.16954007430216594,
          -0.1549881583469317,
          -0.14046885733724157,
          -0.12709891627692108,
          -0.11265363383644632,
          -0.09825226016981832,
          -0.08389818030413881,
          -0.06959452629354974,
          -0.056438401475047084,
          -0.0422395805806306,
          -0.028098867320587858,
          -0.014018384503054128,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.4707400792931686,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.14641419170959896,
        0.08594600406151687,
        -0.0003032221959191866
      ],
      "tangent_gradient": [
        -0.14641419170961317,
        0.08594600406150765,
        -0.00030322219591915397
      ],
      "reverse_gradient": [
        -0.1464141917096008,
        0.08594600406152075,
        -0.00030322219591916166
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.002406493666362225,
      "amplitude_gradient_error": 0.002406493666362225,
      "phase_gradient_error": 0.0007901457485023217,
      "viscosity_gradient_error": 0.0003032221959191866,
      "gradient_duality_error": 1.4210854715202004e-14,
      "gradient_reverse_error": 3.885780586188048e-15,
      "reverse_state_adjoint_error": 2.6664434549239502e-14,
      "transpose_relative_error": 4.947265464684183e-14,
      "state_l1_error": 0.0002923829964812057,
      "state_linf_error": 0.0006151086471366529,
      "primal_residual_inf": 1.8096635301390052e-14,
      "primal_residual_density_inf": 7.412381819449365e-11,
      "newton_correction_inf": 2.258213140376267e-14,
      "tangent_residual_inf": 3.3084646133829665e-14,
      "adjoint_residual_inf": 2.4805027823426862e-14,
      "jacobian_nonzeros": 12287,
      "psi_0": -1.4269819333194158,
      "psi_N": -0.022576888318899955,
      "exact_nodal_residual_inf": 4.7061745367393826e-07,
      "exact_nodal_residual_boundary_rows_inf": 2.0108583986822026e-07,
      "exact_nodal_residual_inner_rows_inf": 4.7061745367393826e-07,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4711984660390878,
      "objective_quadrature_error": 5.647735168423651e-09,
      "objective_quadrature_remainder": 3.2613008474389357e-16,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.12063039046550371,
        "adjoint_directional_gradient": -0.12063039049114391,
        "absolute_error": 2.5640198297871564e-11,
        "perturbed_primal_residuals_inf": [
          1.7763568394002505e-14,
          1.6431300764452317e-14
        ],
        "axis_central_differences": [
          -0.14641419170402514,
          0.08594600399147721,
          -0.0003032222029020204
        ],
        "axis_absolute_errors": [
          5.573819183979367e-12,
          7.00396546315929e-11,
          6.9828337990324174e-12
        ]
      },
      "adjoint_l1_reference_error": 0.000510943203675488,
      "adjoint_linf_reference_error": 0.013404516574273773,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.00041396792853065634,
      "psi_N_boundary_flux_error": 0.0005423368615832327,
      "elapsed_seconds": 0.04668333299923688,
      "cells": 4096,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 4.7061745367393826e-07,
          "correction_inf": 0.0006149056238229792,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 2.3418555983312217e-10,
          "correction_inf": 2.0399541614335519e-07,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 1.7541523789077473e-14,
          "correction_inf": 2.258213140376267e-14,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.0005173800960359,
      "state_linf_observed_order": 1.0007355277171237,
      "gradient_observed_order": 1.0005660698920704,
      "amplitude_gradient_observed_order": 1.0005660698920704,
      "phase_gradient_observed_order": 0.992451160105216,
      "viscosity_gradient_observed_order": 0.9500661742884899,
      "adjoint_l1_observed_order": 0.9962219430926699,
      "psi_0_observed_order": 1.0003000843950716,
      "psi_N_observed_order": 1.0002242463101176,
      "profile": {
        "x": [
          0.0,
          0.006103515625,
          0.012451171875,
          0.0185546875,
          0.02490234375,
          0.03125,
          0.037353515625,
          0.043701171875,
          0.0498046875,
          0.05615234375,
          0.0625,
          0.068603515625,
          0.074951171875,
          0.0810546875,
          0.08740234375,
          0.09375,
          0.099853515625,
          0.106201171875,
          0.1123046875,
          0.11865234375,
          0.125,
          0.131103515625,
          0.137451171875,
          0.1435546875,
          0.14990234375,
          0.15625,
          0.162353515625,
          0.168701171875,
          0.1748046875,
          0.18115234375,
          0.1875,
          0.193603515625,
          0.199951171875,
          0.2060546875,
          0.21240234375,
          0.21875,
          0.224853515625,
          0.231201171875,
          0.2373046875,
          0.24365234375,
          0.25,
          0.256103515625,
          0.262451171875,
          0.2685546875,
          0.27490234375,
          0.28125,
          0.287353515625,
          0.293701171875,
          0.2998046875,
          0.30615234375,
          0.3125,
          0.318603515625,
          0.324951171875,
          0.3310546875,
          0.33740234375,
          0.34375,
          0.349853515625,
          0.356201171875,
          0.3623046875,
          0.36865234375,
          0.375,
          0.381103515625,
          0.387451171875,
          0.3935546875,
          0.39990234375,
          0.40625,
          0.412353515625,
          0.418701171875,
          0.4248046875,
          0.43115234375,
          0.4375,
          0.443603515625,
          0.449951171875,
          0.4560546875,
          0.46240234375,
          0.46875,
          0.474853515625,
          0.481201171875,
          0.4873046875,
          0.49365234375,
          0.5,
          0.506103515625,
          0.512451171875,
          0.5185546875,
          0.52490234375,
          0.53125,
          0.537353515625,
          0.543701171875,
          0.5498046875,
          0.55615234375,
          0.5625,
          0.568603515625,
          0.574951171875,
          0.5810546875,
          0.58740234375,
          0.59375,
          0.599853515625,
          0.606201171875,
          0.6123046875,
          0.61865234375,
          0.625,
          0.631103515625,
          0.637451171875,
          0.6435546875,
          0.64990234375,
          0.65625,
          0.662353515625,
          0.668701171875,
          0.6748046875,
          0.68115234375,
          0.6875,
          0.693603515625,
          0.699951171875,
          0.7060546875,
          0.71240234375,
          0.71875,
          0.724853515625,
          0.731201171875,
          0.7373046875,
          0.74365234375,
          0.75,
          0.756103515625,
          0.762451171875,
          0.7685546875,
          0.77490234375,
          0.78125,
          0.787353515625,
          0.793701171875,
          0.7998046875,
          0.80615234375,
          0.8125,
          0.818603515625,
          0.824951171875,
          0.8310546875,
          0.83740234375,
          0.84375,
          0.849853515625,
          0.856201171875,
          0.8623046875,
          0.86865234375,
          0.875,
          0.881103515625,
          0.887451171875,
          0.8935546875,
          0.89990234375,
          0.90625,
          0.912353515625,
          0.918701171875,
          0.9248046875,
          0.93115234375,
          0.9375,
          0.943603515625,
          0.949951171875,
          0.9560546875,
          0.96240234375,
          0.96875,
          0.974853515625,
          0.981201171875,
          0.9873046875,
          0.99365234375,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.921849278738532,
          0.9292558536058534,
          0.9364833162643404,
          0.9440983005702072,
          0.951801692049166,
          0.9592807774932901,
          0.9671219175369103,
          0.9747104988674213,
          0.9826414660421071,
          0.9905995955735584,
          0.9982654855616019,
          1.0062401404333083,
          1.0138984797953334,
          1.021840915221533,
          1.0297482160193268,
          1.037306555362181,
          1.0451085033750829,
          1.0525425147051077,
          1.060191411176959,
          1.067744212964798,
          1.0749047208448257,
          1.0822343125210587,
          1.0891584651479898,
          1.096220025276745,
          1.103128208003595,
          1.1096158201972575,
          1.1161914824185508,
          1.1223397652811544,
          1.1285426852334024,
          1.1345408235853633,
          1.140106260416381,
          1.1456753162028201,
          1.1508114612316542,
          1.1559173590896963,
          1.160774926403125,
          1.1652042773113571,
          1.1695526623531325,
          1.173479231241538,
          1.1772918163057944,
          1.18082205293679,
          1.1839450067457853,
          1.1869055067314307,
          1.1894714895772815,
          1.1918441179782273,
          1.1939112212175313,
          1.1956076239420075,
          1.1970663143330467,
          1.1981729465616937,
          1.1990142713319754,
          1.1995386292175483,
          1.1997431162407086,
          1.1996437559458624,
          1.1992483290663452,
          1.1985258267202499,
          1.1974870939050641,
          1.1961916179304537,
          1.1945378275211354,
          1.1926553468611245,
          1.1903965846083973,
          1.1878344818002695,
          1.1850886392180575,
          1.1819437798054888,
          1.1786464053911574,
          1.1749380001824896,
          1.1709508063481335,
          1.1668599493982694,
          1.1623447067443968,
          1.1577589987175225,
          1.1527433079989597,
          1.14748410310841,
          1.1422053101758967,
          1.1364930765892765,
          1.130795150660041,
          1.1246648215374755,
          1.1183356236500763,
          1.1120716818599479,
          1.1053819124795343,
          1.0987906905931553,
          1.091781275659332,
          1.0846252962315819,
          1.0776169260013062,
          1.070206722889198,
          1.0629755364089397,
          1.0553564575714887,
          1.0476487698799661,
          1.0401653873127599,
          1.0323196314144072,
          1.0247264959584412,
          1.0167906995003984,
          1.0088276744228857,
          1.0011570420262457,
          0.993177447214132,
          0.9855143777813292,
          0.9775670726392176,
          0.9696549819786424,
          0.962092139691726,
          0.9542856434714782,
          0.9468474146087357,
          0.9391943206196248,
          0.93163754008481,
          0.9244734366442561,
          0.9171403685352075,
          0.9102131471151026,
          0.9031487010413279,
          0.8962379633641884,
          0.8897482231855989,
          0.8831707049495182,
          0.8770209932991888,
          0.8708169684302308,
          0.8648181224263431,
          0.8592523857448511,
          0.8536834175755154,
          0.8485477419201156,
          0.8434427312066679,
          0.8385864535666605,
          0.8341587157334568,
          0.8298123866846486,
          0.825888147038896,
          0.8220783361300364,
          0.8185512147976457,
          0.8154315594189381,
          0.8124747831089025,
          0.809912640125584,
          0.8075442492209497,
          0.8054816042864854,
          0.8037896687503764,
          0.8023357815064249,
          0.8012338891425154,
          0.8003975879496825,
          0.7998783161795624,
          0.7996787467847032,
          0.7997832164271945,
          0.800183519988111,
          0.8009110238453092,
          0.8019546539360952,
          0.8032547105989245,
          0.8049131015244416,
          0.8067998213477094,
          0.8090627732484703,
          0.8116288161794432,
          0.814378189086683,
          0.8175264295340456,
          0.8208267567447655,
          0.8245379049879229,
          0.8285274917377115,
          0.832620306660068,
          0.8371372180835112,
          0.8417241691922539,
          0.8467407705524238,
          0.8520004925265386,
          0.8572794100737615,
          0.8629913866032393,
          0.8686886965044432,
          0.8748180066330257,
          0.8811458073767662,
          0.8874080582948589,
          0.8940957193263143,
          0.9006845903060754,
          0.9076912389347392,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9218449883846314,
          0.929247636445234,
          0.9364718327671492,
          0.9440839435382744,
          0.9517849878333923,
          0.9592623050551339,
          0.9671021056914025,
          0.9746898706406245,
          0.9826204693273637,
          0.9905787098580715,
          0.9982451484964051,
          1.0062208225664988,
          1.0138805625912966,
          1.0218248807336492,
          1.0297344867793845,
          1.0372954298968273,
          1.045100476719042,
          1.0525378323058943,
          1.0601905742128748,
          1.0677475840490582,
          1.0749124688418328,
          1.0822469448439112,
          1.0891761025885325,
          1.0962431776803625,
          1.1031571796570094,
          1.109650663620643,
          1.1162327090030468,
          1.1223873852592277,
          1.1285972098033896,
          1.1346025027019546,
          1.1401750448893124,
          1.1457517153392496,
          1.150895389350047,
          1.1560093232718187,
          1.160875127054017,
          1.1653125777939564,
          1.1696695649934687,
          1.1736045682512535,
          1.1774260859379484,
          1.180965410493204,
          1.1840972410423405,
          1.187067108416777,
          1.1896422209531279,
          1.1920244636231778,
          1.1941012946937084,
          1.1958071505603896,
          1.1972757677720716,
          1.1983920294563561,
          1.1992434488599284,
          1.199777974992394,
          1.199992301092318,
          1.1999032300054107,
          1.1995177435271087,
          1.1988056200940054,
          1.197777299748901,
          1.1964918596502432,
          1.1948485232166648,
          1.192976102604954,
          1.190727802839346,
          1.188176153790845,
          1.185440346235714,
          1.1823058969530131,
          1.179018498281936,
          1.1753204230829546,
          1.17134350377301,
          1.1672624643114904,
          1.162757357307782,
          1.158181313464674,
          1.1531755777883113,
          1.147926218995722,
          1.142656779685647,
          1.1369541436965904,
          1.1312653094800666,
          1.1251442809411167,
          1.1188242125804078,
          1.112568875019328,
          1.1058878591479075,
          1.0993048532665743,
          1.0923037595590763,
          1.0851558583130145,
          1.0781550116153689,
          1.070752363554766,
          1.063528167232851,
          1.0559160564617256,
          1.0482150121666078,
          1.0407376949448661,
          1.0328978943085976,
          1.0253101293593756,
          1.0173795306726363,
          1.0094212901419286,
          1.001754851503595,
          0.9937791774335013,
          0.9861194374087034,
          0.9781751192663508,
          0.9702655132206155,
          0.9627045701031727,
          0.9548995232809581,
          0.9474621676941057,
          0.9398094257871252,
          0.9322524159509418,
          0.9250875311581674,
          0.917753055156089,
          0.9108238974114677,
          0.9037568223196376,
          0.8968428203429906,
          0.8903493363793572,
          0.8837672909969533,
          0.8776126147407726,
          0.8714027901966104,
          0.8653974972980454,
          0.8598249551106877,
          0.8542482846607504,
          0.849104610649953,
          0.8439906767281813,
          0.8391248729459831,
          0.8346874222060436,
          0.8303304350065313,
          0.8263954317487465,
          0.8225739140620518,
          0.8190345895067961,
          0.8159027589576596,
          0.812932891583223,
          0.8103577790468722,
          0.8079755363768223,
          0.8058987053062915,
          0.8041928494396106,
          0.8027242322279283,
          0.8016079705436439,
          0.8007565511400716,
          0.800222025007606,
          0.8000076989076821,
          0.8000967699945892,
          0.8004822564728913,
          0.8011943799059946,
          0.8022227002510991,
          0.8035081403497568,
          0.8051514767833352,
          0.807023897395046,
          0.809272197160654,
          0.8118238462091549,
          0.8145596537642861,
          0.8176941030469868,
          0.8209815017180638,
          0.8246795769170454,
          0.82865649622699,
          0.8327375356885095,
          0.8372426426922179,
          0.8418186865353261,
          0.8468244222116887,
          0.852073781004278,
          0.8573432203143528,
          0.8630458563034095,
          0.8687346905199331,
          0.8748557190588833,
          0.8811757874195922,
          0.8874311249806717,
          0.8941121408520925,
          0.9006951467334254,
          0.9076962404409235,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4269819333194158,
          -0.6535253795584812,
          -1.0391437450108951,
          -1.2469008664629806,
          -1.3663528456863698,
          -1.4298627796841876,
          -1.4611719316173184,
          -1.4763441903590968,
          -1.4815121927971031,
          -1.4814377625381672,
          -1.4782870599257916,
          -1.4736653121682748,
          -1.4679561955771374,
          -1.461994812059164,
          -1.4555343834693406,
          -1.4489361538277006,
          -1.4425274441674751,
          -1.4358322213868406,
          -1.429384058595842,
          -1.4226773416829066,
          -1.415975213750321,
          -1.4095374800120404,
          -1.402849998031099,
          -1.396427244926306,
          -1.389755002661905,
          -1.3830896506447818,
          -1.3766863654181656,
          -1.3700319572072224,
          -1.363637354138157,
          -1.3569899306990831,
          -1.3503444022694076,
          -1.3439551552852786,
          -1.3373098644007553,
          -1.3309185467621325,
          -1.3242686418172138,
          -1.317614431675629,
          -1.3112108245210623,
          -1.3045441825823947,
          -1.2981260164302348,
          -1.2914414662835219,
          -1.2847456070559282,
          -1.2782952109786812,
          -1.271572758735899,
          -1.265093925730035,
          -1.2583388665423931,
          -1.2515648050386399,
          -1.245031836659692,
          -1.2382157105269056,
          -1.2316391898255863,
          -1.2247744911839376,
          -1.2178824639950596,
          -1.21122809870424,
          -1.204277312395002,
          -1.1975631131036797,
          -1.190546583898819,
          -1.183493790582895,
          -1.1766763018058364,
          -1.1695468665094761,
          -1.1626521230277915,
          -1.1554385933224716,
          -1.1481792644817888,
          -1.1411540798090012,
          -1.1337990567530132,
          -1.1266780774951604,
          -1.1192194513604299,
          -1.1117049079324226,
          -1.1044246763298142,
          -1.0967942616915545,
          -1.0893986294788116,
          -1.0816440135914696,
          -1.0738228250605488,
          -1.0662376017583601,
          -1.0582793582342096,
          -1.0505581958593626,
          -1.0424542259093579,
          -1.0342725938433373,
          -1.026330268784789,
          -1.0179896394604968,
          -1.0098901755682173,
          -1.0013816860726796,
          -0.9927842038201389,
          -0.9844313236797541,
          -0.9756525893554302,
          -0.9671211844371517,
          -0.9581523929945857,
          -0.9490833572157485,
          -0.940266513889967,
          -0.9309943772954697,
          -0.9219781890254712,
          -0.9124945835484386,
          -0.9029000472979863,
          -0.8935680152810938,
          -0.8837500005189969,
          -0.8741994667114006,
          -0.8641505763241387,
          -0.8539813174778131,
          -0.8440880985311408,
          -0.8336779188980329,
          -0.82355019153077,
          -0.8128933624711646,
          -0.8021088676364347,
          -0.7916177155780302,
          -0.7805796572436523,
          -0.7698430021444111,
          -0.7585481572487456,
          -0.747121557857876,
          -0.7360098786839894,
          -0.7243240408882491,
          -0.7129629969937274,
          -0.7010181048094097,
          -0.6889417260823446,
          -0.6772064614568586,
          -0.6648743733875948,
          -0.6528951375656162,
          -0.6403117574180709,
          -0.627602564635642,
          -0.61526529242248,
          -0.6023150283306238,
          -0.5897501438713192,
          -0.576568010291445,
          -0.5632718405174381,
          -0.5503824576774436,
          -0.5368720093126943,
          -0.5237831150774652,
          -0.5100724280525505,
          -0.496265645311862,
          -0.4829033108923011,
          -0.4689208454478934,
          -0.4553981870821301,
          -0.441258298475978,
          -0.4270456256575092,
          -0.413315845331206,
          -0.3989757913424469,
          -0.38513360060433605,
          -0.37068731696774493,
          -0.35619523918767226,
          -0.34222269303178104,
          -0.32765744893798604,
          -0.3136252093452606,
          -0.2990089667462231,
          -0.28437521227886,
          -0.2702930534921744,
          -0.25564132707595205,
          -0.24155213338305126,
          -0.22690353907493493,
          -0.21226436267076523,
          -0.19820184517344944,
          -0.18359574090293174,
          -0.16957394020389807,
          -0.15501908421156668,
          -0.1404968518799503,
          -0.12656774566572362,
          -0.11212117769518598,
          -0.09827175409281123,
          -0.08391479556502836,
          -0.0696082810820625,
          -0.055902269729674894,
          -0.04170282208791603,
          -0.028104382736452067,
          -0.014021128714733936,
          -0.022576888318899955
        ],
        "amplitude_tangent": [
          -0.42577929156507,
          -0.3907526205900639,
          -0.3537191705166107,
          -0.3175816717997911,
          -0.279506873567262,
          -0.24099029494009985,
          -0.2035954113625623,
          -0.16439040130305263,
          -0.1264482218436193,
          -0.08679415170026879,
          -0.04700422472193909,
          -0.008675376786893186,
          0.031197413059104614,
          0.06948882135909651,
          0.10920092273771491,
          0.14873761650479123,
          0.18652977728464742,
          0.2255403215191223,
          0.2627114843295272,
          0.30095748472797246,
          0.3387234046991148,
          0.3745281660155912,
          0.4111788458607755,
          0.4458026279067229,
          0.48111399088832585,
          0.5156588992353147,
          0.5481012075491702,
          0.5809843540634868,
          0.6117308132221593,
          0.6427510612838424,
          0.672747798634866,
          0.7005811567707937,
          0.728433215499704,
          0.754120787135933,
          0.779657716855605,
          0.8039532974496844,
          0.8261077613668651,
          0.8478579523867894,
          0.8674989574490554,
          0.8865705624497909,
          0.9042305911654108,
          0.9198539920026725,
          0.9346655681366469,
          0.9475042730743478,
          0.9593765890940078,
          0.969721275513808,
          0.9782120682166477,
          0.9855145733722932,
          0.9910563295704629,
          0.995271739484711,
          0.9979021193696834,
          0.9989325920218011,
          0.9984438781296019,
          0.9964742208751516,
          0.9928691332852083,
          0.9876824925807349,
          0.9812114484579695,
          0.9729486102006308,
          0.9635415893565543,
          0.9522528187520068,
          0.9394467357169236,
          0.925721169515858,
          0.9099999865694969,
          0.8935154190384268,
          0.8749750336107347,
          0.8550398955632211,
          0.8345856112310992,
          0.8120085321810698,
          0.7890782943016446,
          0.7639971427045464,
          0.7376974384066913,
          0.7112989820783728,
          0.6827321251515684,
          0.6542360244208826,
          0.6235765872400605,
          0.5919217059254396,
          0.5605923959486413,
          0.5271324605736218,
          0.4941646223891954,
          0.45910423873207723,
          0.4233099029750989,
          0.3882531112314872,
          0.3511854716913365,
          0.3150125293317026,
          0.2768984041863161,
          0.2383402066816284,
          0.20090336274223286,
          0.16165293168423595,
          0.12366559846822378,
          0.08396328410590133,
          0.04412407052739912,
          0.005747106776859956,
          -0.034176203147889675,
          -0.07251638484058491,
          -0.11227913195594406,
          -0.1518661000446181,
          -0.18970597492628605,
          -0.22876520228462513,
          -0.26598199993204524,
          -0.30427395280587627,
          -0.342084001334449,
          -0.3779292087963929,
          -0.4146196195058926,
          -0.4492791144988284,
          -0.4846247807233106,
          -0.5192008579107591,
          -0.5516699677847503,
          -0.5845774886266646,
          -0.6153438441743349,
          -0.6463809380853126,
          -0.6763904554202659,
          -0.7042321555358901,
          -0.7320886955196324,
          -0.7577764838842329,
          -0.7833093499907082,
          -0.8075964911043295,
          -0.8297387406162027,
          -0.8514720250588819,
          -0.8710928186454392,
          -0.8901394130936919,
          -0.9077705192027781,
          -0.9233625971615076,
          -0.9381381568017195,
          -0.9509391493813596,
          -0.9627693046739001,
          -0.9730691259944473,
          -0.9815145248043969,
          -0.9887678013281602,
          -0.9942606038663936,
          -0.9984237706253838,
          -1.0010009173108683,
          -1.0019796220416242,
          -1.001436831662785,
          -0.9994152968364837,
          -0.9957567425420117,
          -0.9905174924545701,
          -0.9839970024600587,
          -0.9756842582637442,
          -0.9662310112581676,
          -0.9548962961078582,
          -0.9420467271837895,
          -0.9282819163204307,
          -0.9125228282240944,
          -0.896004814685391,
          -0.8774329576284715,
          -0.8574698946206205,
          -0.8369922400949658,
          -0.814394592410302,
          -0.7914482566581659,
          -0.7663542573443983,
          -0.7400457195891151,
          -0.7136425740136885,
          -0.6850747935526339,
          -0.6565815820485786,
          -0.6259290316493107,
          -0.5942849272181143,
          -0.562969565580994,
          -0.5295277615387712,
          -0.496580727541615,
          -0.4615453473110566,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.6652205892890733,
          -1.052399021603968,
          -1.2580584378964412,
          -1.3745589282297428,
          -1.435452258974065,
          -1.4648394508253937,
          -1.478600910499279,
          -1.482859069398939,
          -1.4821717113779327,
          -1.4786383980768152,
          -1.473790134055014,
          -1.4679384049664161,
          -1.4618954696565736,
          -1.4553852621255448,
          -1.4487585756787476,
          -1.4423343165271996,
          -1.4356300541286842,
          -1.4291771640992195,
          -1.422467872517196,
          -1.415764514000809,
          -1.4093263023306768,
          -1.402638728062454,
          -1.3962161006604692,
          -1.3895441097823995,
          -1.3828790750042284,
          -1.3764761274747535,
          -1.369822087980246,
          -1.3634278479427417,
          -1.3567808062691529,
          -1.3501356615065214,
          -1.3437467841357378,
          -1.3371018779055857,
          -1.3307109302581637,
          -1.3240614103115422,
          -1.3174075855632377,
          -1.3110043495851376,
          -1.3043380945825716,
          -1.2979203016551337,
          -1.2912361412085478,
          -1.2845406736100697,
          -1.2780906562644356,
          -1.2713686005276479,
          -1.2648901516683984,
          -1.2581354953985968,
          -1.2513618407046998,
          -1.2448292675675279,
          -1.238013557165167,
          -1.231437441131548,
          -1.2245731689335362,
          -1.2176815743703033,
          -1.211027631374902,
          -1.2040772913156208,
          -1.1973635284038,
          -1.1903474611508602,
          -1.1832951386352595,
          -1.176478111439736,
          -1.1693491660286963,
          -1.1624549036243028,
          -1.1552418853059692,
          -1.1479830797943542,
          -1.140958410226059,
          -1.1336039359465833,
          -1.126483497597273,
          -1.1190254485073488,
          -1.1115114976775105,
          -1.1042318512956786,
          -1.0966020621191033,
          -1.089207048278804,
          -1.081453093992384,
          -1.0736325868078067,
          -1.066048038128641,
          -1.0580905173937647,
          -1.0503700712703463,
          -1.042266869299878,
          -1.0340860297515553,
          -1.0261444908404413,
          -1.0178047052146766,
          -1.0097060786668848,
          -1.0011984882143903,
          -0.9926019348639512,
          -0.9842499771077899,
          -0.9754722335431991,
          -0.9669418126008665,
          -0.9579740781815531,
          -0.9489061349092898,
          -0.9400903765986964,
          -0.9308194054282024,
          -0.9218043743727847,
          -0.912322011543518,
          -0.9027287589134401,
          -0.8933980007556636,
          -0.883581352970551,
          -0.8740321749839263,
          -0.863984738601081,
          -0.8538169794012982,
          -0.8439252461839564,
          -0.8335166578937042,
          -0.8233905056330193,
          -0.8127353619543484,
          -0.8019526011111301,
          -0.7914631624852335,
          -0.7804269342923069,
          -0.7696920853376245,
          -0.758399167040905,
          -0.7469745432344487,
          -0.7358648095773551,
          -0.7241810424520683,
          -0.7128220345799463,
          -0.7008793059767929,
          -0.6888051370372679,
          -0.6770720398961687,
          -0.6647422493701716,
          -0.6527652633287384,
          -0.6401842639365873,
          -0.6274774923346687,
          -0.6151425849420674,
          -0.6021948170149817,
          -0.589632366593696,
          -0.5764527980729037,
          -0.5631592260425939,
          -0.5502723703025786,
          -0.5367645789475708,
          -0.5236782657258161,
          -0.5099702886228165,
          -0.49616624040342966,
          -0.48280655708990106,
          -0.4688268699783695,
          -0.45530690213400904,
          -0.441169830145739,
          -0.4269599914822432,
          -0.41323295166953017,
          -0.39889576262438065,
          -0.38505633981100806,
          -0.3706129474234196,
          -0.3561237726601953,
          -0.3421540279524704,
          -0.327591706802881,
          -0.31356228580002554,
          -0.29894898183693497,
          -0.28431817230583833,
          -0.2702388500045594,
          -0.25559007731353767,
          -0.24150372614877288,
          -0.2268580892099719,
          -0.21222186987012365,
          -0.19816219395970827,
          -0.18355904153575395,
          -0.16954007430216594,
          -0.1549881583469317,
          -0.14046885733724157,
          -0.12654255972748557,
          -0.11209890047341375,
          -0.09825226016981832,
          -0.08389818030413881,
          -0.06959452629354974,
          -0.05589124646755711,
          -0.04169461812511507,
          -0.028098867320587858,
          -0.014018384503054128,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.470969306874175,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.14521070624576746,
        0.0855519637230105,
        -0.0001541977647372142
      ],
      "tangent_gradient": [
        -0.14521070624577437,
        0.0855519637229934,
        -0.00015419776473720917
      ],
      "reverse_gradient": [
        -0.14521070624576837,
        0.08555196372300644,
        -0.0001541977647374626
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.0012030082025307198,
      "amplitude_gradient_error": 0.0012030082025307198,
      "phase_gradient_error": 0.0003961054099959477,
      "viscosity_gradient_error": 0.0001541977647372142,
      "gradient_duality_error": 1.709743457922741e-14,
      "gradient_reverse_error": 4.052314039881821e-15,
      "reverse_state_adjoint_error": 4.696243394164412e-14,
      "transpose_relative_error": 9.993503699653932e-14,
      "state_l1_error": 0.00014616508268815094,
      "state_linf_error": 0.0003074754920969758,
      "primal_residual_inf": 3.47499806707674e-14,
      "primal_residual_density_inf": 2.8467184165492654e-10,
      "newton_correction_inf": 1.4611632627897432e-15,
      "tangent_residual_inf": 1.1168843627729075e-13,
      "adjoint_residual_inf": 5.307624999228988e-14,
      "jacobian_nonzeros": 24575,
      "psi_0": -1.4267749261628349,
      "psi_N": -0.022305698806684773,
      "exact_nodal_residual_inf": 1.1765462615276334e-07,
      "exact_nodal_residual_boundary_rows_inf": 5.0183271815829045e-08,
      "exact_nodal_residual_inner_rows_inf": 1.1765462615276334e-07,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4711984618032865,
      "objective_quadrature_error": 1.4119339031282152e-09,
      "objective_quadrature_remainder": 1.9255482364848905e-16,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.11954511710543513,
        "adjoint_directional_gradient": -0.11954511712886431,
        "absolute_error": 2.3429189144330564e-11,
        "perturbed_primal_residuals_inf": [
          3.5416114485542494e-14,
          3.552713678800501e-14
        ],
        "axis_central_differences": [
          -0.14521070623718657,
          0.08555196366888394,
          -0.00015419776566716337
        ],
        "axis_absolute_errors": [
          8.58088600175222e-12,
          5.412655046388437e-11,
          9.299491786438768e-13
        ]
      },
      "adjoint_l1_reference_error": 0.0002558049562175476,
      "adjoint_linf_reference_error": 0.0067493510390552736,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.00020696077194970464,
      "psi_N_boundary_flux_error": 0.0002711473493680512,
      "elapsed_seconds": 0.07922533300006762,
      "cells": 8192,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 1.1765462615276334e-07,
          "correction_inf": 0.00030742475505094976,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 2.928191022988358e-11,
          "correction_inf": 5.0985111876826764e-08,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 3.47499806707674e-14,
          "correction_inf": 1.4611632627897432e-15,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.000260706199993,
      "state_linf_observed_order": 1.000369834991767,
      "gradient_observed_order": 1.000286146939493,
      "amplitude_gradient_observed_order": 1.000286146939493,
      "phase_gradient_observed_order": 0.9962343884459118,
      "viscosity_gradient_observed_order": 0.9755935109253516,
      "adjoint_l1_observed_order": 0.9981187137521825,
      "psi_0_observed_order": 1.000161661380588,
      "psi_N_observed_order": 1.0001121636742296,
      "profile": {
        "x": [
          0.0,
          0.0062255859375,
          0.012451171875,
          0.0186767578125,
          0.02490234375,
          0.03125,
          0.0374755859375,
          0.043701171875,
          0.0499267578125,
          0.05615234375,
          0.0625,
          0.0687255859375,
          0.074951171875,
          0.0811767578125,
          0.08740234375,
          0.09375,
          0.0999755859375,
          0.106201171875,
          0.1124267578125,
          0.11865234375,
          0.125,
          0.1312255859375,
          0.137451171875,
          0.1436767578125,
          0.14990234375,
          0.15625,
          0.1624755859375,
          0.168701171875,
          0.1749267578125,
          0.18115234375,
          0.1875,
          0.1937255859375,
          0.199951171875,
          0.2061767578125,
          0.21240234375,
          0.21875,
          0.2249755859375,
          0.231201171875,
          0.2374267578125,
          0.24365234375,
          0.25,
          0.2562255859375,
          0.262451171875,
          0.2686767578125,
          0.27490234375,
          0.28125,
          0.2874755859375,
          0.293701171875,
          0.2999267578125,
          0.30615234375,
          0.3125,
          0.3187255859375,
          0.324951171875,
          0.3311767578125,
          0.33740234375,
          0.34375,
          0.3499755859375,
          0.356201171875,
          0.3624267578125,
          0.36865234375,
          0.375,
          0.3812255859375,
          0.387451171875,
          0.3936767578125,
          0.39990234375,
          0.40625,
          0.4124755859375,
          0.418701171875,
          0.4249267578125,
          0.43115234375,
          0.4375,
          0.4437255859375,
          0.449951171875,
          0.4561767578125,
          0.46240234375,
          0.46875,
          0.4749755859375,
          0.481201171875,
          0.4874267578125,
          0.49365234375,
          0.5,
          0.5062255859375,
          0.512451171875,
          0.5186767578125,
          0.52490234375,
          0.53125,
          0.5374755859375,
          0.543701171875,
          0.5499267578125,
          0.55615234375,
          0.5625,
          0.5687255859375,
          0.574951171875,
          0.5811767578125,
          0.58740234375,
          0.59375,
          0.5999755859375,
          0.606201171875,
          0.6124267578125,
          0.61865234375,
          0.625,
          0.6312255859375,
          0.637451171875,
          0.6436767578125,
          0.64990234375,
          0.65625,
          0.6624755859375,
          0.668701171875,
          0.6749267578125,
          0.68115234375,
          0.6875,
          0.6937255859375,
          0.699951171875,
          0.7061767578125,
          0.71240234375,
          0.71875,
          0.7249755859375,
          0.731201171875,
          0.7374267578125,
          0.74365234375,
          0.75,
          0.7562255859375,
          0.762451171875,
          0.7686767578125,
          0.77490234375,
          0.78125,
          0.7874755859375,
          0.793701171875,
          0.7999267578125,
          0.80615234375,
          0.8125,
          0.8187255859375,
          0.824951171875,
          0.8311767578125,
          0.83740234375,
          0.84375,
          0.8499755859375,
          0.856201171875,
          0.8624267578125,
          0.86865234375,
          0.875,
          0.8812255859375,
          0.887451171875,
          0.8936767578125,
          0.89990234375,
          0.90625,
          0.9124755859375,
          0.918701171875,
          0.9249267578125,
          0.93115234375,
          0.9375,
          0.9437255859375,
          0.949951171875,
          0.9561767578125,
          0.96240234375,
          0.96875,
          0.9749755859375,
          0.981201171875,
          0.9874267578125,
          0.99365234375,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9219884026268548,
          0.9292517547697605,
          0.9366230914531714,
          0.944091140873016,
          0.9517933631160246,
          0.9594217779777958,
          0.9671120427914359,
          0.974852397710617,
          0.9826310061459986,
          0.9905891946178571,
          0.9984087471447175,
          1.0062305296321277,
          1.014042580212994,
          1.0218329516818079,
          1.0297414077044396,
          1.037451719784505,
          1.0451045510140604,
          1.0526881967194854,
          1.0601910577852836,
          1.0677459655098807,
          1.0750508271377726,
          1.082240699101083,
          1.0893045835093924,
          1.0962316749154861,
          1.103142768671313,
          1.1097615144222899,
          1.1162121730767358,
          1.1224848761568844,
          1.1285700271502825,
          1.134571743847589,
          1.1402500373487776,
          1.1457135984453568,
          1.1509540674388077,
          1.1559634256879485,
          1.160825112130909,
          1.1653447225566904,
          1.16961120077907,
          1.173618017353432,
          1.1773590398910625,
          1.1808938213270876,
          1.1840810148894025,
          1.1869863988472331,
          1.1896055252035402,
          1.1919343837651322,
          1.194006351800546,
          1.1957385747947038,
          1.1971711366708115,
          1.198301842118237,
          1.1991289575589283,
          1.1996584005385975,
          1.1998689965264657,
          1.1997735933750042,
          1.199372333153692,
          1.1986658258535603,
          1.1976323003467961,
          1.1963130798997175,
          1.1946932810464845,
          1.1927753781275392,
          1.190562301616032,
          1.18800542683227,
          1.185206990970683,
          1.1821249496755688,
          1.178764014841504,
          1.1751293251816615,
          1.1711472697433771,
          1.1669770746044967,
          1.1625511488771116,
          1.1578762613202782,
          1.1529595617967234,
          1.147705280938415,
          1.1423235179370357,
          1.1367237317942882,
          1.1309144883989086,
          1.1249046743790836,
          1.118580041882326,
          1.112193491336467,
          1.1056350104994452,
          1.098914633555258,
          1.0920426427232588,
          1.0848907023844956,
          1.0777447960016417,
          1.0704796678331672,
          1.0631064349965365,
          1.0556363803777102,
          1.0479320134233507,
          1.040301409198451,
          1.0326088826714723,
          1.0248662067156866,
          1.0170852312817744,
          1.009124596207104,
          1.0013026256441835,
          0.9934784208957347,
          0.9856639578928743,
          0.9778711979130891,
          0.9699603456837185,
          0.9622477359667289,
          0.9545926728383369,
          0.947006874360545,
          0.9395019526824941,
          0.9319450518886162,
          0.924638353680561,
          0.9174467737307015,
          0.9103813207710578,
          0.9034528103551976,
          0.8965404333654716,
          0.8899205980579333,
          0.883469024709157,
          0.8771955882324541,
          0.8711098905016789,
          0.8651078129124075,
          0.8594293613395069,
          0.8539658379820306,
          0.8487256031023792,
          0.843716674631077,
          0.8388556257707694,
          0.8343368328507695,
          0.8300713578248918,
          0.826065724265128,
          0.8223260574477141,
          0.8187928275127785,
          0.815607311931866,
          0.8127037501219971,
          0.8100865784978685,
          0.8077597947388,
          0.805690051969492,
          0.803960104783235,
          0.8025298963062023,
          0.8014016065811788,
          0.8005769535108913,
          0.8000500526673355,
          0.7998419644091539,
          0.7999398733456853,
          0.8003436213033517,
          0.8010525823798831,
          0.8020885586420315,
          0.8034101171323966,
          0.8050321743304356,
          0.8069522418620665,
          0.8091673759318645,
          0.8117262254154078,
          0.8145264653260804,
          0.8176101685007487,
          0.8209726133291483,
          0.824608652421604,
          0.8285919105678412,
          0.8327631088458417,
          0.837189857605565,
          0.8418653838910064,
          0.8467825347902889,
          0.852037081008807,
          0.8574189123809317,
          0.8630185772451475,
          0.868827511190408,
          0.8748368301405774,
          0.8811607704772285,
          0.8875464630836123,
          0.8941039142544187,
          0.9008230963258378,
          0.9076937344813586,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9219862121745078,
          0.929247636445234,
          0.9366173052006371,
          0.9440839435382744,
          0.9517849878333923,
          0.9594124992264225,
          0.9671021056914025,
          0.9748420428511818,
          0.9826204693273637,
          0.9905787098580715,
          0.998398541171333,
          1.0062208225664988,
          1.0140335866862107,
          1.0218248807336492,
          1.0297344867793845,
          1.0374461262809207,
          1.045100476719042,
          1.0526858276550144,
          1.0601905742128748,
          1.0677475840490582,
          1.075054677757562,
          1.0822469448439112,
          1.0893133818135887,
          1.0962431776803625,
          1.1031571796570094,
          1.1097789200591286,
          1.1162327090030468,
          1.1225086727965883,
          1.1285972098033896,
          1.1346025027019546,
          1.1402844200275506,
          1.1457517153392496,
          1.1509960241876702,
          1.1560093232718187,
          1.160875127054017,
          1.165398868406723,
          1.1696695649934687,
          1.1736806830487658,
          1.1774260859379484,
          1.180965410493204,
          1.1841571310297787,
          1.187067108416777,
          1.1896908906615467,
          1.1920244636231778,
          1.1941012946937084,
          1.195838338383869,
          1.1972757677720716,
          1.1984113837260812,
          1.1992434488599284,
          1.199777974992394,
          1.1999935882212729,
          1.1999032300054107,
          1.1995070385844084,
          1.1988056200940054,
          1.197777299748901,
          1.1964631966210297,
          1.1948485232166648,
          1.192935749834773,
          1.190727802839346,
          1.188176153790845,
          1.1853828345524702,
          1.1823058969530131,
          1.1789500484186024,
          1.1753204230829546,
          1.17134350377301,
          1.1671783141159506,
          1.162757357307782,
          1.158087396998048,
          1.1531755777883113,
          1.147926218995722,
          1.1425492248226337,
          1.1369541436965904,
          1.1311495355672925,
          1.1251442809411167,
          1.1188242125804078,
          1.1124420487619093,
          1.1058878591479075,
          1.0991716710341928,
          1.0923037595590763,
          1.0851558583130145,
          1.078013787825492,
          1.070752363554766,
          1.063382694799363,
          1.0559160564617256,
          1.0482150121666078,
          1.0405875007735776,
          1.0328978943085976,
          1.0251579571488183,
          1.0173795306726363,
          1.0094212901419286,
          1.001601458828667,
          0.9937791774335013,
          0.9859664133137894,
          0.9781751192663508,
          0.9702655132206155,
          0.9625538737190794,
          0.9548995232809581,
          0.9473141723449856,
          0.9398094257871252,
          0.9322524159509418,
          0.924945322242438,
          0.917753055156089,
          0.9106866181864114,
          0.9037568223196376,
          0.8968428203429906,
          0.8902210799408714,
          0.8837672909969533,
          0.8774913272034118,
          0.8714027901966104,
          0.8653974972980454,
          0.8597155799724495,
          0.8542482846607504,
          0.8490039758123299,
          0.8439906767281813,
          0.8391248729459831,
          0.8346011315932772,
          0.8303304350065313,
          0.8263193169512342,
          0.8225739140620518,
          0.8190345895067961,
          0.8158428689702213,
          0.812932891583223,
          0.8103091093384535,
          0.8079755363768223,
          0.8058987053062915,
          0.8041616616161309,
          0.8027242322279283,
          0.8015886162739189,
          0.8007565511400716,
          0.800222025007606,
          0.8000064117787271,
          0.8000967699945892,
          0.8004929614155916,
          0.8011943799059946,
          0.8022227002510991,
          0.8035368033789704,
          0.8051514767833352,
          0.807064250165227,
          0.809272197160654,
          0.8118238462091549,
          0.8146171654475298,
          0.8176941030469868,
          0.8210499515813976,
          0.8246795769170454,
          0.82865649622699,
          0.8328216858840494,
          0.8372426426922179,
          0.8419126030019518,
          0.8468244222116887,
          0.852073781004278,
          0.8574507751773662,
          0.8630458563034095,
          0.8688504644327073,
          0.8748557190588833,
          0.8811757874195922,
          0.8875579512380907,
          0.8941121408520925,
          0.9008283289658071,
          0.9076962404409235,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4267749261628349,
          -0.669095373860573,
          -1.0457310773095114,
          -1.2554920363131996,
          -1.37045969155578,
          -1.4326704867524003,
          -1.4634321455244692,
          -1.477486829539761,
          -1.48223090301348,
          -1.4818136421084052,
          -1.4784690998184817,
          -1.473627529272077,
          -1.4679502486574443,
          -1.4618241840883157,
          -1.4554610484644552,
          -1.4488481239066413,
          -1.4423026846433211,
          -1.4357314197808482,
          -1.4291517538109262,
          -1.4225727061054367,
          -1.4158699209283023,
          -1.4093032404835641,
          -1.4027443821151775,
          -1.3961933040009846,
          -1.3896495630561956,
          -1.382984367332966,
          -1.376453238872993,
          -1.3699270255680465,
          -1.3634047474919988,
          -1.356885371542615,
          -1.350240035214237,
          -1.3437231913972396,
          -1.3372058751660456,
          -1.3306868960820084,
          -1.3241650308444775,
          -1.3175110138008512,
          -1.3109794622920492,
          -1.3044411445574229,
          -1.2978947174958397,
          -1.2913388105170736,
          -1.284643147510249,
          -1.2780638068509886,
          -1.2714706876067259,
          -1.2648623150490865,
          -1.2582371897455067,
          -1.2514633320560449,
          -1.2447997014935321,
          -1.2381146438375692,
          -1.2314065633543088,
          -1.2246738408640903,
          -1.2177820304077565,
          -1.2109945083558162,
          -1.204177313911105,
          -1.1973287347205537,
          -1.190447035425661,
          -1.183394477946451,
          -1.1764405038413477,
          -1.1694480304790018,
          -1.1624152306295068,
          -1.1553402544196134,
          -1.1480811877092558,
          -1.140915299345243,
          -1.1337015128557368,
          -1.1264378890999924,
          -1.1191224674053548,
          -1.1116082207815885,
          -1.1041821231823892,
          -1.0966981809001926,
          -1.0891543514985578,
          -1.0815485738438733,
          -1.0737277265409033,
          -1.0659904810733645,
          -1.0581849595416555,
          -1.0503090357417848,
          -1.0423605704983174,
          -1.0341793353034874,
          -1.0260777974033823,
          -1.017897197080448,
          -1.009635361081975,
          -1.0012901131705036,
          -0.9926930960415831,
          -0.9841727545047614,
          -0.9755624395020367,
          -0.9668599918277895,
          -0.9580632650359452,
          -0.9489947762362044,
          -0.9400011703337514,
          -0.9309069229833363,
          -0.9217099819449447,
          -0.9124083306395535,
          -0.9028144369554348,
          -0.893295337276452,
          -0.88366571208003,
          -0.8739237470052784,
          -0.8640676942721972,
          -0.853899185990147,
          -0.8438077003908967,
          -0.8335973273645609,
          -0.8232666615011356,
          -0.8128144025308647,
          -0.8020307753440646,
          -0.7913294541037706,
          -0.7805033379275084,
          -0.769551635755751,
          -0.7584737053455912,
          -0.7470480942092833,
          -0.7357139274250029,
          -0.7242525860822148,
          -0.7126641148038109,
          -0.7009487503137186,
          -0.6888734766353171,
          -0.6769033841246946,
          -0.6648083565320115,
          -0.6525894771649348,
          -0.6402480555823515,
          -0.6275400731297575,
          -0.6149561053311239,
          -0.6022549665311675,
          -0.5894389143786405,
          -0.57651044687917,
          -0.5632155752390722,
          -0.5500686676710999,
          -0.5368183343593045,
          -0.5234680207430258,
          -0.5100213964765278,
          -0.49621597980049287,
          -0.4825869118200351,
          -0.4688738920777467,
          -0.45508140204751374,
          -0.44121409582941623,
          -0.4270028385524083,
          -0.4129992546711027,
          -0.39893580382655847,
          -0.3848176773116808,
          -0.37065015579086125,
          -0.3561595278456186,
          -0.34190861517127663,
          -0.32762459652271636,
          -0.3133129119462917,
          -0.29897898975610265,
          -0.28434670618704083,
          -0.2699842718777452,
          -0.25561571316249854,
          -0.241246207623884,
          -0.22688082243744778,
          -0.2122431233184627,
          -0.19790097052689845,
          -0.18357739607677684,
          -0.16927685726708216,
          -0.15500362431328085,
          -0.14048285686232154,
          -0.1262769704005824,
          -0.11211004010862521,
          -0.0979854834931479,
          -0.08390648813049838,
          -0.06960140361366213,
          -0.0556231841092136,
          -0.04169871979144603,
          -0.027830245057865136,
          -0.014019756415973488,
          -0.022305698806684773
        ],
        "amplitude_tangent": [
          -0.42577929156515354,
          -0.39005748052777284,
          -0.3537404348633653,
          -0.31688365501502247,
          -0.27954346743500463,
          -0.2410325443083393,
          -0.20289074770942922,
          -0.16443976329394197,
          -0.12573836128911656,
          -0.08684569697423307,
          -0.04705511816711175,
          -0.00795766577390801,
          0.03115100539292814,
          0.07021110722113644,
          0.1091629231421342,
          0.14870529221869475,
          0.18725708465109464,
          0.22552163032733855,
          0.2634404181097685,
          0.3009554628828849,
          0.3387309500058751,
          0.37525638634758285,
          0.41120707577548676,
          0.4465280325831444,
          0.4811652317354063,
          0.5157226910224845,
          0.5488185813750525,
          0.5810742414691429,
          0.6124403255086582,
          0.6428688462835569,
          0.6728804467714762,
          0.7012750593641618,
          0.7285961861603542,
          0.7548020196437369,
          0.7798524566410691,
          0.8041647567276096,
          0.8267667381902982,
          0.8481031805873269,
          0.8681414234612796,
          0.88685079094189,
          0.9045291188301889,
          0.9204694878015564,
          0.9350008577203422,
          0.9481009723142118,
          0.9597497638393212,
          0.9701141894577686,
          0.9787797822834162,
          0.9859470321374763,
          0.9916049440643732,
          0.9957448314503047,
          0.9983963446272687,
          0.9994534260367234,
          0.998980379087859,
          0.9969778944463843,
          0.9934490022338652,
          0.9882848924971617,
          0.9816920259149691,
          0.973596034700892,
          0.9640092705091812,
          0.952946365715612,
          0.9401642168313006,
          0.9261739042108718,
          0.9107652323095059,
          0.8939617413968118,
          0.8757891061914472,
          0.8558792578312782,
          0.8350282920174926,
          0.812898249131356,
          0.7895229563619838,
          0.7649381472073771,
          0.7386649201394265,
          0.7117538270975413,
          0.6837521199536138,
          0.6547026166575207,
          0.6246497402515866,
          0.5930221525811789,
          0.5610845190112415,
          0.5282866934352577,
          0.49467884376614435,
          0.46031238025286175,
          0.42454548259171665,
          0.3888083489203642,
          0.3524745741343288,
          0.3155997533150121,
          0.2782403133647419,
          0.23970862285489872,
          0.20154545539136434,
          0.16307222340889446,
          0.12434781711787998,
          0.08543151571387486,
          0.0456163169317905,
          0.006494341418419705,
          -0.03263909149568253,
          -0.07172405790502306,
          -0.11070070357756923,
          -0.15026820930752754,
          -0.1888443363234154,
          -0.22713275995254587,
          -0.2650748293037672,
          -0.3026124205723214,
          -0.34040999759126117,
          -0.3769560811371469,
          -0.4129262780762398,
          -0.44826547620065693,
          -0.48291952920995623,
          -0.5174926250662895,
          -0.5506022236916918,
          -0.582869879987373,
          -0.6142461577268856,
          -0.6446829893957065,
          -0.6747010534927008,
          -0.70309997569905,
          -0.7304233574956784,
          -0.7566293606104975,
          -0.7816778652600894,
          -0.8059860289567696,
          -0.8285818425314716,
          -0.8499100552611423,
          -0.86993805069267,
          -0.8886352122147897,
          -0.9062991553396865,
          -0.9222236044095361,
          -0.9367373638815847,
          -0.9498182936764659,
          -0.961446454478243,
          -0.9717885008312561,
          -0.9804309786758206,
          -0.9875741181119684,
          -0.9932070897154193,
          -0.9973213781162434,
          -0.999946294018098,
          -1.0009769838125842,
          -1.0004774226629585,
          -0.9984484798212571,
          -0.9948933619751557,
          -0.9897029311981778,
          -0.9830848314970374,
          -0.9749643464026173,
          -0.9653539823353688,
          -0.9542685181102254,
          -0.9414645808242742,
          -0.9274542179828115,
          -0.912026919280495,
          -0.8952063299934622,
          -0.8770182182138214,
          -0.8570943439930011,
          -0.8362314129046164,
          -0.8140912356914953,
          -0.7907076845198008,
          -0.7661165259362744,
          -0.7398388124809503,
          -0.712925278604926,
          -0.6849230695292675,
          -0.6558749911068122,
          -0.6258254440013419,
          -0.5942031782816747,
          -0.5622726122536107,
          -0.5294836332488065,
          -0.49588635006825865,
          -0.46153210587997984,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.6750493092947951,
          -1.052399021603968,
          -1.2610578521214475,
          -1.3745589282297428,
          -1.435452258974065,
          -1.4652342875575328,
          -1.478600910499279,
          -1.4828853229844987,
          -1.4821717113779327,
          -1.4786383980768152,
          -1.4736837873677726,
          -1.4679384049664161,
          -1.4617719715516895,
          -1.4553852621255448,
          -1.4487585756787476,
          -1.4422055394685014,
          -1.4356300541286842,
          -1.4290481044910601,
          -1.422467872517196,
          -1.415764514000809,
          -1.409197616205559,
          -1.402638728062454,
          -1.3960877226409807,
          -1.3895441097823995,
          -1.3828790750042284,
          -1.3763481199710799,
          -1.369822087980246,
          -1.3632999951378473,
          -1.3567808062691529,
          -1.3501356615065214,
          -1.34361900586775,
          -1.3371018779055857,
          -1.330583087139099,
          -1.3240614103115422,
          -1.3174075855632377,
          -1.3108762229621584,
          -1.3043380945825716,
          -1.2977918574745844,
          -1.2912361412085478,
          -1.2845406736100697,
          -1.277961525717266,
          -1.2713686005276479,
          -1.2647604235008794,
          -1.2581354953985968,
          -1.2513618407046998,
          -1.244698411334468,
          -1.238013557165167,
          -1.2313056826822848,
          -1.2245731689335362,
          -1.2176815743703033,
          -1.210894267309204,
          -1.2040772913156208,
          -1.1972289342970284,
          -1.1903474611508602,
          -1.1832951386352595,
          -1.1763413995485932,
          -1.1693491660286963,
          -1.162316611135642,
          -1.1552418853059692,
          -1.1479830797943542,
          -1.1408174537315967,
          -1.1336039359465833,
          -1.1263405876440074,
          -1.1190254485073488,
          -1.1115114976775105,
          -1.1040856981160776,
          -1.0966020621191033,
          -1.0890585476514443,
          -1.081453093992384,
          -1.0736325868078067,
          -1.0658956849433996,
          -1.0580905173937647,
          -1.0502149584142515,
          -1.042266869299878,
          -1.0340860297515553,
          -1.0259848922980137,
          -1.0178047052146766,
          -1.0095432957596044,
          -1.0011984882143903,
          -0.9926019348639512,
          -0.9840820632215719,
          -0.9754722335431991,
          -0.9667702871642676,
          -0.9579740781815531,
          -0.9489061349092898,
          -0.939913081820526,
          -0.9308194054282024,
          -0.9216230540221169,
          -0.912322011543518,
          -0.9027287589134401,
          -0.8932103083607262,
          -0.883581352970551,
          -0.8738400788346755,
          -0.863984738601081,
          -0.8538169794012982,
          -0.8437262510291468,
          -0.8335166578937042,
          -0.8231867948761874,
          -0.8127353619543484,
          -0.8019526011111301,
          -0.7912521533417786,
          -0.7804269342923069,
          -0.7694761529447968,
          -0.758399167040905,
          -0.7469745432344487,
          -0.7356413684899791,
          -0.7241810424520683,
          -0.7125936094814449,
          -0.7008793059767929,
          -0.6888051370372679,
          -0.6768361500761032,
          -0.6647422493701716,
          -0.6525245176718587,
          -0.6401842639365873,
          -0.6274774923346687,
          -0.6148947311205434,
          -0.6021948170149817,
          -0.5893800069196613,
          -0.5764527980729037,
          -0.5631592260425939,
          -0.5500136082553084,
          -0.5367645789475708,
          -0.523415582775475,
          -0.5099702886228165,
          -0.49616624040342966,
          -0.48253852584363227,
          -0.4688268699783695,
          -0.4550357535978362,
          -0.441169830145739,
          -0.4269599914822432,
          -0.41295780688752415,
          -0.39889576262438065,
          -0.38477904942840346,
          -0.3706129474234196,
          -0.3561237726601953,
          -0.3418742904116331,
          -0.327591706802881,
          -0.3132814613529394,
          -0.29894898183693497,
          -0.28431817230583833,
          -0.2699571861157477,
          -0.25559007731353767,
          -0.24122202284375324,
          -0.2268580892099719,
          -0.21222186987012365,
          -0.19788116741333653,
          -0.18355904153575395,
          -0.16925994872304248,
          -0.1549881583469317,
          -0.14046885733724157,
          -0.1262644038728137,
          -0.11209890047341375,
          -0.0979757637307564,
          -0.08389818030413881,
          -0.06959452629354974,
          -0.05561769993443299,
          -0.04169461812511507,
          -0.02782751441599883,
          -0.014018384503054128,
          -5.817375132447619e-20
        ]
      }
    },
    {
      "objective": 1.471083892941082,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.1446091421847576,
        0.08535416934101478,
        -7.774652571882192e-05
      ],
      "tangent_gradient": [
        -0.14460914218476975,
        0.08535416934102964,
        -7.774652571881664e-05
      ],
      "reverse_gradient": [
        -0.14460914218475707,
        0.08535416934101425,
        -7.774652571845841e-05
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.0006014441415208571,
      "amplitude_gradient_error": 0.0006014441415208571,
      "phase_gradient_error": 0.0001983110280002337,
      "viscosity_gradient_error": 7.774652571882192e-05,
      "gradient_duality_error": 1.4863110742169283e-14,
      "gradient_reverse_error": 5.273559366969494e-16,
      "reverse_state_adjoint_error": 1.306454944227653e-13,
      "transpose_relative_error": 8.909925903384961e-14,
      "state_l1_error": 7.307591322752924e-05,
      "state_linf_error": 0.00015371798932206637,
      "primal_residual_inf": 6.961098364399732e-14,
      "primal_residual_density_inf": 1.140506356023252e-09,
      "newton_correction_inf": 1.746970166669631e-16,
      "tangent_residual_inf": 6.350475700855895e-13,
      "adjoint_residual_inf": 1.1666630660676913e-13,
      "jacobian_nonzeros": 49151,
      "psi_0": -1.4266714397446987,
      "psi_N": -0.022170119861036328,
      "exact_nodal_residual_inf": 2.941371513021096e-08,
      "exact_nodal_residual_boundary_rows_inf": 1.2534775217787342e-08,
      "exact_nodal_residual_inner_rows_inf": 2.941371513021096e-08,
      "exact_nodal_residual_constraint_rows_inf": 0.0,
      "exact_nodal_objective": 1.4711984607443362,
      "objective_quadrature_error": 3.529836423155075e-10,
      "objective_quadrature_remainder": 2.1467215960589574e-16,
      "gradient_check": {
        "step": 1e-05,
        "direction_amplitude_phase_nu": [
          1.0,
          0.3,
          0.0
        ],
        "full_rerun_central_difference": -0.11900289133004448,
        "adjoint_directional_gradient": -0.11900289138245317,
        "absolute_error": 5.240868850009406e-11,
        "perturbed_primal_residuals_inf": [
          7.005507285384738e-14,
          7.016609515630989e-14
        ],
        "axis_central_differences": [
          -0.14460914217195864,
          0.0853541692991122,
          -7.774653143499677e-05
        ],
        "axis_absolute_errors": [
          1.2798956339210577e-11,
          4.190257862912716e-11,
          5.716174847911551e-12
        ]
      },
      "adjoint_l1_reference_error": 0.0001279857168273056,
      "adjoint_linf_reference_error": 0.0033866238312771912,
      "continuous_bvp_max_rms_residual": 9.993028169263288e-10,
      "continuous_adjoint_gradient_amplitude_phase": [
        -0.14400769804322888,
        0.08515585831373018
      ],
      "nu_lambda_x_0": -1.4265679653908852,
      "minus_nu_lambda_x_1": -0.022034551457316722,
      "psi_0_boundary_flux_error": 0.00010347435381352632,
      "psi_N_boundary_flux_error": 0.00013556840371960546,
      "elapsed_seconds": 0.14215754099859623,
      "cells": 16384,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "first",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 2.941371513021096e-08,
          "correction_inf": 0.00015370530798444033,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 3.68816088780477e-12,
          "correction_inf": 1.2744546345811997e-08,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 7.149836278586008e-14,
          "correction_inf": 1.746970166669631e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 1.0001308490967047,
      "state_linf_observed_order": 1.0001854116088442,
      "gradient_observed_order": 1.0001438193648606,
      "amplitude_gradient_observed_order": 1.0001438193648606,
      "phase_gradient_observed_order": 0.9981194981475482,
      "viscosity_gradient_observed_order": 0.9879317403136528,
      "adjoint_l1_observed_order": 0.9990614018696603,
      "psi_0_observed_order": 1.0000841011831112,
      "psi_N_observed_order": 1.0000560915832422,
      "profile": {
        "x": [
          0.0,
          0.0062255859375,
          0.012451171875,
          0.01873779296875,
          0.02496337890625,
          0.03125,
          0.0374755859375,
          0.043701171875,
          0.04998779296875,
          0.05621337890625,
          0.0625,
          0.0687255859375,
          0.074951171875,
          0.08123779296875,
          0.08746337890625,
          0.09375,
          0.0999755859375,
          0.106201171875,
          0.11248779296875,
          0.11871337890625,
          0.125,
          0.1312255859375,
          0.137451171875,
          0.14373779296875,
          0.14996337890625,
          0.15625,
          0.1624755859375,
          0.168701171875,
          0.17498779296875,
          0.18121337890625,
          0.1875,
          0.1937255859375,
          0.199951171875,
          0.20623779296875,
          0.21246337890625,
          0.21875,
          0.2249755859375,
          0.231201171875,
          0.23748779296875,
          0.24371337890625,
          0.25,
          0.2562255859375,
          0.262451171875,
          0.26873779296875,
          0.27496337890625,
          0.28125,
          0.2874755859375,
          0.293701171875,
          0.29998779296875,
          0.30621337890625,
          0.3125,
          0.3187255859375,
          0.324951171875,
          0.33123779296875,
          0.33746337890625,
          0.34375,
          0.3499755859375,
          0.356201171875,
          0.36248779296875,
          0.36871337890625,
          0.375,
          0.3812255859375,
          0.387451171875,
          0.39373779296875,
          0.39996337890625,
          0.40625,
          0.4124755859375,
          0.418701171875,
          0.42498779296875,
          0.43121337890625,
          0.4375,
          0.4437255859375,
          0.449951171875,
          0.45623779296875,
          0.46246337890625,
          0.46875,
          0.4749755859375,
          0.481201171875,
          0.48748779296875,
          0.49371337890625,
          0.5,
          0.5062255859375,
          0.512451171875,
          0.51873779296875,
          0.52496337890625,
          0.53125,
          0.5374755859375,
          0.543701171875,
          0.54998779296875,
          0.55621337890625,
          0.5625,
          0.5687255859375,
          0.574951171875,
          0.58123779296875,
          0.58746337890625,
          0.59375,
          0.5999755859375,
          0.606201171875,
          0.61248779296875,
          0.61871337890625,
          0.625,
          0.6312255859375,
          0.637451171875,
          0.64373779296875,
          0.64996337890625,
          0.65625,
          0.6624755859375,
          0.668701171875,
          0.67498779296875,
          0.68121337890625,
          0.6875,
          0.6937255859375,
          0.699951171875,
          0.70623779296875,
          0.71246337890625,
          0.71875,
          0.7249755859375,
          0.731201171875,
          0.73748779296875,
          0.74371337890625,
          0.75,
          0.7562255859375,
          0.762451171875,
          0.76873779296875,
          0.77496337890625,
          0.78125,
          0.7874755859375,
          0.793701171875,
          0.79998779296875,
          0.80621337890625,
          0.8125,
          0.8187255859375,
          0.824951171875,
          0.83123779296875,
          0.83746337890625,
          0.84375,
          0.8499755859375,
          0.856201171875,
          0.86248779296875,
          0.86871337890625,
          0.875,
          0.8812255859375,
          0.887451171875,
          0.89373779296875,
          0.89996337890625,
          0.90625,
          0.9124755859375,
          0.918701171875,
          0.92498779296875,
          0.93121337890625,
          0.9375,
          0.9437255859375,
          0.949951171875,
          0.95623779296875,
          0.96246337890625,
          0.96875,
          0.9749755859375,
          0.981201171875,
          0.98748779296875,
          0.99371337890625,
          1.0
        ],
        "u": [
          0.9148441416869855,
          0.9219873086401665,
          0.9292496980462507,
          0.9366929596763175,
          0.9441611977829525,
          0.9517891812751835,
          0.9594171454267281,
          0.9671070820451172,
          0.974923322148606,
          0.9827021578706538,
          0.9905839627264243,
          0.9984036554474879,
          1.0062256881474019,
          1.0141146011594302,
          1.0219051640203374,
          1.029737961335879,
          1.037448937727837,
          1.0451025291274314,
          1.0527610052327392,
          1.0602639613859528,
          1.067746791551015,
          1.0750527696599061,
          1.082243839598756,
          1.0893776077023654,
          1.0963046585201655,
          1.103149992896807,
          1.1097702362980433,
          1.1162224604040305,
          1.1225573945834548,
          1.1286423541509698,
          1.1345871434734645,
          1.140267249138085,
          1.1457326775834327,
          1.1510253317750483,
          1.1560343568284397,
          1.1608501409651009,
          1.1653718170688345,
          1.169640404684295,
          1.1736873700123143,
          1.1774279484699663,
          1.1809296383338683,
          1.1841190955900243,
          1.1870267764703095,
          1.1896725010213234,
          1.1920008531266975,
          1.1940538467272541,
          1.1957884802886258,
          1.1972234761441058,
          1.1983662462691331,
          1.1991928535560283,
          1.199718212390767,
          1.1999313172418744,
          1.199838436806092,
          1.1994342898571162,
          1.1987273392591844,
          1.1977048259426386,
          1.1963881644224716,
          1.1947709285650578,
          1.1928353465954513,
          1.1906219572585592,
          1.1880908175838172,
          1.1852949403156998,
          1.1822154511509042,
          1.1788227704582248,
          1.175187956083868,
          1.1712454154408518,
          1.1670777233166125,
          1.1626542823169914,
          1.157934841494537,
          1.1530182480597693,
          1.1478157799506126,
          1.142436401591688,
          1.1368389681706914,
          1.1309741041746237,
          1.1249646482809907,
          1.1187021581868901,
          1.1123178011340342,
          1.1057614660102593,
          1.0989765502860478,
          1.0921051638853865,
          1.0850233116449928,
          1.077879323170166,
          1.0706160468676607,
          1.0631718286243146,
          1.0557025883455193,
          1.0480735434211736,
          1.0404444853208743,
          1.0327534184730525,
          1.024936006871701,
          1.0171559878639758,
          1.0092729716941096,
          1.0014520701280247,
          0.9936288263521086,
          0.9857386952846273,
          0.9779469381329793,
          0.9701129540280591,
          0.9624008283871895,
          0.9547461204875152,
          0.9470865569841469,
          0.9395825702205797,
          0.9320987524615603,
          0.9247918550489335,
          0.9175999299965207,
          0.9104653690559791,
          0.903537608171129,
          0.8966916373250294,
          0.8900708476543377,
          0.8836181646361496,
          0.8772828589751787,
          0.8711976252796472,
          0.8652526559740761,
          0.8595724695089769,
          0.8541070581464477,
          0.8488145208303126,
          0.8438057098267541,
          0.8389902400967152,
          0.8344689709951052,
          0.8302008832681432,
          0.8261545140083412,
          0.8224146126487124,
          0.8189136899504885,
          0.8157250702652785,
          0.8128182991401499,
          0.8101735606259206,
          0.8078462453915416,
          0.8057943530112935,
          0.8040608565325932,
          0.8026270366967022,
          0.8014854858645469,
          0.8006601095689597,
          0.8001360094093618,
          0.7999241583448149,
          0.8000182917464141,
          0.8004236949131737,
          0.8011318725652015,
          0.8021555998608577,
          0.8034734310553819,
          0.8050917968691691,
          0.8070284724192647,
          0.8092428910045573,
          0.8117750093743991,
          0.814571789900385,
          0.8176521113275109,
          0.821045555444581,
          0.824681045200301,
          0.8286241825388673,
          0.832792377812407,
          0.8372162319461087,
          0.8419359964643146,
          0.8468528163267877,
          0.8520554170589765,
          0.8574348312734078,
          0.8630322057142682,
          0.8688969146615609,
          0.874906123728858,
          0.8811682722123181,
          0.8875522018238431,
          0.8941080235907903,
          0.9008923370551417,
          0.9077630477144136,
          0.9148441416869854
        ],
        "exact_nodal_value": [
          0.9148441416869855,
          0.9219862121745078,
          0.929247636445234,
          0.936690055405133,
          0.944157588107717,
          0.9517849878333923,
          0.9594124992264225,
          0.9671021056914025,
          0.9749181345119724,
          0.982696879509148,
          0.9905787098580715,
          0.998398541171333,
          1.0062208225664988,
          1.0141100956434446,
          1.0219011201273405,
          1.0297344867793845,
          1.0374461262809207,
          1.045100476719042,
          1.0527598137123722,
          1.060263712981329,
          1.0677475840490582,
          1.075054677757562,
          1.0822469448439112,
          1.0893820017283775,
          1.096310405141725,
          1.1031571796570094,
          1.1097789200591286,
          1.1162327090030468,
          1.1225692895439654,
          1.1286559424440215,
          1.1346025027019546,
          1.1402844200275506,
          1.1457517153392496,
          1.1510463083000282,
          1.1560573040292783,
          1.160875127054017,
          1.165398868406723,
          1.1696695649934687,
          1.1737187021358664,
          1.177461470938634,
          1.180965410493204,
          1.1841571310297787,
          1.187067108416777,
          1.1897151836711939,
          1.1920458930413578,
          1.1941012946937084,
          1.195838338383869,
          1.1972757677720716,
          1.1984210170915381,
          1.1992500991750796,
          1.199777974992394,
          1.1999935882212729,
          1.1999032300054107,
          1.1995016421008429,
          1.1987972357382461,
          1.197777299748901,
          1.1964631966210297,
          1.1948485232166648,
          1.1929155308860222,
          1.190704706018766,
          1.188176153790845,
          1.1853828345524702,
          1.1823058969530131,
          1.1789157840075277,
          1.1752835013954162,
          1.17134350377301,
          1.1671783141159506,
          1.162757357307782,
          1.1580404038867518,
          1.1531262501135604,
          1.147926218995722,
          1.1425492248226337,
          1.1369541436965904,
          1.1310916196746872,
          1.1250844429140308,
          1.1188242125804078,
          1.1124420487619093,
          1.1058878591479075,
          1.099105058035552,
          1.0922357107214788,
          1.0851558583130145,
          1.078013787825492,
          1.070752363554766,
          1.063309944594867,
          1.0558424118922831,
          1.0482150121666078,
          1.0405875007735776,
          1.0328978943085976,
          1.0250818654880276,
          1.017303120490852,
          1.0094212901419286,
          1.001601458828667,
          0.9937791774335013,
          0.9858899043565554,
          0.9780988798726595,
          0.9702655132206155,
          0.9625538737190794,
          0.9548995232809581,
          0.947240186287628,
          0.939736287018671,
          0.9322524159509418,
          0.924945322242438,
          0.917753055156089,
          0.9106179982716226,
          0.9036895948582753,
          0.8968428203429906,
          0.8902210799408714,
          0.8837672909969533,
          0.8774307104560347,
          0.8713440575559785,
          0.8653974972980454,
          0.8597155799724495,
          0.8542482846607504,
          0.8489536916999719,
          0.8439426959707219,
          0.8391248729459831,
          0.8346011315932772,
          0.8303304350065313,
          0.8262812978641336,
          0.822538529061366,
          0.8190345895067961,
          0.8158428689702213,
          0.812932891583223,
          0.8102848163288061,
          0.8079541069586423,
          0.8058987053062915,
          0.8041616616161309,
          0.8027242322279283,
          0.8015789829084619,
          0.8007499008249204,
          0.800222025007606,
          0.8000064117787271,
          0.8000967699945892,
          0.800498357899157,
          0.8012027642617539,
          0.8022227002510991,
          0.8035368033789704,
          0.8051514767833352,
          0.8070844691139777,
          0.8092952939812339,
          0.8118238462091549,
          0.8146171654475298,
          0.8176941030469868,
          0.8210842159924722,
          0.8247164986045838,
          0.82865649622699,
          0.8328216858840494,
          0.8372426426922179,
          0.8419595961132483,
          0.8468737498864396,
          0.852073781004278,
          0.8574507751773662,
          0.8630458563034095,
          0.8689083803253127,
          0.874915557085969,
          0.8811757874195922,
          0.8875579512380907,
          0.8941121408520925,
          0.900894941964448,
          0.9077642892785209,
          0.9148441416869854
        ],
        "adjoint": [
          -1.4266714397446987,
          -0.6720581070280228,
          -1.0490548964952324,
          -1.2597647489720676,
          -1.3733156514003533,
          -1.434064691933452,
          -1.4643371163172765,
          -1.4780474657656983,
          -1.4825752673508195,
          -1.4819728287406595,
          -1.478555331205366,
          -1.4736567475554152,
          -1.4679450530550038,
          -1.4617369169280805,
          -1.4553602453078487,
          -1.4488035344571641,
          -1.442254224996765,
          -1.435680804943951,
          -1.4290354477342346,
          -1.4224558287538835,
          -1.4158172309779464,
          -1.4092504360902778,
          -1.4026915595154354,
          -1.396076327401321,
          -1.389532718554589,
          -1.3829317221579323,
          -1.3764006801595843,
          -1.3698745574163225,
          -1.3632884450532228,
          -1.3567691858759103,
          -1.3501878491060426,
          -1.3436710994613768,
          -1.337153877455876,
          -1.3305710697288964,
          -1.324049264338126,
          -1.3174593008953668,
          -1.310927843939755,
          -1.3043896209822003,
          -1.2977790646092326,
          -1.2912231532765643,
          -1.2845919122734837,
          -1.278012668097235,
          -1.271419645980348,
          -1.2647465038294297,
          -1.2581213054902685,
          -1.2514125885981444,
          -1.2447490587331993,
          -1.2380641029223862,
          -1.2312902417502232,
          -1.224557374065964,
          -1.2177318051202195,
          -1.2109443906668937,
          -1.2041273055532933,
          -1.197211534629106,
          -1.1903296151630385,
          -1.1833448115521856,
          -1.176390955066015,
          -1.169398601734336,
          -1.162296770939448,
          -1.155221497334735,
          -1.148032137574753,
          -1.1408663804778187,
          -1.1336527284588254,
          -1.1263177787410916,
          -1.1190019808846472,
          -1.1115598636564208,
          -1.1041339152027216,
          -1.096650126192083,
          -1.0890321935816443,
          -1.08142596050579,
          -1.073680161761256,
          -1.0659430882345176,
          -1.058137743835835,
          -1.0501844338925133,
          -1.04223543509925,
          -1.0341326883417536,
          -1.0260313508185197,
          -1.017850957271937,
          -1.00950792910503,
          -1.0011620730685309,
          -0.9926475220678161,
          -0.984127415646506,
          -0.975517343476999,
          -0.9667293678202116,
          -0.9579319653134213,
          -0.9489504630589716,
          -0.9399571337439538,
          -0.9308631720550319,
          -0.9215758478123555,
          -0.9122734647794067,
          -0.9027716063423739,
          -0.8932528314127844,
          -0.8836235413055668,
          -0.8737858539273403,
          -0.8639290308152348,
          -0.8538580920314258,
          -0.8437669852252286,
          -0.8335570023204941,
          -0.8231248611541491,
          -0.812671817333008,
          -0.801991698421192,
          -0.7912908140698084,
          -0.7804651466021224,
          -0.7694059160137556,
          -0.7583272179030514,
          -0.7470113295921633,
          -0.7356776589290018,
          -0.7242168253261747,
          -0.7125146372850513,
          -0.700798561231677,
          -0.6888393180635387,
          -0.6768697783479978,
          -0.6647753141994548,
          -0.6524366124741148,
          -0.6400945807222771,
          -0.6275087938561582,
          -0.6149254292639986,
          -0.6022249027023318,
          -0.589283269268008,
          -0.5763543420683199,
          -0.563187411098093,
          -0.5500411482168287,
          -0.5367914666800896,
          -0.5233104496805997,
          -0.5098635649281843,
          -0.4961911193097578,
          -0.48256272772738606,
          -0.46885038959303776,
          -0.454922994222582,
          -0.4410556691510731,
          -0.42698142248930654,
          -0.4129785378641853,
          -0.39891578991418924,
          -0.38465971039271696,
          -0.3704924403745114,
          -0.3561416557135802,
          -0.3418914578428379,
          -0.3276081563076183,
          -0.3131567683940041,
          -0.2988233759272075,
          -0.2843324427041244,
          -0.26997073208232186,
          -0.25560289796549124,
          -0.24109325944180574,
          -0.2267286647758757,
          -0.21223249834420777,
          -0.1978910704360286,
          -0.18356822001015033,
          -0.1691283380244417,
          -0.15485611431814864,
          -0.14047585765522466,
          -0.1262706875267544,
          -0.11210447054076723,
          -0.09784237515361091,
          -0.083764547311683,
          -0.06959796493121366,
          -0.05562044195837129,
          -0.04169666887723675,
          -0.0276932048783177,
          -0.013883973155226015,
          -0.022170119861036328
        ],
        "amplitude_tangent": [
          -0.42577929156523103,
          -0.39006320214820317,
          -0.3537511114663107,
          -0.31653475415197,
          -0.2791935934687091,
          -0.24105376910100332,
          -0.20291408713098383,
          -0.16446457403655634,
          -0.12538356207363804,
          -0.08648957295260326,
          -0.047080729421568934,
          -0.007982421890877462,
          0.031127619869332223,
          0.0705721076574043,
          0.10952490047952014,
          0.14868892997341096,
          0.18724392641312937,
          0.2255120765717719,
          0.2638047382326352,
          0.30131988793122844,
          0.33873450718202847,
          0.37526496009226046,
          0.4112209728548448,
          0.4468905870458787,
          0.4815267115055453,
          0.5157543678900199,
          0.548856664050508,
          0.5811189663914711,
          0.6127949331287571,
          0.6432211133346695,
          0.672946552973903,
          0.7013486524882344,
          0.7286774540956442,
          0.7551424856038205,
          0.7801894333826688,
          0.8042702687307792,
          0.8268806129925287,
          0.8482255758862254,
          0.8684625024342767,
          0.887167521928563,
          0.904678160018698,
          0.9206276464798964,
          0.9351682756606648,
          0.9483991616805654,
          0.9600431715552127,
          0.9703104102934685,
          0.9789858172324188,
          0.9861630170808979,
          0.9918790818478551,
          0.9960142735658414,
          0.9986431967178302,
          0.999710772595859,
          0.999248355854509,
          0.9972295488354683,
          0.9936966184335733,
          0.9885857948531918,
          0.9820041067337691,
          0.9739194307909752,
          0.9642429109737806,
          0.9531772039427169,
          0.9405226090027955,
          0.9265441585155232,
          0.9111474826681243,
          0.8941846786340907,
          0.876011014507746,
          0.856298525948297,
          0.8354600737040287,
          0.8133426652075813,
          0.7897450321487813,
          0.7651614109384267,
          0.7391481708264805,
          0.7122501443977889,
          0.6842615936434652,
          0.6549356179054836,
          0.624886437628822,
          0.5935717996557281,
          0.5616475792065534,
          0.5288631982702056,
          0.49493561214911,
          0.460575428423718,
          0.42516260826586943,
          0.38943887080534556,
          0.3531184281645247,
          0.3158929708476086,
          0.27854218942622644,
          0.240392088996963,
          0.20224173108653704,
          0.1637811028273099,
          0.12468848206297634,
          0.08578267835171198,
          0.046361647859091214,
          0.007251083474822248,
          -0.031871335526355585,
          -0.07132837497860549,
          -0.11029358080609518,
          -0.14947005706477534,
          -0.1880372218625832,
          -0.2263173133171429,
          -0.2646217318215549,
          -0.30214815573553044,
          -0.3395737177529263,
          -0.376114501824888,
          -0.41208027722124246,
          -0.4477591084423744,
          -0.4824036642193732,
          -0.5166390727584749,
          -0.5497482369961715,
          -0.5820165525182143,
          -0.6136976777846521,
          -0.6441280211590962,
          -0.6738566748295718,
          -0.7022609479235657,
          -0.7295908964349325,
          -0.7560560284882262,
          -0.781102020013463,
          -0.8051808224757743,
          -0.8277881032358662,
          -0.8491289715856984,
          -0.8693607394368258,
          -0.8880596659858031,
          -0.9055631952327323,
          -0.92150473969575,
          -0.9360365806131884,
          -0.9492577924699355,
          -0.9608914947596708,
          -0.9711476615948533,
          -0.9798115226439639,
          -0.9869766772825588,
          -0.992680156256717,
          -0.9968025522626537,
          -0.9994183084536881,
          -1.0004726915366908,
          -0.9999970189267174,
          -0.9979648529998916,
          -0.9944188090823335,
          -0.9892949486849685,
          -0.9827006384423804,
          -0.9746037084701483,
          -0.9649152668736173,
          -0.9538382757010664,
          -0.9411728831228916,
          -0.9271843952968395,
          -0.9117783928216985,
          -0.894806945477052,
          -0.8766255363477706,
          -0.8569060908941192,
          -0.8360616399598857,
          -0.8139391478333059,
          -0.7903373328557435,
          -0.7657505293752558,
          -0.7397350551834364,
          -0.7128357912495555,
          -0.6848469725187254,
          -0.6555217039215692,
          -0.6254741809422791,
          -0.5941621664893029,
          -0.562241463869635,
          -0.529461490704916,
          -0.49553922859686655,
          -0.4611851479643179,
          -0.425779291565073
        ],
        "continuous_adjoint": [
          9.845428114990824e-27,
          -0.6750493092947951,
          -1.052399021603968,
          -1.262544181447345,
          -1.3753572187330407,
          -1.435452258974065,
          -1.4652342875575328,
          -1.478600910499279,
          -1.482897748729123,
          -1.482148506491179,
          -1.4786383980768152,
          -1.4736837873677726,
          -1.4679384049664161,
          -1.4617101917318562,
          -1.4553219675380757,
          -1.4487585756787476,
          -1.4422055394685014,
          -1.4356300541286842,
          -1.4289835749797974,
          -1.4224033844852362,
          -1.415764514000809,
          -1.409197616205559,
          -1.402638728062454,
          -1.3960235346997798,
          -1.3894799911091873,
          -1.3828790750042284,
          -1.3763481199710799,
          -1.369822087980246,
          -1.3632360691551049,
          -1.356716903482344,
          -1.3501356615065214,
          -1.34361900586775,
          -1.3371018779055857,
          -1.3305191651644293,
          -1.3239974538818435,
          -1.3174075855632377,
          -1.3108762229621584,
          -1.3043380945825716,
          -1.2977276340186303,
          -1.291171817946704,
          -1.2845406736100697,
          -1.277961525717266,
          -1.2713686005276479,
          -1.26469555700304,
          -1.2580704571722632,
          -1.2513618407046998,
          -1.244698411334468,
          -1.238013557165167,
          -1.2312397999063631,
          -1.224507036504964,
          -1.2176815743703033,
          -1.210894267309204,
          -1.2040772913156208,
          -1.1971616324701915,
          -1.1902798259912042,
          -1.1832951386352595,
          -1.1763413995485932,
          -1.1693491660286963,
          -1.1622474588124847,
          -1.155172310312114,
          -1.1479830797943542,
          -1.1408174537315967,
          -1.1336039359465833,
          -1.1262691252016033,
          -1.1189534685376399,
          -1.1115114976775105,
          -1.1040856981160776,
          -1.0966020621191033,
          -1.0889842884088563,
          -1.0813782172423572,
          -1.0736325868078067,
          -1.0658956849433996,
          -1.0580905173937647,
          -1.0501373915302994,
          -1.0421885807104738,
          -1.0340860297515553,
          -1.0259848922980137,
          -1.0178047052146766,
          -1.009461892283048,
          -1.0011162563362224,
          -0.9926019348639512,
          -0.9840820632215719,
          -0.9754722335431991,
          -0.9666845108564345,
          -0.9578873671603167,
          -0.9489061349092898,
          -0.939913081820526,
          -0.9308194054282024,
          -0.9215323787533578,
          -0.9122303000439672,
          -0.9027287589134401,
          -0.8932103083607262,
          -0.883581352970551,
          -0.8737440143144634,
          -0.8638875473746878,
          -0.8538169794012982,
          -0.8437262510291468,
          -0.8335166578937042,
          -0.8230849219696056,
          -0.8126322911202414,
          -0.8019526011111301,
          -0.7912521533417786,
          -0.7804269342923069,
          -0.7693681685511878,
          -0.7582899426840637,
          -0.7469745432344487,
          -0.7356413684899791,
          -0.7241810424520683,
          -0.7124793786380177,
          -0.7007638331314108,
          -0.6888051370372679,
          -0.6768361500761032,
          -0.6647422493701716,
          -0.6524041271753117,
          -0.6400626794854221,
          -0.6274774923346687,
          -0.6148947311205434,
          -0.6021948170149817,
          -0.5892538108733338,
          -0.5763255132357377,
          -0.5631592260425939,
          -0.5500136082553084,
          -0.5367645789475708,
          -0.5232842274121446,
          -0.5098380080484719,
          -0.49616624040342966,
          -0.48253852584363227,
          -0.4688268699783695,
          -0.45490016854028176,
          -0.4410335352574799,
          -0.4269599914822432,
          -0.41295780688752415,
          -0.39889576262438065,
          -0.38464039711310466,
          -0.3704738372893692,
          -0.3561237726601953,
          -0.3418742904116331,
          -0.327591706802881,
          -0.3131410459216288,
          -0.29880837520186504,
          -0.28431817230583833,
          -0.2699571861157477,
          -0.25559007731353767,
          -0.24108117178454633,
          -0.226717303219871,
          -0.21222186987012365,
          -0.19788116741333653,
          -0.18355904153575395,
          -0.16911988987023907,
          -0.1548483876488487,
          -0.14046885733724157,
          -0.1262644038728137,
          -0.11209890047341375,
          -0.09783752208023637,
          -0.08376040025506183,
          -0.06959452629354974,
          -0.05561769993443299,
          -0.04169461812511507,
          -0.027691846324052003,
          -0.013883293876163797,
          -5.817375132447619e-20
        ]
      }
    }
  ]
}