{
  "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 smooth --gradient-check --continuous-adjoint --output examples/refinement_smooth.json",
    "python": "3.11.12",
    "numpy": "2.3.1",
    "scipy": "1.16.0",
    "platform": "macOS-26.6.2-arm64-arm-64bit",
    "generated_utc": "2026-10-03T22:54:01Z",
    "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": 1.4717066226110007,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.1368370911661347,
        0.09646049164827306,
        -0.07428477381044037
      ],
      "tangent_gradient": [
        -0.13683709116613466,
        0.0964604916482735,
        -0.07428477381044038
      ],
      "reverse_gradient": [
        -0.13683709116613463,
        0.09646049164827297,
        -0.07428477381044041
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.07428477381044037,
      "amplitude_gradient_error": 0.007170606877102026,
      "phase_gradient_error": 0.01130463333525851,
      "viscosity_gradient_error": 0.07428477381044037,
      "gradient_duality_error": 4.440892098500626e-16,
      "gradient_reverse_error": 8.326672684688674e-17,
      "reverse_state_adjoint_error": 8.465450562766819e-16,
      "transpose_relative_error": 3.751386892580543e-16,
      "state_l1_error": 0.0025429833534098903,
      "state_linf_error": 0.0057367729898333275,
      "primal_residual_inf": 8.881784197001252e-16,
      "primal_residual_density_inf": 2.842170943040401e-14,
      "newton_correction_inf": 2.6923721306484356e-16,
      "tangent_residual_inf": 6.661338147750939e-16,
      "adjoint_residual_inf": 4.371503159461554e-16,
      "jacobian_nonzeros": 155,
      "psi_0": -1.4106163834362624,
      "psi_N": -0.039250771526290425,
      "exact_nodal_residual_inf": 0.00539321546418281,
      "exact_nodal_residual_boundary_rows_inf": 0.0020008455802324465,
      "exact_nodal_residual_inner_rows_inf": 0.00539321546418281,
      "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": -0.1078989436353872,
        "adjoint_directional_gradient": -0.1078989436716528,
        "absolute_error": 3.626560163283443e-11,
        "perturbed_primal_residuals_inf": [
          7.771561172376096e-16,
          3.3306690738754696e-16
        ],
        "axis_central_differences": [
          -0.13683709116918408,
          0.0964604913722411,
          -0.07428477735160754
        ],
        "axis_absolute_errors": [
          3.0493663150110706e-12,
          2.760319611772033e-10,
          3.541167178933158e-09
        ]
      },
      "adjoint_l1_reference_error": 0.023704514273827033,
      "adjoint_linf_reference_error": 0.12296562865811889,
      "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": 0.015951581954622762,
      "psi_N_boundary_flux_error": 0.017216220068973703,
      "elapsed_seconds": 0.05561554199812235,
      "cells": 32,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.00539321546418281,
          "correction_inf": 0.005826006941465508,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 0.0007356153550998612,
          "correction_inf": 0.00038986147134772715,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 9.08998758342161e-06,
          "correction_inf": 4.5932860710320235e-06,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 1.3288826705704082e-09,
          "correction_inf": 8.809904317578498e-10,
          "step": 1.0
        },
        {
          "iteration": 4,
          "residual_inf": 6.661338147750939e-16,
          "correction_inf": 2.6923721306484356e-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,
          0.9533378222614993,
          0.9923066410405895,
          1.0313507094020415,
          1.0692474947561614,
          1.1046057658359332,
          1.1361400107696382,
          1.162931591834778,
          1.1840881426809704,
          1.1968014122212112,
          1.1983268465494097,
          1.194110489686815,
          1.1842911239179612,
          1.1679725690377363,
          1.1451632780034124,
          1.1165756660753092,
          1.0833076657686398,
          1.046666003805097,
          1.0080789022109578,
          0.9690435151188856,
          0.931066879467475,
          0.8955158905116252,
          0.8633853072384017,
          0.8355988776066627,
          0.8146459574150829,
          0.8043361357902399,
          0.803718286044946,
          0.8079474071052978,
          0.8175606191989883,
          0.8336006771463681,
          0.8561212024843607,
          0.8839907728940698,
          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": [
          -1.4106163834362624,
          -1.5497820201984545,
          -1.601604026734934,
          -1.4596702346224952,
          -1.391884778098328,
          -1.3597622819897137,
          -1.3300605023138494,
          -1.2980060899486345,
          -1.2662003737300906,
          -1.233065858923423,
          -1.2043759528342939,
          -1.170066894875537,
          -1.127100307325393,
          -1.0897257151569928,
          -1.052931437815637,
          -1.0141451753045265,
          -0.9730142671246887,
          -0.9294888761048818,
          -0.8834129239687657,
          -0.8345384831060959,
          -0.7825542116152655,
          -0.727257796788272,
          -0.6692713246911816,
          -0.6102301348034739,
          -0.5477761824493486,
          -0.47534455231403194,
          -0.4227567361171785,
          -0.35174857496353285,
          -0.26262607013478934,
          -0.1878232363383363,
          -0.12063310549759443,
          -0.056416243357000025,
          -0.039250771526290425
        ],
        "amplitude_tangent": [
          -0.42577929156507316,
          -0.24060779335987012,
          -0.04754449956653571,
          0.14709835531430193,
          0.33610330753954454,
          0.5120937733849249,
          0.6676908992545074,
          0.7975562203891212,
          0.9040507369555398,
          0.9835884031291123,
          1.000128342360057,
          0.9850969878642352,
          0.9398073047807096,
          0.8584985763039977,
          0.7431952232262246,
          0.5988936497047945,
          0.4316015858863241,
          0.2479312417800232,
          0.05497918430594171,
          -0.13979696058210372,
          -0.328823218433865,
          -0.5052843435710787,
          -0.6647397109025104,
          -0.8044249192304405,
          -0.914716237469409,
          -0.9742016195927546,
          -0.982107237074923,
          -0.968019825136426,
          -0.925030115000197,
          -0.8461673816840417,
          -0.7324609653641719,
          -0.58856313796964,
          -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": 1.469910178487639,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.13734917738346517,
        0.08047847439547917,
        -0.10722982711738
      ],
      "tangent_gradient": [
        -0.13734917738346497,
        0.08047847439547838,
        -0.10722982711738002
      ],
      "reverse_gradient": [
        -0.13734917738346447,
        0.0804784743954785,
        -0.10722982711737972
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.10722982711738,
      "amplitude_gradient_error": 0.006658520659771572,
      "phase_gradient_error": 0.004677383917535374,
      "viscosity_gradient_error": 0.10722982711738,
      "gradient_duality_error": 7.91033905045424e-16,
      "gradient_reverse_error": 6.938893903907228e-16,
      "reverse_state_adjoint_error": 1.2212453270876722e-15,
      "transpose_relative_error": 3.77679715443829e-16,
      "state_l1_error": 0.0026648890944904764,
      "state_linf_error": 0.005031956138713989,
      "primal_residual_inf": 5.551115123125783e-16,
      "primal_residual_density_inf": 3.552713678800501e-14,
      "newton_correction_inf": 2.918911735190581e-16,
      "tangent_residual_inf": 8.881784197001252e-16,
      "adjoint_residual_inf": 1.0061396160665481e-15,
      "jacobian_nonzeros": 315,
      "psi_0": -1.4245423405979976,
      "psi_N": -0.02584215297834351,
      "exact_nodal_residual_inf": 0.001999087326563509,
      "exact_nodal_residual_boundary_rows_inf": 0.001999087326563509,
      "exact_nodal_residual_inner_rows_inf": 0.0018507854188622996,
      "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": -0.11320563503280921,
        "adjoint_directional_gradient": -0.11320563506482141,
        "absolute_error": 3.201219844761738e-11,
        "perturbed_primal_residuals_inf": [
          6.661338147750939e-16,
          7.771561172376096e-16
        ],
        "axis_central_differences": [
          -0.13734917738705832,
          0.08047847432912647,
          -0.10722984222777397
        ],
        "axis_absolute_errors": [
          3.5931535524724723e-12,
          6.63527011113274e-11,
          1.511039397772418e-08
        ]
      },
      "adjoint_l1_reference_error": 0.009465484439639345,
      "adjoint_linf_reference_error": 0.08932916257627799,
      "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": 0.0020256247928875926,
      "psi_N_boundary_flux_error": 0.0038076015210267884,
      "elapsed_seconds": 0.0229937499971129,
      "cells": 64,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.001999087326563509,
          "correction_inf": 0.005016717489251252,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 0.0002512426935559753,
          "correction_inf": 0.00019972325772118436,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 7.619791096979966e-07,
          "correction_inf": 1.8742668400053609e-07,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 1.5989987112163817e-12,
          "correction_inf": 5.370418744783104e-13,
          "step": 1.0
        },
        {
          "iteration": 4,
          "residual_inf": 5.551115123125783e-16,
          "correction_inf": 2.918911735190581e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": -0.06755347509853792,
      "state_linf_observed_order": 0.1891200832009921,
      "gradient_observed_order": -0.5295678263864018,
      "amplitude_gradient_observed_order": 0.10689353941514047,
      "phase_gradient_observed_order": 1.2731404446880057,
      "viscosity_gradient_observed_order": -0.5295678263864018,
      "adjoint_l1_observed_order": 1.324413581811566,
      "psi_0_observed_order": 2.9772606332843274,
      "psi_N_observed_order": 2.176814016078606,
      "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,
          0.9343086113567323,
          0.9533196955437955,
          0.9725656916969024,
          0.9920533011066734,
          1.0116375696983395,
          1.0311389907166966,
          1.0503716896458413,
          1.0691512336991922,
          1.0872977304885665,
          1.104637776293381,
          1.1210060101575898,
          1.1362463958472315,
          1.150213074815218,
          1.1627691184899285,
          1.1737752605954477,
          1.183051085085266,
          1.1903172844862109,
          1.1952544021816667,
          1.19781189550098,
          1.1983376214874988,
          1.1971702249431189,
          1.1944381600176295,
          1.1901478968705674,
          1.1842576264276228,
          1.1767261299508727,
          1.1675438565787775,
          1.1567443086492344,
          1.1444009547518184,
          1.1306185521385668,
          1.1155248369447324,
          1.0992644718703926,
          1.0819949884019096,
          1.063883959605135,
          1.0451067970821646,
          1.0258448176441997,
          1.0062834043747202,
          0.986610187913161,
          0.9670132264538889,
          0.9476791916599634,
          0.9287915833490888,
          0.9105289875573577,
          0.8930633276982899,
          0.8765579897816623,
          0.8611662261892656,
          0.8470332990972046,
          0.8343137315935664,
          0.823220764996636,
          0.8140907688688698,
          0.8073317426456823,
          0.8031216011003584,
          0.8011705321026723,
          0.8010144862263162,
          0.8023873263438704,
          0.8052118733464432,
          0.8095089746906496,
          0.8153425320732212,
          0.8227758898877415,
          0.8318393158250326,
          0.8425151960485806,
          0.8547351002218757,
          0.8683654921616849,
          0.8831489080089524,
          0.8986518419048934,
          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": [
          -1.4245423405979976,
          -1.2411207291493445,
          -1.524781421550343,
          -1.521320446821921,
          -1.4868618178036355,
          -1.4623206593933047,
          -1.444005752799661,
          -1.4273648340042995,
          -1.410924469507057,
          -1.3944651440381894,
          -1.3780078411581682,
          -1.3615684911767585,
          -1.3451462363387934,
          -1.328744089872849,
          -1.3123913407906163,
          -1.2961752525298187,
          -1.280282532824205,
          -1.2650447819984556,
          -1.2509213219261248,
          -1.2379064950331735,
          -1.2245121960466219,
          -1.208687281444648,
          -1.1896607960898855,
          -1.1684755609310882,
          -1.1470039992958736,
          -1.1263802115237995,
          -1.1066234229039758,
          -1.0872779999808952,
          -1.0679310714985273,
          -1.048331062121119,
          -1.028340042547469,
          -1.0078775623022496,
          -0.9868888433588094,
          -0.9653302172029037,
          -0.9431629211710255,
          -0.9203505472079571,
          -0.8968581014039386,
          -0.8726518247695587,
          -0.8476994196148736,
          -0.8219705435258142,
          -0.7954375576779341,
          -0.7680766747683008,
          -0.7398700960273501,
          -0.710811023521966,
          -0.6809161550187331,
          -0.6502527565253197,
          -0.6189827869204093,
          -0.5874177400796937,
          -0.5561363945875505,
          -0.5263328580400811,
          -0.49960806519326767,
          -0.4752599782405071,
          -0.4493342093733358,
          -0.4180222718275616,
          -0.37964546748416006,
          -0.33562780123051594,
          -0.2899451831484956,
          -0.24622757257061725,
          -0.20571717516664384,
          -0.1678335390531249,
          -0.13159030656214588,
          -0.09632598856223892,
          -0.061769584479020256,
          -0.02822786162988542,
          -0.02584215297834351
        ],
        "amplitude_tangent": [
          -0.4257792915650725,
          -0.33846146727095267,
          -0.24546778450676382,
          -0.149546840125237,
          -0.05207131015888819,
          0.045895101909079514,
          0.14337376321491752,
          0.23941773962984833,
          0.3331044067757262,
          0.4235414110089064,
          0.5098770850419075,
          0.5913130045399027,
          0.6671193730062989,
          0.736664616575348,
          0.7995039750183665,
          0.8555801341848476,
          0.9052632814274068,
          0.94809199790496,
          0.9803172294189846,
          0.9975087990983456,
          1.002085144105952,
          0.9986771165050262,
          0.9884658785309786,
          0.9708704233951949,
          0.9448787813162836,
          0.9097604149835716,
          0.8653681739969771,
          0.8120653244359136,
          0.7505061422376326,
          0.6814635967640137,
          0.6057489896096633,
          0.5241905368234409,
          0.43763428410544875,
          0.34694829434743873,
          0.25302388949227356,
          0.1567732405469151,
          0.05912412003167897,
          -0.038987302722716416,
          -0.13662502153912812,
          -0.23286277124759558,
          -0.3267944446671703,
          -0.4175453189670791,
          -0.5042850221141735,
          -0.5862477517160202,
          -0.6627775721693118,
          -0.7334273931292218,
          -0.7980795250849012,
          -0.8567650734478212,
          -0.9084711794152291,
          -0.9494051583187975,
          -0.9749367144383226,
          -0.9858450648994198,
          -0.9876178174423281,
          -0.983377470677937,
          -0.9733731498048667,
          -0.9566539572286699,
          -0.931908658779144,
          -0.8981131191104574,
          -0.8549047106118652,
          -0.8025642003108625,
          -0.7417694427459591,
          -0.6732805287891591,
          -0.5974985648957158,
          -0.5142283067402409,
          -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": 1.4679075549741636,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.14004507403402697,
        0.07697507692100933,
        -0.13799347591010727
      ],
      "tangent_gradient": [
        -0.14004507403402655,
        0.07697507692100991,
        -0.13799347591010747
      ],
      "reverse_gradient": [
        -0.14004507403402688,
        0.07697507692100913,
        -0.13799347591010713
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.13799347591010727,
      "amplitude_gradient_error": 0.00396262400920977,
      "phase_gradient_error": 0.008180781392005218,
      "viscosity_gradient_error": 0.13799347591010727,
      "gradient_duality_error": 5.828670879282072e-16,
      "gradient_reverse_error": 1.942890293094024e-16,
      "reverse_state_adjoint_error": 1.5265566588595902e-15,
      "transpose_relative_error": 1.5299420502491235e-15,
      "state_l1_error": 0.0030960591586732525,
      "state_linf_error": 0.006495654156242425,
      "primal_residual_inf": 8.881784197001252e-16,
      "primal_residual_density_inf": 1.1368683772161603e-13,
      "newton_correction_inf": 2.2379164310200873e-16,
      "tangent_residual_inf": 1.2715523078909996e-15,
      "adjoint_residual_inf": 1.3652273755937472e-15,
      "jacobian_nonzeros": 635,
      "psi_0": -1.4295102013320697,
      "psi_N": -0.023354402704494095,
      "exact_nodal_residual_inf": 0.0025702581776900213,
      "exact_nodal_residual_boundary_rows_inf": 0.0025702581776900213,
      "exact_nodal_residual_inner_rows_inf": 0.00048024827490766864,
      "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": -0.11695255095478528,
        "adjoint_directional_gradient": -0.11695255095772417,
        "absolute_error": 2.9388852462730597e-12,
        "perturbed_primal_residuals_inf": [
          7.771561172376096e-16,
          9.992007221626409e-16
        ],
        "axis_central_differences": [
          -0.14004507407072708,
          0.07697507689030658,
          -0.13799352868160142
        ],
        "axis_absolute_errors": [
          3.67001151690971e-11,
          3.070274590122324e-11,
          5.2771494146730547e-08
        ]
      },
      "adjoint_l1_reference_error": 0.0053436774484813135,
      "adjoint_linf_reference_error": 0.057045032804293516,
      "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": 0.00294223594118459,
      "psi_N_boundary_flux_error": 0.0013198512471773727,
      "elapsed_seconds": 0.023807124998711515,
      "cells": 128,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.0025702581776900213,
          "correction_inf": 0.006463414716074465,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 1.799753900266765e-05,
          "correction_inf": 3.332084109144926e-05,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 1.7030555299335504e-09,
          "correction_inf": 2.719471591747634e-09,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 7.771561172376096e-16,
          "correction_inf": 2.2379164310200873e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": -0.21635754522772654,
      "state_linf_observed_order": -0.36835547517163275,
      "gradient_observed_order": -0.36389379792505744,
      "amplitude_gradient_observed_order": 0.7487456010270316,
      "phase_gradient_observed_order": -0.8065368002221263,
      "viscosity_gradient_observed_order": -0.36389379792505744,
      "adjoint_l1_observed_order": 0.8248434169256315,
      "psi_0_observed_order": -0.5385459745244733,
      "psi_N_observed_order": 1.528507162496859,
      "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,
          0.9250725622125351,
          0.9344177905239514,
          0.9437508690167724,
          0.9531952333869464,
          0.9627531096635896,
          0.9724058083182789,
          0.9821308241961272,
          0.9919048297257109,
          1.0017042424499272,
          1.0115053725736722,
          1.0212844963918208,
          1.031017915253516,
          1.0406820102083096,
          1.0502532938414622,
          1.0597084592245503,
          1.069024425534118,
          1.0781783797099578,
          1.087147813356886,
          1.0959105539078464,
          1.1044447888623534,
          1.1127290817150404,
          1.1207423780561794,
          1.1284640004006767,
          1.135873630874805,
          1.1429512825039014,
          1.1496772634007837,
          1.1560321449041961,
          1.16199675585458,
          1.1675522406164087,
          1.1726802343632696,
          1.177363215252761,
          1.1815850726612047,
          1.185331868528486,
          1.1885926701503613,
          1.1913602397862457,
          1.1936313477357903,
          1.19540657336704,
          1.1966896355187522,
          1.197486447409933,
          1.1978041393444194,
          1.197650236370846,
          1.1970320797539373,
          1.1959564988955433,
          1.1944296954473352,
          1.1924572871274246,
          1.1900444609407663,
          1.1871961934110362,
          1.183917503779295,
          1.180213713302932,
          1.176090689890706,
          1.1715550628604714,
          1.1666143979412202,
          1.161277327732632,
          1.1555536373801354,
          1.149454308843674,
          1.1429915295712387,
          1.1361786725869003,
          1.1290302551319793,
          1.121561882355143,
          1.1137901814658393,
          1.1057327305355826,
          1.0974079849596032,
          1.088835203594698,
          1.080034375812346,
          1.0710261501452643,
          1.0618317648304276,
          1.0524729803227757,
          1.0429720137328173,
          1.0333514750956654,
          1.023634305383802,
          1.013843716213584,
          1.0040031312549555,
          0.9941361294288743,
          0.9842663900654802,
          0.9744176402992071,
          0.9646136050990346,
          0.9548779604799669,
          0.9452342906257902,
          0.9357060498865594,
          0.9263165309128217,
          0.9170888405674614,
          0.9080458857213191,
          0.8992103715683776,
          0.8906048156011073,
          0.8822515806394277,
          0.8741729298290501,
          0.8663911044361173,
          0.8589284201519657,
          0.8518073675975841,
          0.8450506860171942,
          0.8386813557718521,
          0.8327224299592987,
          0.827196611418694,
          0.8221255007306362,
          0.8175285164783191,
          0.813421622775643,
          0.8098161460125727,
          0.8067180326638241,
          0.8041278130985702,
          0.802041305510466,
          0.8004508432774061,
          0.7993466803566392,
          0.7987182665283317,
          0.7985552186163352,
          0.7988479477695292,
          0.7995879843666314,
          0.800768070874396,
          0.8023820906492518,
          0.8044248869495438,
          0.8068920122448231,
          0.8097794372471608,
          0.813083242241641,
          0.8167993090684087,
          0.8209230289431062,
          0.8254490377381876,
          0.8303709851415332,
          0.8356813359837176,
          0.8413711888770793,
          0.8474300744512847,
          0.8538456519805144,
          0.8606031342643958,
          0.8676840815829593,
          0.8750638029747407,
          0.8827058040795801,
          0.8905506732424442,
          0.8985001015185372,
          0.9064465851332029,
          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": [
          -1.4295102013320697,
          -0.8382919105518629,
          -1.231314363502357,
          -1.3937921537716706,
          -1.4595399179689164,
          -1.4835740002682813,
          -1.4893022548422779,
          -1.487003722128555,
          -1.4812198776795977,
          -1.473945766457774,
          -1.4660492287134899,
          -1.4579035732726087,
          -1.4496674640547467,
          -1.4414074270599913,
          -1.433150872079309,
          -1.4249087904183253,
          -1.416685374922739,
          -1.4084820668595908,
          -1.4002992568662918,
          -1.3921370119868781,
          -1.3839954056571613,
          -1.3758746903957408,
          -1.3677754111732405,
          -1.3596984975698185,
          -1.3516453462852251,
          -1.3436178913549752,
          -1.3356186480535455,
          -1.3276507031103486,
          -1.3197176060062399,
          -1.311823093918861,
          -1.3039705620086157,
          -1.2961621867992457,
          -1.288397651002394,
          -1.2806725331921138,
          -1.2729766172465062,
          -1.2652925786353855,
          -1.2575955829129064,
          -1.2498541707818946,
          -1.2420324375522083,
          -1.2340931416819905,
          -1.226001196220395,
          -1.2177270334783663,
          -1.2092494571690304,
          -1.2005576814783847,
          -1.1916522859388068,
          -1.1825448607225804,
          -1.173256260266857,
          -1.1638136427871992,
          -1.1542467761277067,
          -1.1445843016297563,
          -1.134850651700042,
          -1.1250640971772319,
          -1.1152360554415859,
          -1.105371468677766,
          -1.0954698752522596,
          -1.0855267712716028,
          -1.075534947349722,
          -1.065485615868125,
          -1.055369260681257,
          -1.0451762189822908,
          -1.0348970433077276,
          -1.0245227016632175,
          -1.0140446683226623,
          -1.0034549465425113,
          -0.9927460527069624,
          -0.9819109816433675,
          -0.9709431655865681,
          -0.959836434269951,
          -0.9485849803677351,
          -0.937183332503845,
          -0.925626336874656,
          -0.9139091479149309,
          -0.9020272281713189,
          -0.8899763575087773,
          -0.8777526518842153,
          -0.8653525921337276,
          -0.852773063512506,
          -0.8400114070920045,
          -0.8270654845589873,
          -0.8139337584829714,
          -0.8006153907309957,
          -0.787110362415132,
          -0.7734196195446996,
          -0.7595452493640287,
          -0.7454906930318614,
          -0.7312610004748276,
          -0.7168631321364987,
          -0.7023063083538229,
          -0.687602397239101,
          -0.6727663111465687,
          -0.6578163426096855,
          -0.6427743049115674,
          -0.6276652479260274,
          -0.6125164149053545,
          -0.5973550508896259,
          -0.5822047807972442,
          -0.5670806660663674,
          -0.5519837207886846,
          -0.5368963431748549,
          -0.5217802902082895,
          -0.5065781636779134,
          -0.49121817225908554,
          -0.4756209548031576,
          -0.4597070401545629,
          -0.44340395332305726,
          -0.42665253807770137,
          -0.40941236427568034,
          -0.3916660624540115,
          -0.3734222221785475,
          -0.35471629889752204,
          -0.3356089654374798,
          -0.31618162052061954,
          -0.2965293147752308,
          -0.2767520166106929,
          -0.25694565299882927,
          -0.23719447973856617,
          -0.21756598050557097,
          -0.19810880263768257,
          -0.17885349294470015,
          -0.15981526979191385,
          -0.140997892797957,
          -0.12239784362510762,
          -0.10400838152276325,
          -0.08582337190009329,
          -0.067840533193115,
          -0.05006109523266702,
          -0.032478709296370575,
          -0.01514968614391643,
          -0.023354402704494095
        ],
        "amplitude_tangent": [
          -0.42577929156507277,
          -0.38247421045767815,
          -0.33692767203795887,
          -0.29051901474163094,
          -0.2434031228653181,
          -0.19567451024931173,
          -0.14744303006054663,
          -0.09882566888563588,
          -0.04994145487607194,
          -0.0009097909500200776,
          0.04815015681622651,
          0.09711981623068805,
          0.14588151333771524,
          0.194318769182815,
          0.2423165977989617,
          0.28976180579489763,
          0.3365432912374418,
          0.3825523375609627,
          0.42768289565355816,
          0.47183184326716787,
          0.5148992044564095,
          0.5567883012632797,
          0.5974057928661836,
          0.6366615305289425,
          0.6744681164892693,
          0.7107400012026486,
          0.7453918973508585,
          0.7783362690132445,
          0.8094797556951409,
          0.8387187509769587,
          0.865935107068744,
          0.8909940294579718,
          0.9137471513641252,
          0.9340434645857867,
          0.9517481768318463,
          0.9667650204869244,
          0.9790537800031645,
          0.9886353780839532,
          0.995582399532458,
          0.9999996262146345,
          1.00200229843021,
          1.0016983315808212,
          0.9991771390832201,
          0.9945048031566613,
          0.9877240266204375,
          0.978857157541636,
          0.9679109153043354,
          0.9548818380772689,
          0.9397617697432165,
          0.9225429058993216,
          0.9032220649928215,
          0.8818039788378144,
          0.8583035223704024,
          0.8327469213117632,
          0.8051720738364574,
          0.7756281846044679,
          0.7441749312254095,
          0.7108813691469801,
          0.6758247428995185,
          0.6390893233462732,
          0.6007653435447509,
          0.5609480671030449,
          0.5197369952344358,
          0.477235201634189,
          0.4335487757163673,
          0.38878635207869183,
          0.3430587049866825,
          0.2964783894180345,
          0.24915941360577717,
          0.20121693137223434,
          0.152766945511423,
          0.10392601593410825,
          0.05481096824412705,
          0.005538599939338225,
          -0.043774617371690104,
          -0.09301284035782494,
          -0.1420611606668428,
          -0.19080591464789864,
          -0.23913499348064796,
          -0.28693814908876525,
          -0.33410728791374544,
          -0.38053673899971535,
          -0.4261234731814019,
          -0.4707672337723653,
          -0.5143705121142386,
          -0.5568382589096437,
          -0.5980771607188344,
          -0.637994233007953,
          -0.676494406811988,
          -0.7134767711054655,
          -0.7488292884022302,
          -0.7824222929620861,
          -0.8141020621957459,
          -0.8436871681544507,
          -0.8709716003937357,
          -0.8957385572648767,
          -0.9177859146062314,
          -0.936958632823375,
          -0.9531775593057451,
          -0.9664529629955606,
          -0.9768771037154504,
          -0.9845997288498791,
          -0.98979682326854,
          -0.9926426666836405,
          -0.9932905230289701,
          -0.99186247108709,
          -0.988446332355024,
          -0.9830971834235954,
          -0.9758414687291408,
          -0.9666824326846687,
          -0.955606122042115,
          -0.9425875145520732,
          -0.9275964641523822,
          -0.910603193275607,
          -0.8915830757761536,
          -0.8705204840306563,
          -0.8474115398905901,
          -0.8222657058883688,
          -0.7951062583295609,
          -0.7659697726774006,
          -0.734904813723377,
          -0.7019700865067956,
          -0.6672324774505296,
          -0.6307659556623856,
          -0.5926534941948634,
          -0.5529941903940699,
          -0.5119004314340208,
          -0.4693972897083266,
          -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": 1.4671378545248352,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.1529736403599232,
        0.0835590138778368,
        -0.087921125165878
      ],
      "tangent_gradient": [
        -0.15297364035992528,
        0.08355901387783495,
        -0.08792112516587813
      ],
      "reverse_gradient": [
        -0.15297364035992234,
        0.08355901387783704,
        -0.08792112516587824
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.087921125165878,
      "amplitude_gradient_error": 0.00896594231668646,
      "phase_gradient_error": 0.001596844435177741,
      "viscosity_gradient_error": 0.087921125165878,
      "gradient_duality_error": 2.0816681711721685e-15,
      "gradient_reverse_error": 8.604228440844963e-16,
      "reverse_state_adjoint_error": 2.233456475320139e-15,
      "transpose_relative_error": 1.9397027914876736e-16,
      "state_l1_error": 0.0028583681461452452,
      "state_linf_error": 0.006267644573062392,
      "primal_residual_inf": 1.2212453270876722e-15,
      "primal_residual_density_inf": 3.126388037344441e-13,
      "newton_correction_inf": 2.67106766475771e-16,
      "tangent_residual_inf": 5.0133508455729725e-15,
      "adjoint_residual_inf": 2.6662699825763525e-15,
      "jacobian_nonzeros": 1275,
      "psi_0": -1.4302773053108335,
      "psi_N": -0.025337773125630392,
      "exact_nodal_residual_inf": 0.0023553792874035917,
      "exact_nodal_residual_boundary_rows_inf": 0.0023553792874035917,
      "exact_nodal_residual_inner_rows_inf": 0.00012044400602750915,
      "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": -0.127905936186945,
        "adjoint_directional_gradient": -0.12790593619657215,
        "absolute_error": 9.627132424583351e-12,
        "perturbed_primal_residuals_inf": [
          1.5543122344752192e-15,
          1.4432899320127035e-15
        ],
        "axis_central_differences": [
          -0.15297364036603867,
          0.08355901381928987,
          -0.08792118325606778
        ],
        "axis_absolute_errors": [
          6.115469242118365e-12,
          5.854693119200505e-11,
          5.809018978342184e-08
        ]
      },
      "adjoint_l1_reference_error": 0.0037247886991343916,
      "adjoint_linf_reference_error": 0.036314813970076854,
      "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": 0.0037093399199483734,
      "psi_N_boundary_flux_error": 0.0033032216683136703,
      "elapsed_seconds": 0.02585049999470357,
      "cells": 256,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.0023553792874035917,
          "correction_inf": 0.006246897863112855,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 2.098255267146687e-06,
          "correction_inf": 2.0753803138386887e-05,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 1.371330826671624e-11,
          "correction_inf": 2.3464960733288524e-10,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 1.5543122344752192e-15,
          "correction_inf": 2.67106766475771e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 0.11524129674717766,
      "state_linf_observed_order": 0.05155145265421321,
      "gradient_observed_order": 0.6503183061903912,
      "amplitude_gradient_observed_order": -1.1779991329950816,
      "phase_gradient_observed_order": 2.3570148775595188,
      "viscosity_gradient_observed_order": 0.6503183061903912,
      "adjoint_l1_observed_order": 0.5206743411533881,
      "psi_0_observed_order": -0.33424953837404187,
      "psi_N_observed_order": -1.3234984464713075,
      "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,
          0.920039488906274,
          0.929183671888616,
          0.9337937347439744,
          0.9431286368268236,
          0.9525987593867855,
          0.9573775325331668,
          0.9670083022031968,
          0.9718545602868988,
          0.9815943529217124,
          0.9913777286705304,
          0.9962784255510156,
          1.0060830999984876,
          1.0109811680679688,
          1.0207539775292065,
          1.030475977902811,
          1.035310548919198,
          1.0449121394380256,
          1.0496733101795892,
          1.0591018730847177,
          1.0683862013950618,
          1.0729671459435985,
          1.0819925131646912,
          1.0864313729524506,
          1.0951477337630398,
          1.1036310053170124,
          1.1077786223656625,
          1.1158729003926071,
          1.1198145060052358,
          1.1274743140994787,
          1.1348203077396193,
          1.1383698190594524,
          1.1452106936543776,
          1.1484977443239381,
          1.154794711290338,
          1.1607090441673504,
          1.1635180377191308,
          1.168830887536176,
          1.171331435325276,
          1.1760130486651295,
          1.180259258833657,
          1.1822158436410344,
          1.1857901804190987,
          1.1874058583762834,
          1.190289661821849,
          1.1927049228301403,
          1.1937352286515766,
          1.1954386534765908,
          1.1961109948217916,
          1.197095570215212,
          1.1975990570557737,
          1.1976703099076154,
          1.1974522833926766,
          1.197163386749016,
          1.1962272743981086,
          1.1948160734513078,
          1.1939335471987664,
          1.1918176344582616,
          1.190585621426514,
          1.1877773513488405,
          1.1845159188239498,
          1.1827176666912356,
          1.178791387908233,
          1.176665650192097,
          1.1720951250445824,
          1.1671080559542208,
          1.1644618500042476,
          1.1588716527927012,
          1.1559308524638228,
          1.14976624223945,
          1.1432361186399547,
          1.1398386296922711,
          1.1327885437242253,
          1.1291400013893316,
          1.121606435316026,
          1.11377215828113,
          1.109747905707441,
          1.101496878117428,
          1.097274916877792,
          1.0886504471743328,
          1.0798021730938507,
          1.0753005962369175,
          1.0661558421451882,
          1.0615180740856534,
          1.0521255038248571,
          1.0425955387459243,
          1.037786120393103,
          1.028092781215074,
          1.023214666897978,
          1.0134101923554082,
          1.0035610817320895,
          0.998627216078097,
          0.9887557994435965,
          0.9838242417799506,
          0.9739844393092347,
          0.9641957495384841,
          0.9593280773316399,
          0.9496610537653951,
          0.9448676727039331,
          0.9353760285016182,
          0.9260308784306653,
          0.9214205605540422,
          0.9123389318331753,
          0.9078733578643328,
          0.8991068603518287,
          0.8905784850416222,
          0.8864104536373547,
          0.878280136292494,
          0.8743231135363334,
          0.8666381922986047,
          0.8592753802040654,
          0.8557208071047195,
          0.8488769315211697,
          0.8455920910162854,
          0.8393072696791096,
          0.8334156567993273,
          0.8306220421628542,
          0.8253479663284348,
          0.8228707571042971,
          0.8182434578317987,
          0.8140611937019174,
          0.812139926322581,
          0.8086422454004244,
          0.8070675983118305,
          0.8042704090552635,
          0.8019465930440949,
          0.8009633346112632,
          0.7993556550824039,
          0.7987316115882618,
          0.7978435012233733,
          0.7974350542672074,
          0.7974103438298252,
          0.7977186887669345,
          0.7980510662719003,
          0.7990701255227479,
          0.800558172115724,
          0.8014765947822903,
          0.803658867587127,
          0.8049212243707444,
          0.8077842853369943,
          0.8110924564824392,
          0.8129110184834271,
          0.8168717824225782,
          0.8190117074229718,
          0.823604561516891,
          0.8286060194728384,
          0.8312564904338872,
          0.8368494358075257,
          0.8397887311960046,
          0.8459445095703498,
          0.8524576929362404,
          0.8558434005496837,
          0.8628622102211978,
          0.8664905118134847,
          0.873971242949837,
          0.8817286540927269,
          0.8857008316758752,
          0.8938040978713582,
          0.8979198125711166,
          0.9062240373640372,
          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": [
          -1.4302773053108335,
          -0.4715585834747964,
          -0.9861785211690788,
          -1.1379545167279865,
          -1.3232877746498917,
          -1.4149596312469783,
          -1.440635472497277,
          -1.4687125446963414,
          -1.4752804261315389,
          -1.4799021584347256,
          -1.4779908411513099,
          -1.4756800131973988,
          -1.4695506647508811,
          -1.466017203632972,
          -1.4584402200396487,
          -1.4504932795677472,
          -1.4464495663607253,
          -1.4382943336400398,
          -1.4341994949026446,
          -1.425999535270214,
          -1.4178024755927514,
          -1.413708456276896,
          -1.4055325773692644,
          -1.4014512676055875,
          -1.3933022826100894,
          -1.3851710679988076,
          -1.3811117976325642,
          -1.373005017516132,
          -1.3689570807383555,
          -1.3608709237943633,
          -1.3527959644027265,
          -1.3487619704464329,
          -1.3406993952136432,
          -1.3366701416298727,
          -1.3286138886566703,
          -1.320557996818628,
          -1.3165291159706227,
          -1.3084671473093943,
          -1.3044330537348028,
          -1.2963559508543778,
          -1.2882630782727396,
          -1.2842091829196667,
          -1.2760831870478153,
          -1.2720097115808555,
          -1.2638382434567674,
          -1.255629193657275,
          -1.2515087148666113,
          -1.2432321189104323,
          -1.239074525605851,
          -1.2307171477457919,
          -1.2222989287747617,
          -1.2180653754850592,
          -1.209546382613275,
          -1.2052598442997509,
          -1.1966302091312238,
          -1.1879222991697207,
          -1.1835380563306581,
          -1.1747074326626499,
          -1.1702605225554688,
          -1.161302387960975,
          -1.1522572664852075,
          -1.1477016826570556,
          -1.1385237478743853,
          -1.1339011191619202,
          -1.1245878276574737,
          -1.1151827885924024,
          -1.1104454308672993,
          -1.1009000386319487,
          -1.0960915498821764,
          -1.0864017037430544,
          -1.0766127491486108,
          -1.0716802976619224,
          -1.0617376543007206,
          -1.0567266888245648,
          -1.046623405335217,
          -1.0364087153410066,
          -1.0312584400496714,
          -1.0208696202319942,
          -1.0156300830960363,
          -1.0050582152010925,
          -0.9943591703404028,
          -0.9889606477820565,
          -0.9780629677838543,
          -0.9725627559311529,
          -0.9614569637767172,
          -0.9502072172890901,
          -0.944527080227966,
          -0.9330537714670932,
          -0.927259620370825,
          -0.9155539461654914,
          -0.9036887310035663,
          -0.8976952001153118,
          -0.8855842226462342,
          -0.8794659948963686,
          -0.8671022364730812,
          -0.8545665253930229,
          -0.8482334328014068,
          -0.8354354550055394,
          -0.8289701125465483,
          -0.8159057637765029,
          -0.80266222667681,
          -0.7959730016140565,
          -0.7824593651318862,
          -0.775634931690414,
          -0.7618510000841118,
          -0.74788754462694,
          -0.7408388135961876,
          -0.7266082193996702,
          -0.7194267814273818,
          -0.7049328529419511,
          -0.690266039344127,
          -0.6828685452235143,
          -0.6679469379719766,
          -0.6604234500686222,
          -0.6452526213712434,
          -0.6299185125674311,
          -0.6221908428475459,
          -0.6066152478985763,
          -0.5987676064288504,
          -0.5829530436358182,
          -0.5669794880757513,
          -0.5589329463046186,
          -0.5427197094354757,
          -0.5345526668595417,
          -0.5180966984928382,
          -0.5014767410836898,
          -0.4931047425212875,
          -0.47623589399020794,
          -0.4677388613903813,
          -0.4506196353613807,
          -0.4333346383183281,
          -0.42463079608121196,
          -0.40710315103024974,
          -0.39828085063977986,
          -0.3805241447666429,
          -0.36262617858451734,
          -0.35362785955659604,
          -0.33554106425692026,
          -0.32645638541571737,
          -0.30821481706641773,
          -0.2898918707257942,
          -0.2807057376524689,
          -0.2622962749420787,
          -0.25307785879560335,
          -0.23462591370707347,
          -0.21616984600696848,
          -0.20694609652190601,
          -0.18851825198117533,
          -0.1793183517048196,
          -0.16095641055320928,
          -0.142656934061608,
          -0.13353475965650452,
          -0.11535303876031062,
          -0.1062962611515879,
          -0.08825737503464742,
          -0.07032647737722565,
          -0.061404812111829,
          -0.043656703595256634,
          -0.0348340951218189,
          -0.01729935071949803,
          -0.025337773125630392
        ],
        "amplitude_tangent": [
          -0.42577929156507344,
          -0.4020403803424494,
          -0.35647364327630965,
          -0.33355658683017403,
          -0.28712017072917023,
          -0.23996168613908758,
          -0.21614659462336366,
          -0.16811597846626405,
          -0.14392927660949992,
          -0.09528579986805069,
          -0.04638000375291244,
          -0.021865606301001338,
          0.02721211037282808,
          0.051745729483150475,
          0.100728176043007,
          0.14949854901792012,
          0.17376714795609208,
          0.22199733029064536,
          0.24592950981701245,
          0.29335495262563244,
          0.3400984902354237,
          0.36317857502085676,
          0.4086841897688043,
          0.43108153001346433,
          0.4750955788055992,
          0.5179771612222943,
          0.538959369556295,
          0.5799399330825704,
          0.5999120283825011,
          0.6387553137069952,
          0.6760465664094715,
          0.6940792820663596,
          0.7288587951281944,
          0.74558220091701,
          0.7776396426507427,
          0.8077722034092659,
          0.8220906555879391,
          0.8491829202743879,
          0.8619382948149691,
          0.8858246375850427,
          0.9074933812282135,
          0.9174786550875266,
          0.9357207167230233,
          0.9439670734584863,
          0.9586886704674482,
          0.9710264631230476,
          0.9762951788096733,
          0.9850244680860399,
          0.9884834498364636,
          0.9935895939071079,
          0.9962841890773171,
          0.9967301138279846,
          0.9958279255893749,
          0.9944841168391071,
          0.9900235876253728,
          0.9832182293933935,
          0.9789440542590112,
          0.9686697730514522,
          0.9626769600942998,
          0.9489993967746729,
          0.9330937002288269,
          0.9243163765630742,
          0.9051365897501183,
          0.8947442721681221,
          0.8723818394624956,
          0.8479545723401788,
          0.8349821814563653,
          0.8075533816701356,
          0.7931112240394795,
          0.7628092169265145,
          0.7306708622858682,
          0.7139343966801525,
          0.6791721948978887,
          0.6611654700526051,
          0.6239504784605957,
          0.585202997225821,
          0.5652816809356269,
          0.5244003929631299,
          0.5034637631417854,
          0.46065864196086687,
          0.41669374728266373,
          0.39430816798749674,
          0.3487959689962565,
          0.32569596088383207,
          0.2788758469104631,
          0.23132090363578833,
          0.2073028413704217,
          0.1588564747995612,
          0.13445684612699385,
          0.08537703505451001,
          0.03602045857135005,
          0.011275102387245392,
          -0.03827587349769285,
          -0.06305182754483857,
          -0.11253028515161173,
          -0.16181139357215643,
          -0.18634061350533834,
          -0.2351016744961314,
          -0.2593036295815243,
          -0.30727570224141637,
          -0.3545724923143023,
          -0.3779303805865703,
          -0.42399069514316795,
          -0.4466633834449626,
          -0.49121960004930304,
          -0.5346248794687102,
          -0.5558589970743674,
          -0.5973166716826326,
          -0.617510978635254,
          -0.6567579621897636,
          -0.6943872312873467,
          -0.712559934171728,
          -0.7475525939990594,
          -0.7643457584671619,
          -0.7964612025372252,
          -0.8265340855357396,
          -0.8407758685118497,
          -0.8676177061548436,
          -0.8801987484496921,
          -0.9036389671385456,
          -0.9247363012117422,
          -0.9343918029722467,
          -0.9518945930796079,
          -0.959735602810568,
          -0.9735870958699513,
          -0.9849934729458328,
          -0.9897805778603688,
          -0.9975293446680066,
          -1.0004951481186939,
          -1.0046228587032977,
          -1.0063665071025747,
          -1.0063530221954147,
          -1.0045740624299897,
          -1.0028162682098083,
          -0.9975834863416768,
          -0.9900870447599426,
          -0.9854996213820763,
          -0.9746655619135078,
          -0.9684265781258536,
          -0.9543239113903599,
          -0.938081020215497,
          -0.9291670113726884,
          -0.9097748097061273,
          -0.8993054113263016,
          -0.8768433199780034,
          -0.8523836844962464,
          -0.8394182642504147,
          -0.8120455504443003,
          -0.797650887623435,
          -0.7674789732804933,
          -0.7355131299960975,
          -0.7188775433054522,
          -0.6843452021679,
          -0.6664678372071619,
          -0.6295451105245344,
          -0.591151682775019,
          -0.5714433460906894,
          -0.5311134856162762,
          -0.5105543710600452,
          -0.468881888594058,
          -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": 1.4682437461250994,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.15676083302359517,
        0.08779364602436104,
        -0.03344497930143045
      ],
      "tangent_gradient": [
        -0.1567608330235835,
        0.08779364602436766,
        -0.033444979301430325
      ],
      "reverse_gradient": [
        -0.15676083302359523,
        0.08779364602436068,
        -0.033444979301430644
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.03344497930143045,
      "amplitude_gradient_error": 0.012753134980358433,
      "phase_gradient_error": 0.002637787711346498,
      "viscosity_gradient_error": 0.03344497930143045,
      "gradient_duality_error": 1.1657341758564144e-14,
      "gradient_reverse_error": 3.608224830031759e-16,
      "reverse_state_adjoint_error": 4.849419477093164e-15,
      "transpose_relative_error": 1.0097047720747827e-14,
      "state_l1_error": 0.0019458793419143488,
      "state_linf_error": 0.004211800585776859,
      "primal_residual_inf": 2.4424906541753444e-15,
      "primal_residual_density_inf": 1.2505552149377763e-12,
      "newton_correction_inf": 2.0704516965595453e-16,
      "tangent_residual_inf": 1.085730897548709e-14,
      "adjoint_residual_inf": 4.474719206282174e-15,
      "jacobian_nonzeros": 2555,
      "psi_0": -1.429330344090733,
      "psi_N": -0.025271229244269847,
      "exact_nodal_residual_inf": 0.0014872789318046142,
      "exact_nodal_residual_boundary_rows_inf": 0.0014872789318046142,
      "exact_nodal_residual_inner_rows_inf": 3.0118107505749947e-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": -0.1304227391973889,
        "adjoint_directional_gradient": -0.13042273921628686,
        "absolute_error": 1.8897966524988874e-11,
        "perturbed_primal_residuals_inf": [
          2.6645352591003757e-15,
          2.55351295663786e-15
        ],
        "axis_central_differences": [
          -0.15676083304771993,
          0.08779364598643367,
          -0.0334450051875379
        ],
        "axis_absolute_errors": [
          2.4124757747046033e-11,
          3.792736957830556e-11,
          2.5886107452022245e-08
        ]
      },
      "adjoint_l1_reference_error": 0.0030939423857888892,
      "adjoint_linf_reference_error": 0.06345762215607942,
      "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": 0.002762378699847856,
      "psi_N_boundary_flux_error": 0.0032366777869531245,
      "elapsed_seconds": 0.03015070800029207,
      "cells": 512,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.0014872789318046142,
          "correction_inf": 0.004202422701353138,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 7.913199993603293e-07,
          "correction_inf": 9.405502063698655e-06,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 7.384093336781916e-13,
          "correction_inf": 4.784907929883849e-11,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 2.55351295663786e-15,
          "correction_inf": 2.0704516965595453e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 0.5547694858893054,
      "state_linf_observed_order": 0.573486238120138,
      "gradient_observed_order": 1.3944201968136136,
      "amplitude_gradient_observed_order": -0.5083248117053124,
      "phase_gradient_observed_order": -0.7241046894093437,
      "viscosity_gradient_observed_order": 1.3944201968136136,
      "adjoint_l1_observed_order": 0.26771225456209957,
      "psi_0_observed_order": 0.4252513659189573,
      "psi_N_observed_order": 0.029360035765188225,
      "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,
          0.9218426854024847,
          0.9286864300351895,
          0.9356244463051138,
          0.9426474341295473,
          0.9521272941464142,
          0.959311719053865,
          0.9665493043825645,
          0.9738303129255717,
          0.9811449409573323,
          0.9909330323783914,
          0.998287705553983,
          1.0056430087989403,
          1.0129890038883544,
          1.020315757575746,
          1.0300376993840983,
          1.0372810572177518,
          1.0444722738083414,
          1.0516015949975506,
          1.0586593442147012,
          1.0679417895927081,
          1.0747954430991105,
          1.0815460022178398,
          1.088184281162552,
          1.0947012423981615,
          1.1031864902992536,
          1.1093861591156635,
          1.1154356185974237,
          1.1213266188554636,
          1.127051124006724,
          1.1344113396827866,
          1.1397173934893354,
          1.1448318572512761,
          1.1497477516229644,
          1.154458368954934,
          1.1604088066962455,
          1.1646159565104144,
          1.1685975532364339,
          1.1723481723152558,
          1.175862707069584,
          1.1801732941186058,
          1.183118943948511,
          1.1858138702395262,
          1.1882544189722473,
          1.190437285578363,
          1.1929418864305634,
          1.1945126363939012,
          1.1958172615447218,
          1.1968540119728122,
          1.1976215026602484,
          1.1982242666739387,
          1.1983601555979873,
          1.198224814031637,
          1.1978184446140925,
          1.19714161504564,
          1.1958201215817565,
          1.1945164647285016,
          1.1929468543384536,
          1.19111341742561,
          1.1890186333097246,
          1.1858239853172619,
          1.183130983818693,
          1.1801873943792254,
          1.176997176141822,
          1.1735646169054355,
          1.1686189116122885,
          1.1646393685945753,
          1.160434076789979,
          1.1560086793598308,
          1.151369114383189,
          1.1448606788957645,
          1.1397460824058745,
          1.134439143816862,
          1.1289469887656567,
          1.1232769941314493,
          1.1154535639835066,
          1.109398639422169,
          1.1031921579771717,
          1.0968424740091423,
          1.0903581400161997,
          1.081518037031589,
          1.074753810072295,
          1.0678847302504997,
          1.060920079107193,
          1.053869275092378,
          1.0443506981849018,
          1.0371361750980141,
          1.0298677241116982,
          1.022555212975567,
          1.0152085788543934,
          1.0053772654466773,
          0.9979899463778166,
          0.9906019590928671,
          0.9832233873569192,
          0.9758643124888015,
          0.9660999334277394,
          0.9588254389324065,
          0.9516038499206111,
          0.9444450763436967,
          0.9373589511213153,
          0.9280406153651649,
          0.9211617033176179,
          0.9143874777784661,
          0.9077272741112187,
          0.9011902751172051,
          0.8926814859727119,
          0.8864667134505014,
          0.8804044735659394,
          0.8745031272655683,
          0.8687708096724622,
          0.8614042649476811,
          0.8560966187379784,
          0.8509833225385497,
          0.8460713869400982,
          0.8413675317755583,
          0.8354304546014132,
          0.8312365418881573,
          0.8272708781623944,
          0.8235388096266896,
          0.8200453433147062,
          0.8157665531295296,
          0.8128473438291669,
          0.81018089827373,
          0.8077706877683282,
          0.8056198187174697,
          0.8031600948696457,
          0.8016243715538782,
          0.8003556862393919,
          0.799355548043741,
          0.798625097648105,
          0.798071962490095,
          0.7979731607688342,
          0.7981452085181281,
          0.7985876707881947,
          0.7992997560540871,
          0.8006665874404398,
          0.8020027367775707,
          0.8036033389133546,
          0.8054660974458646,
          0.8075883789304183,
          0.81081661540711,
          0.8135323468053419,
          0.8164964418530218,
          0.8197048545713755,
          0.8231532240716848,
          0.8281161967145835,
          0.8321057647462062,
          0.8363185228670438,
          0.8407487791506023,
          0.8453905335660582,
          0.8518975719526536,
          0.8570076791963384,
          0.8623068808157361,
          0.8677875943895329,
          0.8734416944843483,
          0.8812347915849639,
          0.8872572960459308,
          0.8934190006958342,
          0.899705401178593,
          0.9060979538409888,
          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": [
          -1.429330344090733,
          -0.6005240099677549,
          -0.9553418044543698,
          -1.1735190963792892,
          -1.3061735897197797,
          -1.403877245285465,
          -1.442213228589683,
          -1.4631556479848131,
          -1.4734130138422352,
          -1.4771361240385208,
          -1.4762051684594655,
          -1.4729752002906946,
          -1.4685221443829686,
          -1.4633391374644935,
          -1.4577243149396528,
          -1.4498653064632416,
          -1.4438206477904247,
          -1.4377099800941444,
          -1.431565055853259,
          -1.4254044390884293,
          -1.41718364295126,
          -1.4110202000935756,
          -1.4048616701164496,
          -1.3987092407103765,
          -1.3925632679028896,
          -1.3843783831395247,
          -1.3782463969089784,
          -1.3721193776199336,
          -1.3659965202670015,
          -1.3598769415660314,
          -1.351720968093888,
          -1.3456052952135826,
          -1.339489588840263,
          -1.333372772811657,
          -1.3272537391939285,
          -1.3190896075815113,
          -1.3129609265168736,
          -1.3068261280675382,
          -1.3006839856348151,
          -1.2945332486914496,
          -1.286316693106942,
          -1.2801409139648234,
          -1.2739522149795819,
          -1.2677492563747808,
          -1.2615306812176537,
          -1.2532125804319048,
          -1.246952203089798,
          -1.2406715788417877,
          -1.234369291225968,
          -1.2280439132190302,
          -1.2195716732945294,
          -1.2131868163171549,
          -1.2067740482513762,
          -1.2003319066318958,
          -1.193858922435504,
          -1.185177748715592,
          -1.1786270506063232,
          -1.1720405682658295,
          -1.1654168055152507,
          -1.1587542593650884,
          -1.1498079233069622,
          -1.1430489956518592,
          -1.1362462187932973,
          -1.1293980538279074,
          -1.122502951809807,
          -1.1132337719517693,
          -1.106223065209528,
          -1.0991601776692264,
          -1.0920435100460038,
          -1.0848714503626258,
          -1.0752197285449365,
          -1.0679120799537007,
          -1.0605435739073545,
          -1.0531125440604747,
          -1.0456173126866382,
          -1.0355208824594004,
          -1.0278692659210078,
          -1.020147785783791,
          -1.0123547275824814,
          -1.0044883724722833,
          -0.9938829065313873,
          -0.9858388316266954,
          -0.9777157258349358,
          -0.9695118770472775,
          -0.9612255818291697,
          -0.9500460164621526,
          -0.94156079416259,
          -0.9329875513436261,
          -0.924324660602852,
          -0.9155705220456134,
          -0.9037536907642133,
          -0.8947806045577992,
          -0.8857111904059247,
          -0.8765440173590597,
          -0.8672777057893772,
          -0.8547661295606888,
          -0.8452634547066019,
          -0.8356574767958412,
          -0.8259470963022126,
          -0.8161312920279874,
          -0.8028779524416444,
          -0.7928126668423627,
          -0.7826391856228957,
          -0.7723568865665623,
          -0.7619652529470606,
          -0.7479389794912117,
          -0.7372908507756695,
          -0.7265324877346997,
          -0.7156638845292055,
          -0.7046851646995228,
          -0.6898760426578986,
          -0.6786416202283301,
          -0.6672984763291302,
          -0.6558473380750028,
          -0.6442890807662661,
          -0.628713237669806,
          -0.6169092943548778,
          -0.6050022571928407,
          -0.5929936763242278,
          -0.580885264352986,
          -0.5645886908318222,
          -0.5522549283030364,
          -0.5398282431185214,
          -0.527311074113667,
          -0.5147060311440148,
          -0.49776744607044165,
          -0.4849684753360403,
          -0.4720915649143414,
          -0.45914006091305115,
          -0.44611747357980913,
          -0.428649815279523,
          -0.41547590449289634,
          -0.40224373079832026,
          -0.3889574482671697,
          -0.3756213361595105,
          -0.35776994746868623,
          -0.3443348193581263,
          -0.3308648669028928,
          -0.3173647566500145,
          -0.30383920140306725,
          -0.28577374205698997,
          -0.27220726356885994,
          -0.25863114281409083,
          -0.2450500735058731,
          -0.23146869262076206,
          -0.2133675699737869,
          -0.19980303304603275,
          -0.18625298926992087,
          -0.17272161721825097,
          -0.15921294657987506,
          -0.1412433594880554,
          -0.1278024005010008,
          -0.11439634947496258,
          -0.10102847037289499,
          -0.08770183893310088,
          -0.07000213533165073,
          -0.05678270940092695,
          -0.04361356274178279,
          -0.030497157783945076,
          -0.01743596552637028,
          -0.025271229244269847
        ],
        "amplitude_tangent": [
          -0.42577929156507255,
          -0.39108625657273544,
          -0.3569366394628453,
          -0.3223099207130802,
          -0.287252012296034,
          -0.23991805434871288,
          -0.20403637343129707,
          -0.1678811712002338,
          -0.13150086438922032,
          -0.09494426697574523,
          -0.046012885054968616,
          -0.009236495803245856,
          0.02755148008702246,
          0.06430130151721443,
          0.10096319965380088,
          0.14962302942348382,
          0.1858865993872859,
          0.2218970539142464,
          0.25760531772328704,
          0.2929626629344415,
          0.33947648536257835,
          0.3738279968817149,
          0.40766956640725305,
          0.4409547737104376,
          0.473637913969793,
          0.516201363959892,
          0.5473064634032373,
          0.5776631757185067,
          0.6072296683489413,
          0.6359651764059322,
          0.6729182121446475,
          0.6995626954725057,
          0.7252488262883448,
          0.7499411817949218,
          0.7736057287542508,
          0.8035035329014509,
          0.8246457196957195,
          0.8446573749332761,
          0.8635110876842484,
          0.8811810979797947,
          0.902858442089964,
          0.9176758604769479,
          0.9312361048191049,
          0.9435209691723031,
          0.9545140599717413,
          0.9671371809692549,
          0.9750626787903798,
          0.9816550311139031,
          0.9869058377667742,
          0.9908085524027375,
          0.9939072873204816,
          0.994649370487882,
          0.9940348503934477,
          0.9920651257903325,
          0.9887433941916564,
          0.9822201571761147,
          0.9757661513503763,
          0.9679835600313118,
          0.9588831637700708,
          0.9484774391442518,
          0.9325973260958343,
          0.919203720806081,
          0.9045583460686645,
          0.8886807742692975,
          0.8715921539939621,
          0.8469629295125912,
          0.8271394439144788,
          0.8061864695267406,
          0.7841316916049216,
          0.7610042297871622,
          0.7285519491065925,
          0.7030426251791781,
          0.6765676353547773,
          0.6491619382916727,
          0.6208617432840722,
          0.5818015538614205,
          0.5515617311821076,
          0.520556610382681,
          0.48882733187169686,
          0.4564160512643668,
          0.412214781651738,
          0.3783814300047125,
          0.3440132799391461,
          0.30915629537585665,
          0.2738571752598157,
          0.22618589327598676,
          0.19004043569688508,
          0.15361308418526035,
          0.11695306040603785,
          0.08011001066256825,
          0.030787719645533538,
          -0.006287391902133377,
          -0.04337775865043023,
          -0.08043260402583734,
          -0.11740105875095111,
          -0.16646998030277985,
          -0.2030389997627746,
          -0.2393522371969033,
          -0.2753591873857613,
          -0.3110096135380188,
          -0.3579027411350079,
          -0.3925279688790965,
          -0.42663210382771083,
          -0.4601669389275298,
          -0.4930849477300408,
          -0.5359354171447002,
          -0.567233798541888,
          -0.5977629459397444,
          -0.6274792821521292,
          -0.6563403812668459,
          -0.6934204878522239,
          -0.7201281964981481,
          -0.7458487348123164,
          -0.770545712744735,
          -0.7941843638678636,
          -0.8239993854811078,
          -0.845043101755408,
          -0.8649252929494492,
          -0.8836190549811227,
          -0.9010994475993008,
          -0.9224798183779618,
          -0.9370433177870381,
          -0.9503249033044717,
          -0.9623084499735862,
          -0.9729798821623852,
          -0.985146871432331,
          -0.9927133549056876,
          -0.9989353666080285,
          -1.0038074523937106,
          -1.0073260522926906,
          -1.0099094008499303,
          -1.0102663257431765,
          -1.0092709952106413,
          -1.0069275280505965,
          -1.0032416932653585,
          -0.996252097402848,
          -0.9894654697774296,
          -0.9813671112015047,
          -0.9719695029183768,
          -0.9612865949746077,
          -0.9450701812164098,
          -0.9314505867345936,
          -0.9166025503661108,
          -0.9005461835823153,
          -0.8833029923181351,
          -0.8585056748630302,
          -0.8385846769830743,
          -0.8175586012521875,
          -0.7954550183518433,
          -0.7723029437527905,
          -0.7398554795824206,
          -0.7143783080160294,
          -0.6879607040295307,
          -0.6606390967634606,
          -0.6324523644772438,
          -0.5935975192672817,
          -0.5635632309153943,
          -0.5328239688733458,
          -0.501445624410275,
          -0.469511023685062,
          -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": 1.46951333839859,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.15246392146061366,
        0.08752306929430427,
        -0.010594415306634675
      ],
      "tangent_gradient": [
        -0.15246392146060997,
        0.08752306929429478,
        -0.01059441530663473
      ],
      "reverse_gradient": [
        -0.15246392146061372,
        0.0875230692943032,
        -0.010594415306635296
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.010594415306634675,
      "amplitude_gradient_error": 0.008456223417376924,
      "phase_gradient_error": 0.0023672109812897246,
      "viscosity_gradient_error": 0.010594415306634675,
      "gradient_duality_error": 9.492406860545088e-15,
      "gradient_reverse_error": 1.0685896612017132e-15,
      "reverse_state_adjoint_error": 9.36208575941233e-15,
      "transpose_relative_error": 2.705904915977969e-15,
      "state_l1_error": 0.0010899910562164974,
      "state_linf_error": 0.0023286198983399897,
      "primal_residual_inf": 4.3298697960381105e-15,
      "primal_residual_density_inf": 4.433786671143025e-12,
      "newton_correction_inf": 1.9797057706258433e-16,
      "tangent_residual_inf": 2.823002248630857e-14,
      "adjoint_residual_inf": 1.0756152912794192e-14,
      "jacobian_nonzeros": 5115,
      "psi_0": -1.4281359022727798,
      "psi_N": -0.024021474869831732,
      "exact_nodal_residual_inf": 0.0007938624389249305,
      "exact_nodal_residual_boundary_rows_inf": 0.0007938624389249305,
      "exact_nodal_residual_inner_rows_inf": 7.529767790726005e-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": -0.12620700066134916,
        "adjoint_directional_gradient": -0.12620700067232238,
        "absolute_error": 1.0973222330790122e-11,
        "perturbed_primal_residuals_inf": [
          4.218847493575595e-15,
          4.6629367034256575e-15
        ],
        "axis_central_differences": [
          -0.1524639214656176,
          0.08752306923653917,
          -0.010594423871523873
        ],
        "axis_absolute_errors": [
          5.003941705439274e-12,
          5.7765098260276204e-11,
          8.564889197176795e-09
        ]
      },
      "adjoint_l1_reference_error": 0.0018444885995911545,
      "adjoint_linf_reference_error": 0.04468916564322534,
      "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": 0.001567936881894605,
      "psi_N_boundary_flux_error": 0.00198692341251501,
      "elapsed_seconds": 0.03397304200188955,
      "cells": 1024,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.0007938624389249305,
          "correction_inf": 0.002325718599535903,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 4.583709595218366e-08,
          "correction_inf": 2.912005269469316e-06,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 3.3084646133829665e-14,
          "correction_inf": 4.585274729117071e-12,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 4.773959005888173e-15,
          "correction_inf": 1.9797057706258433e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 0.8361059585421408,
      "state_linf_observed_order": 0.8549619643348042,
      "gradient_observed_order": 1.658485683145529,
      "amplitude_gradient_observed_order": 0.5927665354948654,
      "phase_gradient_observed_order": 0.156140167239605,
      "viscosity_gradient_observed_order": 1.658485683145529,
      "adjoint_l1_observed_order": 0.7462254596664255,
      "psi_0_observed_order": 0.8170436308212665,
      "psi_N_observed_order": 0.7039774877398935,
      "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,
          0.9216497141875782,
          0.9284873654733306,
          0.9365844666988575,
          0.943616853131062,
          0.9519153282547642,
          0.9590979218560871,
          0.9663345450288374,
          0.974832521282127,
          0.9821526093512426,
          0.9907209540352121,
          0.9980781104670634,
          1.005436644810804,
          1.0140100742519387,
          1.0213374864826876,
          1.0298474375272417,
          1.0370972304593564,
          1.0442956358843944,
          1.0526158360534796,
          1.0596695925434145,
          1.0677947469497657,
          1.0746590420777202,
          1.081421096476857,
          1.0891687256880045,
          1.0956780314472825,
          1.10310639371059,
          1.1093215533386978,
          1.115387494476745,
          1.1222648675921998,
          1.1279795659318284,
          1.134425602233256,
          1.1397526790824053,
          1.1448892550717076,
          1.1506318684563785,
          1.1553321311848337,
          1.1605478351512735,
          1.1647818363037121,
          1.1687913513669808,
          1.173178143059496,
          1.1766829990356225,
          1.1804675142280059,
          1.1834453546767112,
          1.1861733389536637,
          1.1890352635246617,
          1.1912096166232993,
          1.1934170229550214,
          1.1950238450323465,
          1.1963650372992407,
          1.1975916091035652,
          1.198351463717562,
          1.1988964171280945,
          1.1990700256692481,
          1.1989724342121468,
          1.1985159851361051,
          1.1978316791237111,
          1.1966926919414353,
          1.195425941139498,
          1.1938928356735152,
          1.191770337286433,
          1.1896676722082535,
          1.1868879272090511,
          1.184228985779885,
          1.1813187637755858,
          1.177611168671064,
          1.1741704161341684,
          1.1698561096426006,
          1.1659066171050667,
          1.1617305724332447,
          1.1565797258908712,
          1.1519325692819014,
          1.146248869942131,
          1.1411600727807336,
          1.1358781684334698,
          1.1294814250436345,
          1.1238059653072174,
          1.116970753615682,
          1.1109377753317353,
          1.1047525854587525,
          1.0973553373266722,
          1.0908693514574963,
          1.0831449733250387,
          1.0763994293244108,
          1.069548471442397,
          1.0614348578460087,
          1.0543875515995116,
          1.046070879221482,
          1.0388720974900174,
          1.0316188243506694,
          1.0231009476412751,
          1.0157634894014052,
          1.007174633715751,
          0.9997997841602073,
          0.9924235449867358,
          0.9838295622605655,
          0.9764847214753855,
          0.9679547809025993,
          0.9606882491335695,
          0.9534735613577074,
          0.9451350564548235,
          0.938066298936862,
          0.929924561862103,
          0.9230469308582202,
          0.9162724311560698,
          0.90851150436887,
          0.9019919258543847,
          0.8945529799904605,
          0.8883300156295018,
          0.8822574938198525,
          0.8753740504837564,
          0.8696555704118762,
          0.8632068231971264,
          0.8578789064742943,
          0.8527428753116257,
          0.847002654919622,
          0.8423059458426885,
          0.8370961230251853,
          0.8328686250238192,
          0.8288669300245763,
          0.82449087230814,
          0.8209965411559934,
          0.8172257684487948,
          0.814260885710751,
          0.8115468686662961,
          0.8087024063188984,
          0.8065439205457727,
          0.8043559436617607,
          0.8027664483705684,
          0.8014430949024094,
          0.80023783955561,
          0.7994965636569457,
          0.7989734884581721,
          0.7988186792761229,
          0.7989349958521393,
          0.799413050588744,
          0.8001155466119201,
          0.8012752245343236,
          0.8025591398922826,
          0.8041087816615843,
          0.8062496567278341,
          0.8083671905169533,
          0.8111631411610317,
          0.8138349119765862,
          0.8167569142763911,
          0.8204768486974116,
          0.8239269146133231,
          0.8282505495961743,
          0.8322066759775256,
          0.8363880615055519,
          0.8415434642615718,
          0.846193056405595,
          0.8518778341062961,
          0.8569659905367523,
          0.8622457332466126,
          0.8686378705946204,
          0.8743073609047899,
          0.8811327460821406,
          0.887154135049067,
          0.8933236925178608,
          0.9006951307731831,
          0.9071489082422416,
          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": [
          -1.4281359022727798,
          -0.6098846069709566,
          -0.9739430403370113,
          -1.2191196850414545,
          -1.3378142597811102,
          -1.4149178761435028,
          -1.4500242368483842,
          -1.4684312797151935,
          -1.477547958272271,
          -1.4792101797083832,
          -1.4771233709279588,
          -1.4733527015862211,
          -1.4685429646698203,
          -1.4621858374464856,
          -1.4563791819361338,
          -1.4493824222366745,
          -1.4432831834039446,
          -1.4371361575924164,
          -1.4299364698565533,
          -1.4237565551724585,
          -1.416546495294163,
          -1.4103704524938443,
          -1.404199930070771,
          -1.3970087785641128,
          -1.3908516171496854,
          -1.3836755522340958,
          -1.3775302287147275,
          -1.371389320613566,
          -1.3642294510455792,
          -1.358095322240004,
          -1.350940960230264,
          -1.3448093937619894,
          -1.3386774870227727,
          -1.331521826411164,
          -1.3253857066317996,
          -1.3182222673557908,
          -1.312076964943834,
          -1.305925681408238,
          -1.2987401131923766,
          -1.2925719588811735,
          -1.2853635132448114,
          -1.279172960461708,
          -1.2729701489272955,
          -1.2657163861325675,
          -1.259482734091835,
          -1.2521895100967129,
          -1.2459190051276998,
          -1.239629411937888,
          -1.232265641804686,
          -1.2259300771497332,
          -1.2185089306104824,
          -1.2121209346432453,
          -1.2057065119651218,
          -1.1981877085441652,
          -1.1917110964846938,
          -1.184115743661672,
          -1.177570051195747,
          -1.1709901034015864,
          -1.1632681717459539,
          -1.1566087615462042,
          -1.1487898814760438,
          -1.142043695089714,
          -1.1352549447209521,
          -1.1272787908435318,
          -1.120392273459369,
          -1.1122975771891337,
          -1.1053055725900047,
          -1.0982622345279698,
          -1.0899778685488837,
          -1.0828174838295923,
          -1.074391867237639,
          -1.0671063529899911,
          -1.059760325461476,
          -1.0511111302221923,
          -1.0436279419303505,
          -1.0348138658767074,
          -1.0271851660022104,
          -1.0194864712136544,
          -1.0104137970337648,
          -1.002557278239939,
          -0.9932955478312813,
          -0.9852727590274842,
          -0.9771703891074789,
          -0.9676146609423356,
          -0.9593337530611961,
          -0.9495648902071401,
          -0.9410971827883892,
          -0.9325405220608585,
          -0.9224430602030818,
          -0.913687878663622,
          -0.9033542892896125,
          -0.8943929229840407,
          -0.8853339152264842,
          -0.8746396615593419,
          -0.8653640070460001,
          -0.8544131196465772,
          -0.8449143162354723,
          -0.8353105081783847,
          -0.8239717947695137,
          -0.8141365706772967,
          -0.8025250408013,
          -0.7924537720913089,
          -0.7822722678308298,
          -0.7702536342489541,
          -0.7598311430708012,
          -0.7475300491773981,
          -0.7368646359938672,
          -0.7260868171842756,
          -0.7133706511681559,
          -0.7023495248410795,
          -0.6893502048410336,
          -0.6780873674239499,
          -0.6667139622468834,
          -0.6533064014849396,
          -0.6416966165673427,
          -0.6280164239032341,
          -0.6161760955759288,
          -0.6042318435243456,
          -0.5901679789537517,
          -0.5780050662664928,
          -0.5636919310718305,
          -0.5513208191219141,
          -0.5388576643596283,
          -0.5242047431099327,
          -0.5115520355165999,
          -0.49668644661775024,
          -0.4838591350449745,
          -0.4709567373925937,
          -0.45581396217451325,
          -0.44276170159315464,
          -0.42745478252231667,
          -0.4142712989833811,
          -0.4010338572616179,
          -0.38552772352689546,
          -0.37218823720918515,
          -0.35657515560074887,
          -0.3431545075181891,
          -0.3297035616441414,
          -0.3139785665016747,
          -0.30047757605906644,
          -0.2847066152140493,
          -0.2711768040935876,
          -0.2576407398271132,
          -0.24184658070233891,
          -0.22831183407027103,
          -0.21253077727974187,
          -0.1990169190540355,
          -0.1855189850464028,
          -0.16979656517372557,
          -0.15634592934786168,
          -0.1406883931108697,
          -0.12730129386724012,
          -0.1139485314187739,
          -0.09841759459113159,
          -0.08514900955308033,
          -0.06972345764202202,
          -0.05655089024709189,
          -0.04342609918087639,
          -0.028176777057280923,
          -0.015161830374700844,
          -0.024021474869831732
        ],
        "amplitude_tangent": [
          -0.42577929156507105,
          -0.3917876631531759,
          -0.35761057008933766,
          -0.3171380675321937,
          -0.28198696802327067,
          -0.24050652585384563,
          -0.20460292756755144,
          -0.16842817309755062,
          -0.12594652725789054,
          -0.08935165623435208,
          -0.046514492259695256,
          -0.009730818072883892,
          0.02706151432473345,
          0.06993060890973482,
          0.10657141827779171,
          0.1491280315442821,
          0.18538503210523802,
          0.22138709436202678,
          0.26300231736844726,
          0.29828541813681947,
          0.3389303238915543,
          0.37327022350255445,
          0.4071007217015496,
          0.44586464585660773,
          0.47843504636247225,
          0.5156066549260352,
          0.5467095528673208,
          0.5770676913340764,
          0.611489273432502,
          0.6400937235079024,
          0.6723612715075018,
          0.6990296288632428,
          0.7247462387331901,
          0.753499470094003,
          0.7770357865422999,
          0.8031556713953275,
          0.8243614730518961,
          0.8444450585427211,
          0.8664211799993256,
          0.8839816320776087,
          0.9029463350094907,
          0.9178714976992546,
          0.9315471693655148,
          0.9458981494185903,
          0.9568049942419381,
          0.9678824423458029,
          0.9759506993053261,
          0.9826902974689752,
          0.9888616927328452,
          0.9926933391525551,
          0.9954550447905233,
          0.9963539857674548,
          0.9958961731311555,
          0.9936480792073793,
          0.990254890900121,
          0.9845918563315572,
          0.9782843796352066,
          0.9706440757289235,
          0.9600595833653625,
          0.94956894435272,
          0.9356950347651484,
          0.9224200757950186,
          0.9078872031665347,
          0.8893684513898237,
          0.872179274869135,
          0.8506223815520301,
          0.8308852810315145,
          0.8100132600850906,
          0.7842656802823179,
          0.7610329347539625,
          0.7326146652632347,
          0.7071678600860835,
          0.6807525777383052,
          0.648758222671937,
          0.6203682789355696,
          0.5861731517266467,
          0.5559880585192043,
          0.525038209424304,
          0.4880192513040486,
          0.45555701005076943,
          0.41689230925557275,
          0.38312342263080207,
          0.3488232744379482,
          0.30819693644487584,
          0.2729058525318708,
          0.23125348206908136,
          0.19519586608991182,
          0.1588616538125887,
          0.11618801146273189,
          0.07942426871468347,
          0.03638608977648733,
          -0.0005724520852226591,
          -0.037541210140965196,
          -0.08061704774411921,
          -0.11743492101261359,
          -0.16019677590130563,
          -0.19662758812551961,
          -0.23280060738526018,
          -0.2746105107960573,
          -0.3100553887515124,
          -0.3508818575737428,
          -0.3853702266110329,
          -0.41934166986264804,
          -0.45825937849298803,
          -0.49095151041625534,
          -0.528252244976128,
          -0.5594538945228823,
          -0.5898990137112515,
          -0.6244063098694926,
          -0.6530700296334381,
          -0.685389418903051,
          -0.7120868691133189,
          -0.7378180329423142,
          -0.7665695241096911,
          -0.790088124154831,
          -0.8161683465074582,
          -0.8373239509686851,
          -0.8573425777311413,
          -0.8792246603736833,
          -0.8966893385268376,
          -0.9155253578740769,
          -0.9303264347326262,
          -0.9438660889903547,
          -0.9580444401353767,
          -0.9687924449472203,
          -0.9796733357290124,
          -0.9875647328095967,
          -0.9941209538263276,
          -1.0000717775737955,
          -1.0037100925752434,
          -1.006243029002141,
          -1.0069445720740662,
          -1.0062894815854169,
          -1.0038130371387501,
          -1.0002270536045328,
          -0.9943441558531796,
          -0.9878538432214514,
          -0.98003700606232,
          -0.9692558431560232,
          -0.9586056353411446,
          -0.9445572421931406,
          -0.9311435963261243,
          -0.9164827764511728,
          -0.8978291026105332,
          -0.8805371497424068,
          -0.8588759536208109,
          -0.8390632151194031,
          -0.818128553751756,
          -0.7923246173422449,
          -0.7690581164207718,
          -0.7406176972528364,
          -0.7151669289287299,
          -0.6887618907553649,
          -0.6567981593608084,
          -0.6284515059691971,
          -0.594328972661256,
          -0.5642281146550691,
          -0.5333875611590805,
          -0.49653796643013826,
          -0.46427127687950204,
          -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": 1.4703143649165882,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.14860409032424274,
        0.08656648698801828,
        -0.003183718923936525
      ],
      "tangent_gradient": [
        -0.14860409032424673,
        0.08656648698800855,
        -0.0031837189239366597
      ],
      "reverse_gradient": [
        -0.14860409032424515,
        0.08656648698801916,
        -0.0031837189239365404
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.004596392281006001,
      "amplitude_gradient_error": 0.004596392281006001,
      "phase_gradient_error": 0.0014106286750037306,
      "viscosity_gradient_error": 0.003183718923936525,
      "gradient_duality_error": 9.728329253277934e-15,
      "gradient_reverse_error": 2.4147350785597155e-15,
      "reverse_state_adjoint_error": 2.052915129557853e-14,
      "transpose_relative_error": 6.799057245342786e-14,
      "state_l1_error": 0.0005677939199036989,
      "state_linf_error": 0.001203808893706193,
      "primal_residual_inf": 8.548717289613705e-15,
      "primal_residual_density_inf": 1.750777300912887e-11,
      "newton_correction_inf": 1.2830857498535395e-16,
      "tangent_residual_inf": 9.118823317971758e-14,
      "adjoint_residual_inf": 1.852077519126638e-14,
      "jacobian_nonzeros": 10235,
      "psi_0": -1.427381084189035,
      "psi_N": -0.023089057283112304,
      "exact_nodal_residual_inf": 0.00040319060406396323,
      "exact_nodal_residual_boundary_rows_inf": 0.00040319060406396323,
      "exact_nodal_residual_inner_rows_inf": 1.882459865876207e-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": -0.12263414419511064,
        "adjoint_directional_gradient": -0.12263414422783725,
        "absolute_error": 3.272661308617586e-11,
        "perturbed_primal_residuals_inf": [
          8.43769498715119e-15,
          9.103828801926284e-15
        ],
        "axis_central_differences": [
          -0.14860409032202426,
          0.08656648692317857,
          -0.0031837213976260155
        ],
        "axis_absolute_errors": [
          2.2184754033816034e-12,
          6.483970305115605e-11,
          2.473689490658376e-09
        ]
      },
      "adjoint_l1_reference_error": 0.0009807016187334643,
      "adjoint_linf_reference_error": 0.025090779041161082,
      "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": 0.0008131187981499366,
      "psi_N_boundary_flux_error": 0.001054505825795582,
      "elapsed_seconds": 0.04790170799969928,
      "cells": 2048,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.00040319060406396323,
          "correction_inf": 0.0012030322076446794,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 1.820396389184964e-09,
          "correction_inf": 7.800646877270028e-07,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 9.43689570931383e-15,
          "correction_inf": 3.2915078462775615e-13,
          "step": 1.0
        },
        {
          "iteration": 3,
          "residual_inf": 8.548717289613705e-15,
          "correction_inf": 1.2830857498535395e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 0.9408769917242674,
      "state_linf_observed_order": 0.9518687865326879,
      "gradient_observed_order": 1.2047301335005565,
      "amplitude_gradient_observed_order": 0.879511563256477,
      "phase_gradient_observed_order": 0.7468500222333654,
      "viscosity_gradient_observed_order": 1.734519091625608,
      "adjoint_l1_observed_order": 0.9113347078209041,
      "psi_0_observed_order": 0.9473294309838096,
      "psi_N_observed_order": 0.9139691983077065,
      "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,
          0.9215896066726575,
          0.928995241607576,
          0.9365128027170675,
          0.944130358228463,
          0.9518358172325864,
          0.959015994006146,
          0.9668560163975417,
          0.9747478675906815,
          0.9826790185391349,
          0.9906368768930747,
          0.9979953699777963,
          1.0059690535518868,
          1.0139324609625986,
          1.0218729445319938,
          1.029777891846867,
          1.0370323644503312,
          1.0448337438074882,
          1.0525631099869124,
          1.0602081813116635,
          1.0677568088449108,
          1.0746287938589454,
          1.081958381230609,
          1.0891569543383584,
          1.0962130692271508,
          1.1031155072450174,
          1.1093410928635947,
          1.1159173753368463,
          1.122308646172955,
          1.128504739441921,
          1.1344957985334698,
          1.1398357752698498,
          1.145406041945109,
          1.1507443819143994,
          1.1558422988829935,
          1.160691678054941,
          1.164940748984844,
          1.1692908232517933,
          1.1733709459772694,
          1.1771746181023979,
          1.180695779593657,
          1.1836904730823579,
          1.1866529690842968,
          1.1893178456278533,
          1.1916808517342967,
          1.1937382160953585,
          1.195363192419358,
          1.1968239740550823,
          1.1979708937552527,
          1.1988021130206472,
          1.1993162952259993,
          1.1995088026803762,
          1.1994113952049823,
          1.1989959379950854,
          1.1982630767073386,
          1.1972139617969721,
          1.1959662711653678,
          1.1943140563762953,
          1.1923518248239255,
          1.1900826826132689,
          1.1875102242028777,
          1.1848699496845165,
          1.1817260623332335,
          1.1782921090184038,
          1.1745735382144553,
          1.170576251583549,
          1.1666445480879646,
          1.1621294799167334,
          1.1573554545101132,
          1.1523300548563074,
          1.147061264597438,
          1.1419889724031096,
          1.1362759774841078,
          1.1303451044402157,
          1.124205781088395,
          1.117867767991827,
          1.1118496529385347,
          1.1051581303877454,
          1.0982982091796456,
          1.0912808013900182,
          1.0841170711088066,
          1.0773843788229744,
          1.0699714833636498,
          1.062446175621474,
          1.0548204339576184,
          1.0471063981928381,
          1.039918001789416,
          1.032068796413094,
          1.0241675256899887,
          1.01622677438439,
          1.0082591916889505,
          1.0008916621404202,
          0.9929081785172399,
          0.984935017213174,
          0.9769848845965112,
          0.9690704515502737,
          0.9618074179720607,
          0.9539970291262091,
          0.9462589835806463,
          0.9386056176610733,
          0.9310491331864217,
          0.9241703280161304,
          0.9168338659664206,
          0.9096289971176804,
          0.9025672081184932,
          0.8956597568864524,
          0.889430161056338,
          0.8828502326145234,
          0.876456068802685,
          0.8702578583338343,
          0.8642654757124026,
          0.8589249928338702,
          0.8533549602345144,
          0.8480176702855518,
          0.8429216161182532,
          0.8380749037103653,
          0.8338289955405402,
          0.8294830884757272,
          0.8254078787026177,
          0.8216098345127758,
          0.8180949798945824,
          0.8151066752887188,
          0.8121516722049817,
          0.8094948343323165,
          0.807140358639504,
          0.8050919587747912,
          0.803475590071717,
          0.8020244343261946,
          0.80088738957169,
          0.8000662270201541,
          0.7995622148620698,
          0.7993791360406167,
          0.7994867374503911,
          0.799912300506229,
          0.8006551119236075,
          0.8017139551304442,
          0.8029703733469743,
          0.8046317117445327,
          0.8066026649435639,
          0.8088800710810479,
          0.8114602835335141,
          0.8141072212546127,
          0.8172577500038483,
          0.8206977055337203,
          0.8244216036710665,
          0.8284235115306919,
          0.8323588307820066,
          0.8368770904630302,
          0.8416535340361666,
          0.8466805619622808,
          0.8519501752477361,
          0.8570224979375332,
          0.8627347146976126,
          0.8686639307620587,
          0.8748006556332949,
          0.8811350158011182,
          0.8871486487538903,
          0.8938337769630809,
          0.9006850833653103,
          0.9076905284247898,
          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": [
          -1.427381084189035,
          -0.6244714108415469,
          -1.016408045384821,
          -1.236727627978385,
          -1.358688459296588,
          -1.4245357073974456,
          -1.4566771742257716,
          -1.4737055187527366,
          -1.4801503165704284,
          -1.4806734383849347,
          -1.4779020874649706,
          -1.4737060612099988,
          -1.4681718816960025,
          -1.4620689471327122,
          -1.4556612087950265,
          -1.4490936862706407,
          -1.4429586771455376,
          -1.4362747022565714,
          -1.4295746548556834,
          -1.42287123637696,
          -1.4161709321085583,
          -1.409991516752819,
          -1.4033043094706472,
          -1.3966248282901135,
          -1.3899527909441025,
          -1.3832875807096259,
          -1.3771404356618708,
          -1.3704859534937175,
          -1.363835596570785,
          -1.357188277761931,
          -1.3505428568891953,
          -1.3444092819828082,
          -1.337764142534108,
          -1.3311173220973782,
          -1.3244675227273077,
          -1.3178134122798648,
          -1.3116661502002258,
          -1.3049998855483431,
          -1.2983252321467769,
          -1.2916407355333517,
          -1.2849449123363734,
          -1.2787527925059106,
          -1.2720309150264528,
          -1.265293215409575,
          -1.2585381028483809,
          -1.2517639602914172,
          -1.2454925946601714,
          -1.2386772159806214,
          -1.2318379329286553,
          -1.2249730281941638,
          -1.2180807593729495,
          -1.2116928493811763,
          -1.2047429683057438,
          -1.1977604870821983,
          -1.1907435657983183,
          -1.183690339855859,
          -1.1771458132663584,
          -1.1700174395013228,
          -1.162847169819905,
          -1.15563304351923,
          -1.1483730756893715,
          -1.1416291422171296,
          -1.1342753506212642,
          -1.1268697786331308,
          -1.1194103486718823,
          -1.1118949604207036,
          -1.1049061765941934,
          -1.0972771918305202,
          -1.0895859843070839,
          -1.0818303704244856,
          -1.0740081474018832,
          -1.0667265929438843,
          -1.058770018728773,
          -1.050740297443628,
          -1.0426351630614965,
          -1.034452337318882,
          -1.0268280238577696,
          -1.0184893523124774,
          -1.0100662791182167,
          -1.0015564990079617,
          -0.9929577063309873,
          -0.9849393623499537,
          -0.9761629243714308,
          -0.9672907629942414,
          -0.958320604237653,
          -0.9492501921177281,
          -0.9407865898816299,
          -0.9315171295998512,
          -0.9221409702069798,
          -0.9126559746514822,
          -0.9030600502275165,
          -0.8941020494206428,
          -0.8842871106878644,
          -0.8743554421961575,
          -0.8643051905509648,
          -0.8541345817538807,
          -0.8446380415699191,
          -0.8342313195771729,
          -0.8236995882490092,
          -0.8130414666655975,
          -0.802255696273679,
          -0.7921853260374963,
          -0.7811510324833569,
          -0.7699862025552019,
          -0.7586901503525938,
          -0.7472623599482312,
          -0.7365964090410272,
          -0.7249144943728073,
          -0.7131003986073522,
          -0.7011543646571284,
          -0.6890768510326527,
          -0.6778122652118893,
          -0.6654840237027104,
          -0.6530269531750722,
          -0.640442430948186,
          -0.6277320835815452,
          -0.6158893978061781,
          -0.6029425853390595,
          -0.5898761668436728,
          -0.5766927775312396,
          -0.5633953116239823,
          -0.551022197347338,
          -0.537514429980145,
          -0.5239025060768172,
          -0.5101903029304035,
          -0.4963819324097498,
          -0.48355413549025505,
          -0.46957320181929035,
          -0.4555093668415029,
          -0.44136755436165825,
          -0.4271528600574584,
          -0.4139714541287676,
          -0.3996314780979003,
          -0.3852343346115044,
          -0.3707856175829738,
          -0.3562909979291179,
          -0.3428755583998442,
          -0.32830878714977074,
          -0.31371292357943964,
          -0.2990937259015653,
          -0.2844569188646883,
          -0.2709352942470217,
          -0.25628048960369615,
          -0.24162440958844963,
          -0.22697243713114723,
          -0.2123298179701253,
          -0.1988262607999726,
          -0.18421578667707758,
          -0.16962904649001392,
          -0.1550705833912776,
          -0.1405447264199447,
          -0.12716873626480846,
          -0.1127169145652791,
          -0.0983090274085624,
          -0.08394847080717893,
          -0.06963838680228743,
          -0.05647637538913856,
          -0.04227123582404949,
          -0.02812426675374819,
          -0.014037586743295227,
          -0.023089057283112304
        ],
        "amplitude_tangent": [
          -0.42577929156507016,
          -0.3920561724009103,
          -0.3550291588217153,
          -0.3174430781385462,
          -0.27935744269998597,
          -0.2408325654264421,
          -0.20493404047669772,
          -0.16573650066819684,
          -0.12627971534410964,
          -0.08662621564203447,
          -0.0468388576755034,
          -0.010047808276651584,
          0.029819557964861493,
          0.06963612229514758,
          0.10933871660104116,
          0.14886434000838666,
          0.18513819747506496,
          0.22414748645385238,
          0.2627975482392463,
          0.3010270018585559,
          0.33877512215645855,
          0.37314044315703276,
          0.4097950933981472,
          0.4457955734170513,
          0.48108465580177817,
          0.5156062337598796,
          0.5467435922310635,
          0.579636026854711,
          0.6116042138462378,
          0.6425972909497024,
          0.6725659386307803,
          0.6992787710153987,
          0.727144767369122,
          0.7538517461612978,
          0.7793571775862801,
          0.8036204370574942,
          0.8248813099979849,
          0.8466488897574083,
          0.8670670701348447,
          0.8861032985063101,
          0.9037272160953994,
          0.9187175640560764,
          0.9335484514495845,
          0.9468913063703429,
          0.9587248113030632,
          0.9690300462138044,
          0.9771718145159807,
          0.984493836371663,
          0.9902462968439024,
          0.9944199366491793,
          0.9970080050133749,
          0.9979859778499898,
          0.9975151618465676,
          0.9954535081741953,
          0.9918041739159279,
          0.9865728392189665,
          0.9803468173923083,
          0.9720983689040722,
          0.9622988882907685,
          0.9509638305807374,
          0.9381110918854094,
          0.9249174950969664,
          0.9092052802914329,
          0.8920414103897977,
          0.8734530504154874,
          0.8534696315990482,
          0.833812517064714,
          0.8112371307448202,
          0.7873652579087833,
          0.7622347409165268,
          0.7358854276552056,
          0.7105173227170539,
          0.6819432546278873,
          0.6522777654558793,
          0.6215679386026066,
          0.5898625266475587,
          0.5597558510463277,
          0.5262786658271046,
          0.491957242936446,
          0.4568461218732736,
          0.4210011118914622,
          0.38731129825724486,
          0.3502160929530592,
          0.31255658142639864,
          0.2743926913558997,
          0.23578517197806922,
          0.1998068618212858,
          0.16051953995092802,
          0.12096996853984819,
          0.08122118500278776,
          0.04133656653629783,
          0.004454445902624582,
          -0.0355124690153989,
          -0.07542896317985004,
          -0.1152313027533398,
          -0.15485591387719075,
          -0.19121997228039475,
          -0.23032516457837185,
          -0.2690686762651115,
          -0.3073885473603287,
          -0.345223479245459,
          -0.3796652451746444,
          -0.4163981970661827,
          -0.4524717622032522,
          -0.48782819749572187,
          -0.522410905614503,
          -0.5535987697187681,
          -0.586539102244716,
          -0.618547718305216,
          -0.6495734087006391,
          -0.6795665549342388,
          -0.706294584684661,
          -0.7341688296111135,
          -0.760875382457815,
          -0.7863716408635217,
          -0.81061697293435,
          -0.8318535779427894,
          -0.8535866221165018,
          -0.8739618796049305,
          -0.8929470574900965,
          -0.9105121237103225,
          -0.9254415611156916,
          -0.9401997498440773,
          -0.9534634209688134,
          -0.9652118185951359,
          -0.9754266332533098,
          -0.9834807857919239,
          -0.9907040395742753,
          -0.9963544276856645,
          -1.0004234330869712,
          -1.0029050636275954,
          -1.0037838493425548,
          -1.0032052867210843,
          -1.0010363257626547,
          -0.9972808765085581,
          -0.9919453537312064,
          -0.985625483205205,
          -0.9772785222910912,
          -0.9673844430191432,
          -0.955959308928091,
          -0.9430215815739601,
          -0.9297544993231946,
          -0.9139684974914947,
          -0.8967373083379859,
          -0.8780884704794989,
          -0.8580517378939279,
          -0.8383520062182892,
          -0.8157378095246425,
          -0.7918349587718534,
          -0.7666814445256536,
          -0.7403172355990073,
          -0.7149426660413509,
          -0.6863696005493856,
          -0.6567136069058872,
          -0.6260220507980739,
          -0.594344182757882,
          -0.5642719192965817,
          -0.5308431807463609,
          -0.49658439681903643,
          -0.46155466926752153,
          -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": 1.470747710713071,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.1463700112241898,
        0.08590925458019905,
        -0.0009810185409595057
      ],
      "tangent_gradient": [
        -0.14637001122419038,
        0.08590925458005946,
        -0.0009810185409595653
      ],
      "reverse_gradient": [
        -0.14637001122419047,
        0.08590925458019694,
        -0.0009810185409597771
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.002362313180953063,
      "amplitude_gradient_error": 0.002362313180953063,
      "phase_gradient_error": 0.0007533962671845001,
      "viscosity_gradient_error": 0.0009810185409595057,
      "gradient_duality_error": 1.395827897709978e-13,
      "gradient_reverse_error": 2.1094237467877974e-15,
      "reverse_state_adjoint_error": 3.89235085135331e-14,
      "transpose_relative_error": 6.478525202504697e-14,
      "state_l1_error": 0.0002884844307135979,
      "state_linf_error": 0.0006092484171077439,
      "primal_residual_inf": 1.6653345369377348e-14,
      "primal_residual_density_inf": 6.821210263296962e-11,
      "newton_correction_inf": 2.169343898543048e-14,
      "tangent_residual_inf": 4.105817248689636e-13,
      "adjoint_residual_inf": 3.888496512630124e-14,
      "jacobian_nonzeros": 20475,
      "psi_0": -1.4269791152337712,
      "psi_N": -0.022571423500036797,
      "exact_nodal_residual_inf": 0.00020225365359849423,
      "exact_nodal_residual_boundary_rows_inf": 0.00020225365359849423,
      "exact_nodal_residual_inner_rows_inf": 4.7061745256371523e-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": -0.12059723482060745,
        "adjoint_directional_gradient": -0.12059723485013009,
        "absolute_error": 2.952263433719793e-11,
        "perturbed_primal_residuals_inf": [
          1.7208456881689926e-14,
          1.687538997430238e-14
        ],
        "axis_central_differences": [
          -0.14637001122252968,
          0.08590925453244579,
          -0.0009810192103110182
        ],
        "axis_absolute_errors": [
          1.6601164887219966e-12,
          4.775325967987243e-11,
          6.693515125846816e-10
        ]
      },
      "adjoint_l1_reference_error": 0.0005022832636646666,
      "adjoint_linf_reference_error": 0.01311823035519133,
      "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": 0.0004111498428860383,
      "psi_N_boundary_flux_error": 0.0005368720427200747,
      "elapsed_seconds": 0.06931500000064261,
      "cells": 4096,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.00020225365359849423,
          "correction_inf": 0.0006090493618225762,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 2.3119112180225443e-10,
          "correction_inf": 1.9999369608049615e-07,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 1.6986412276764895e-14,
          "correction_inf": 2.169343898543048e-14,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 0.976873940550301,
      "state_linf_observed_order": 0.982503877690772,
      "gradient_observed_order": 0.9603016895949928,
      "amplitude_gradient_observed_order": 0.9603016895949928,
      "phase_gradient_observed_order": 0.9048574816004493,
      "viscosity_gradient_observed_order": 1.6983606641969442,
      "adjoint_l1_observed_order": 0.9653130546484561,
      "psi_0_observed_order": 0.9838018705114738,
      "psi_N_observed_order": 0.9739168810518785,
      "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,
          0.9218540711591877,
          0.9292605881822084,
          0.9364879975238775,
          0.9441029289689384,
          0.9518062703943427,
          0.959285310486951,
          0.9671264063570438,
          0.9747149481598525,
          0.9826458773338798,
          0.9906039720475945,
          0.998269831544177,
          1.0062444577685956,
          1.0139027724659497,
          1.021845185144086,
          1.029752466036472,
          1.037310788790298,
          1.0451127220504672,
          1.052546721439348,
          1.0601956076457033,
          1.0677484011691794,
          1.074908902799628,
          1.082238489538703,
          1.089162638726865,
          1.0962241964367323,
          1.1031323777208937,
          1.1096199892612453,
          1.1161956513803946,
          1.1223439345332185,
          1.1285468550280189,
          1.134544994016134,
          1.1401104314191275,
          1.145679487643427,
          1.1508156328500172,
          1.1559215305620552,
          1.160779097333419,
          1.1652084473113569,
          1.1695568309441935,
          1.1734833980579404,
          1.1772959808651513,
          1.180826214866043,
          1.1839491658565837,
          1.1869096626932505,
          1.1894756423971746,
          1.1918482675281605,
          1.1939153676283363,
          1.1956117675955225,
          1.1970704555445717,
          1.1981770859888616,
          1.1990184096591068,
          1.1995427673925414,
          1.199747255332797,
          1.1996478972739113,
          1.1992524739423664,
          1.1985299769095912,
          1.197491251228872,
          1.1961957839796347,
          1.194542004727336,
          1.1926595369209034,
          1.1904007903615488,
          1.1878387057182576,
          1.1850928830101004,
          1.1819480468313988,
          1.1786506972616173,
          1.1749423205144198,
          1.170955157812328,
          1.166864333290702,
          1.162349126905913,
          1.1577634561305366,
          1.1527478065313344,
          1.1474886450654638,
          1.1422098959288496,
          1.1364977098548508,
          1.1307998313322611,
          1.124669553108832,
          1.1183404075343735,
          1.112076517163996,
          1.105386802189367,
          1.0987956332788968,
          1.0917862738795436,
          1.0846303501759793,
          1.0776220334608118,
          1.0702118856830967,
          1.0629807518642975,
          1.0553617269871518,
          1.0476540921968966,
          1.040170759287546,
          1.032325053573156,
          1.0247319647908435,
          1.016796215064194,
          1.0088332347266076,
          1.0011626433550975,
          0.9931830890396595,
          0.9855200563935892,
          0.9775727872276974,
          0.9696607301997375,
          0.9620979180513729,
          0.9542914509229841,
          0.9468532479257762,
          0.9392001787300837,
          0.9316434209497281,
          0.9244793375873271,
          0.9171462886300786,
          0.9102190841118761,
          0.9031546542106993,
          0.8962439314523811,
          0.8897542046087372,
          0.8831766993693051,
          0.8770269995431387,
          0.8708229864379528,
          0.864824151810948,
          0.8592584258366804,
          0.8536894686800972,
          0.8485538035871314,
          0.843448803901817,
          0.8385925373781419,
          0.8341648103304286,
          0.8298184925824518,
          0.8258942638383145,
          0.8220844642252815,
          0.8185573540345599,
          0.8154377090905681,
          0.812480943177333,
          0.8099188095725224,
          0.8075504275665526,
          0.8054877904245371,
          0.8037958611034053,
          0.8023419787404836,
          0.8012400893026289,
          0.8004037890558814,
          0.7998845158341631,
          0.7996849425465256,
          0.7997894053123379,
          0.8001896993394947,
          0.8009171900525087,
          0.801960803539116,
          0.8032608408433812,
          0.8049192080038552,
          0.8068059014170403,
          0.8090688221134572,
          0.8116348300258622,
          0.8143841656908483,
          0.8175323637459007,
          0.8208326467406534,
          0.8245437454760433,
          0.8285332791693211,
          0.832626039702792,
          0.8371428908813179,
          0.8417297801056272,
          0.8467463120726563,
          0.8520059577210017,
          0.8572847922391373,
          0.862996666610726,
          0.8686938534230095,
          0.8748229918511103,
          0.8811505443876072,
          0.8874124317963954,
          0.8940994883951673,
          0.9006873995841742,
          0.9076923569851675,
          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": [
          -1.4269791152337712,
          -0.6539243920383171,
          -1.0393992535896541,
          -1.2470639393023728,
          -1.3664528825246076,
          -1.4299226301774561,
          -1.4612073573640452,
          -1.476363772083141,
          -1.481522412275771,
          -1.481442065415002,
          -1.4782878511379656,
          -1.4736641078731358,
          -1.4679537815395918,
          -1.4619917348923963,
          -1.4555309244559256,
          -1.4489324977030829,
          -1.4425237004967353,
          -1.4358284488314008,
          -1.4293802937701205,
          -1.4226736070025199,
          -1.4159715230824754,
          -1.4095338400161794,
          -1.4028464165712466,
          -1.3964237237522605,
          -1.3897515472903925,
          -1.3830862635304697,
          -1.3766830457658688,
          -1.3700287092201913,
          -1.3636341761820017,
          -1.356986826429732,
          -1.3503413722570565,
          -1.3439521969369708,
          -1.337306980577807,
          -1.3309157343337112,
          -1.3242659030960844,
          -1.3176117658408601,
          -1.3112082277490764,
          -1.304541656325861,
          -1.2981235564888514,
          -1.291439073529776,
          -1.2847432794473763,
          -1.2782929438786932,
          -1.2715705521462548,
          -1.2650917748165447,
          -1.2583367707458364,
          -1.2515627613483389,
          -1.245029840084767,
          -1.2382137597059308,
          -1.231637279758356,
          -1.2247726200193594,
          -1.2178806280856789,
          -1.2112262931768956,
          -1.204275534742451,
          -1.1975613586284746,
          -1.1905448497258426,
          -1.1834920728202494,
          -1.1766745961543177,
          -1.1695451696587105,
          -1.1626504310261516,
          -1.1554369026618747,
          -1.1481775714629414,
          -1.1411523811226452,
          -1.1337973487472703,
          -1.1266763573577303,
          -1.119217715456381,
          -1.1117031532202208,
          -1.1044229008426312,
          -1.0967924620044034,
          -1.0893968042390798,
          -1.0816421596427872,
          -1.0738209404902765,
          -1.0662356862060065,
          -1.058277409154192,
          -1.0505562135795696,
          -1.0424522084281467,
          -1.0342705408227693,
          -1.0263281816163712,
          -1.0179875171751565,
          -1.0098880202629197,
          -1.0013794975991668,
          -0.9927819837891874,
          -0.9844290752249527,
          -0.9756503137615137,
          -0.9671188854860068,
          -0.9581500730357438,
          -0.9490810200451825,
          -0.9402641641724439,
          -0.9309920191304052,
          -0.9219758275745733,
          -0.9124922241388034,
          -0.9028976959224385,
          -0.8935656776735533,
          -0.8837476839067165,
          -0.8741971770613242,
          -0.8641483221124552,
          -0.8539791065808036,
          -0.844085936997774,
          -0.8336758169928334,
          -0.8235481551505113,
          -0.8128914029462263,
          -0.8021069939981597,
          -0.791615933138039,
          -0.7805779786610656,
          -0.7698414320879539,
          -0.7585467090116295,
          -0.7471202404484533,
          -0.7360086953942278,
          -0.7243230054972651,
          -0.7129621116121789,
          -0.7010173831754033,
          -0.6889411756363059,
          -0.6772060821441314,
          -0.6648741782715131,
          -0.6528951249366026,
          -0.6403119394678671,
          -0.6276029455814763,
          -0.6152658678127496,
          -0.6023158084100785,
          -0.5897511222832003,
          -0.5765691956072674,
          -0.563273232401766,
          -0.5503840469194318,
          -0.53687380149102,
          -0.5237850992104169,
          -0.5100746075220544,
          -0.4962680147443453,
          -0.48290585700545136,
          -0.4689235681891854,
          -0.4554010720013714,
          -0.4412613433032436,
          -0.4270488207268642,
          -0.41331917512968536,
          -0.39897925058013267,
          -0.3851371735974445,
          -0.37069099677348355,
          -0.3561990138302577,
          -0.34222654743234715,
          -0.3276613743678758,
          -0.3136291916895105,
          -0.2990129966357906,
          -0.2843792781481968,
          -0.27029714344203526,
          -0.2556454316408655,
          -0.24155624254254457,
          -0.2269076438602772,
          -0.21226845452496007,
          -0.19820591731732462,
          -0.18359978585916087,
          -0.16957795345890259,
          -0.15502305966116312,
          -0.14050078556717296,
          -0.12657163637369595,
          -0.11212502167653256,
          -0.09827555198669113,
          -0.08391854503060019,
          -0.06961198211285226,
          -0.055905924313107064,
          -0.04170642803222158,
          -0.02810794020116833,
          -0.014024630805944602,
          -0.022571423500036797
        ],
        "amplitude_tangent": [
          -0.42577929156507854,
          -0.3907298274005232,
          -0.3536970579533382,
          -0.3175601750993188,
          -0.27948597498635946,
          -0.24096994944495367,
          -0.20357555393133905,
          -0.1643710050892421,
          -0.12642922412461755,
          -0.08677552165294129,
          -0.04698591512219396,
          -0.008657331592235234,
          0.031215227506832952,
          0.069506454965371,
          0.10921840903672751,
          0.14875499482582563,
          0.18654708651598775,
          0.22555759235445788,
          0.26272874771413496,
          0.3009747680225305,
          0.33874073295137264,
          0.3745455580816172,
          0.4111963225170596,
          0.4458202004098372,
          0.4811316750336331,
          0.5156767041110796,
          0.5481191342599198,
          0.58100241066952,
          0.6117489953055951,
          0.6427693720423684,
          0.6727662339678384,
          0.7005997061351609,
          0.7284518757750983,
          0.7541395453151793,
          0.7796765666188804,
          0.8039722274924498,
          0.8261267574064894,
          0.8478770051648326,
          0.8675180533803782,
          0.8865896917319702,
          0.904249742672005,
          0.9198731552400267,
          0.9346847346986658,
          0.947523435619636,
          0.959395741574714,
          0.9697404137824394,
          0.9782311908305927,
          0.9855336797916384,
          0.9910754226679442,
          0.9952908234507969,
          0.9979212015239496,
          0.9989516817377634,
          0.9984629878945019,
          0.9964933639967711,
          0.992888328180154,
          0.987701759072737,
          0.9812308046528505,
          0.9729680834934336,
          0.9635611999842829,
          0.9522725996973933,
          0.9394667165816936,
          0.925741371783954,
          0.9100204504871443,
          0.8935361654631294,
          0.87499610649182,
          0.8550613283838597,
          0.834607421611826,
          0.8120307675159073,
          0.7891009685884525,
          0.7640203039994065,
          0.7377211164098503,
          0.7113231833206927,
          0.682756896063484,
          0.6542613654932325,
          0.6236025420892932,
          0.5919482929938056,
          0.5606196054940439,
          0.527160329539382,
          0.49419313389756775,
          0.4591334239291282,
          0.4233397638819441,
          0.3882836203934545,
          0.3512166500014026,
          0.31504434290813627,
          0.27693086656380306,
          0.23837330239788188,
          0.2009370498430291,
          0.16168721258859683,
          0.12370042735076928,
          0.08399865654289985,
          0.04415995748570384,
          0.0057834593565276185,
          -0.03413939803608985,
          -0.07247917610170933,
          -0.11224153686871857,
          -0.15182815294641658,
          -0.18966772158575892,
          -0.22872666339952005,
          -0.26594321724238273,
          -0.3042349471902733,
          -0.3420448022681648,
          -0.3778898495414833,
          -0.41458011815821244,
          -0.4492394976153974,
          -0.4845850628161395,
          -0.5191610554819187,
          -0.5516300967300741,
          -0.5845375562959804,
          -0.6153038597726433,
          -0.6463409037511396,
          -0.6763503726828951,
          -0.704192025315394,
          -0.7320485127651014,
          -0.7577362458663045,
          -0.7832690481579067,
          -0.807556118029925,
          -0.8296982915984784,
          -0.851431489381553,
          -0.8710521928140728,
          -0.8900986875136292,
          -0.9077296894341387,
          -0.9233216650720946,
          -0.938097118670303,
          -0.9508980125058474,
          -0.9627280718338852,
          -0.9730278078108373,
          -0.9814731383453796,
          -0.9887263622793591,
          -0.9942191359037641,
          -0.9983822992632612,
          -1.0009594738849816,
          -1.0019382387709581,
          -1.0013955492195077,
          -0.9993741512857828,
          -0.9957157838285692,
          -0.9904767684427892,
          -0.9839565511620779,
          -0.97564414094431,
          -0.9661912643211019,
          -0.9548569858903062,
          -0.9420079059455242,
          -0.9282436137656435,
          -0.9124851142629997,
          -0.8959677123597001,
          -0.8773965369881439,
          -0.8574342001592998,
          -0.8369572842741476,
          -0.8143604460021785,
          -0.7914149290124284,
          -0.7663218271701868,
          -0.7400142429043082,
          -0.7136120837530836,
          -0.685045433176927,
          -0.6565534600744305,
          -0.6259024487246637,
          -0.5942602997966071,
          -0.5629474646046764,
          -0.5295094038666479,
          -0.49656774961588596,
          -0.46154107574259995,
          -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": 1.4709711368979197,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.14520100389482926,
        0.0855432563996867,
        -0.00032718103611183657
      ],
      "tangent_gradient": [
        -0.14520100389444546,
        0.08554325640010498,
        -0.00032718103611199145
      ],
      "reverse_gradient": [
        -0.14520100389482915,
        0.08554325639968097,
        -0.00032718103611184546
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.0011933058515925243,
      "amplitude_gradient_error": 0.0011933058515925243,
      "phase_gradient_error": 0.0003873980866721527,
      "viscosity_gradient_error": 0.00032718103611183657,
      "gradient_duality_error": 4.1827652452752773e-13,
      "gradient_reverse_error": 5.731526364627371e-15,
      "reverse_state_adjoint_error": 8.314039018873787e-14,
      "transpose_relative_error": 8.661635602964977e-14,
      "state_l1_error": 0.00014524083452364207,
      "state_linf_error": 0.00030612440276900355,
      "primal_residual_inf": 3.452793606584237e-14,
      "primal_residual_density_inf": 2.828528522513807e-10,
      "newton_correction_inf": 1.4544506245980802e-15,
      "tangent_residual_inf": 4.2793069435220765e-13,
      "adjoint_residual_inf": 7.136430118723225e-14,
      "jacobian_nonzeros": 40955,
      "psi_0": -1.4267743383016032,
      "psi_N": -0.022304605740628362,
      "exact_nodal_residual_inf": 0.00010117462045433623,
      "exact_nodal_residual_boundary_rows_inf": 0.00010117462045433623,
      "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": -0.11953802695474634,
        "adjoint_directional_gradient": -0.11953802697492324,
        "absolute_error": 2.017690181599363e-11,
        "perturbed_primal_residuals_inf": [
          3.4861002973229915e-14,
          3.5083047578154947e-14
        ],
        "axis_central_differences": [
          -0.1452010038982543,
          0.08554325634513303,
          -0.0003271812265559504
        ],
        "axis_absolute_errors": [
          3.425038030968608e-12,
          5.4553667139245476e-11,
          1.9044411382097837e-10
        ]
      },
      "adjoint_l1_reference_error": 0.00025376333735805474,
      "adjoint_linf_reference_error": 0.006684650900312783,
      "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": 0.00020637291071801123,
      "psi_N_boundary_flux_error": 0.00027005428331164025,
      "elapsed_seconds": 0.12365887500345707,
      "cells": 8192,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 0.00010117462045433623,
          "correction_inf": 0.0003060741301762844,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 2.910321983407016e-11,
          "correction_inf": 5.051933735186433e-08,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 3.5638159090467525e-14,
          "correction_inf": 1.4544506245980802e-15,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 0.9900463351118378,
      "state_linf_observed_order": 0.9929125435007079,
      "gradient_observed_order": 0.9852363790537242,
      "amplitude_gradient_observed_order": 0.9852363790537242,
      "phase_gradient_observed_order": 0.9595920566481893,
      "viscosity_gradient_observed_order": 1.5841912732081072,
      "adjoint_l1_observed_order": 0.9850175546501384,
      "psi_0_observed_order": 0.9944106679543898,
      "psi_N_observed_order": 0.9913288484475272,
      "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,
          0.9219896144350936,
          0.9292529547076983,
          0.936624279832675,
          0.9440923180374454,
          0.9517945292275396,
          0.9594229336475306,
          0.9671131884335836,
          0.9748535337546012,
          0.9826321330324028,
          0.9905903126281592,
          0.998409856905104,
          1.00623163159321,
          1.0140436748214037,
          1.0218340393769185,
          1.0297424887924103,
          1.0374527948123564,
          1.0451056203820814,
          1.0526892608103446,
          1.0601921169622435,
          1.067747020028991,
          1.0750518774119067,
          1.0822417454275293,
          1.0893056261623024,
          1.0962327141457964,
          1.1031438046464823,
          1.1097625474122095,
          1.1162132032650112,
          1.122485903706732,
          1.128571052205926,
          1.1345727664906293,
          1.140251057737846,
          1.1457146166780328,
          1.1509550836013778,
          1.1559644398577047,
          1.1608261243415259,
          1.165345732913005,
          1.16961220934596,
          1.1736190241966595,
          1.1773600450797383,
          1.1808948249059052,
          1.1840820169732091,
          1.1869873995294948,
          1.1896065245901306,
          1.1919353819762424,
          1.1940073489535112,
          1.1957395710654255,
          1.1971721322323394,
          1.1983028371635704,
          1.1991299523018255,
          1.199659395215297,
          1.1998699913976951,
          1.1997745887194329,
          1.1993733292713102,
          1.1986668230651323,
          1.1976332990247098,
          1.1963140803791394,
          1.194694283704889,
          1.192776383358337,
          1.1905633098267612,
          1.1880064385135038,
          1.1852080064895554,
          1.1821259694692794,
          1.1787650393522047,
          1.175130354853812,
          1.1711483051353402,
          1.1669781160513302,
          1.1625521968133998,
          1.1578773161716411,
          1.152960623977001,
          1.1477063510023233,
          1.1423245961185566,
          1.1367248184553396,
          1.1309155838791927,
          1.1249057789938577,
          1.1185811561078445,
          1.1121946152505877,
          1.1056361443322573,
          1.0989157775057214,
          1.092043796958214,
          1.0848918672433754,
          1.0777459713815334,
          1.0704808538010182,
          1.0631076315863195,
          1.0556375875910111,
          1.047933231437488,
          1.0403026377445728,
          1.0326101216600958,
          1.0248674560303717,
          1.0170864907811505,
          1.0091258659218239,
          1.0013039051914538,
          0.9934797100732963,
          0.9856652564835813,
          0.9778725056876907,
          0.9699616625766331,
          0.9622490615550828,
          0.9545940068732388,
          0.9470082165919697,
          0.9395033028617185,
          0.9319464099190576,
          0.9246397191692676,
          0.9174481464452848,
          0.9103827004876457,
          0.9034541968593908,
          0.8965418265800147,
          0.8899219976578293,
          0.883470430510319,
          0.8771970000599765,
          0.8711113081886984,
          0.8651092364087353,
          0.8594307903761349,
          0.853967272405451,
          0.8487270427587108,
          0.8437181193632021,
          0.8388570755098949,
          0.8343382873258235,
          0.8300728168498605,
          0.8260671876378556,
          0.8223275249466953,
          0.8187942989676195,
          0.8156087869943386,
          0.8127052284945842,
          0.8100880598530399,
          0.8077612787172563,
          0.8056915382184756,
          0.8039615928282808,
          0.8025313856864335,
          0.801403096802049,
          0.8005784440451374,
          0.8000515429459268,
          0.799843453843368,
          0.7999413613211009,
          0.800345107182362,
          0.8010540655053264,
          0.8020900382672292,
          0.8034115926339654,
          0.8050336450177698,
          0.8069537070426418,
          0.8091688349157756,
          0.8117276773779067,
          0.8145279097229924,
          0.8176116046721466,
          0.8209740406277972,
          0.8246100702094564,
          0.8285933180010557,
          0.8327645054582954,
          0.8371912426808025,
          0.8418667565887551,
          0.8467838940300273,
          0.8520384249535448,
          0.8574202389689818,
          0.8630198827156519,
          0.8688287892841475,
          0.8748380702193147,
          0.8811619528602989,
          0.8875475565185292,
          0.8941048625721658,
          0.9008238008912945,
          0.9076940212886725,
          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": [
          -1.4267743383016032,
          -0.6691885115753584,
          -1.045787352704138,
          -1.2555255956424898,
          -1.3704793721492765,
          -1.432681633398001,
          -1.4634382916249815,
          -1.4774899971408173,
          -1.482232311655476,
          -1.4818140213061668,
          -1.4784688737741603,
          -1.4736269653745848,
          -1.4679494943370215,
          -1.4618233249127595,
          -1.455460133790488,
          -1.448847181719678,
          -1.4423017317265985,
          -1.4357304653028942,
          -1.429150803039875,
          -1.4225717621036988,
          -1.4158689856958424,
          -1.40930231497324,
          -1.4027434670387329,
          -1.3961923998411943,
          -1.3896486701573951,
          -1.3829834861786963,
          -1.376452369431888,
          -1.36992616798464,
          -1.363403901870549,
          -1.3568845379511325,
          -1.3502392139232449,
          -1.3437223821706434,
          -1.3372050779720688,
          -1.3306861108576016,
          -1.324164257495695,
          -1.3175102524327513,
          -1.3109787125193375,
          -1.3044404061982209,
          -1.2978939903409012,
          -1.2913380943309665,
          -1.2846424422395386,
          -1.2780631119980785,
          -1.2714700028639925,
          -1.2648616400876949,
          -1.2582365242166258,
          -1.2514626757668377,
          -1.2447990538789049,
          -1.2381140044987446,
          -1.2314059318794002,
          -1.2246732168297185,
          -1.217781413513918,
          -1.2109938980200148,
          -1.204176709686704,
          -1.1973281361570778,
          -1.1904464420708425,
          -1.1833938894370999,
          -1.1764399196303823,
          -1.169447450121607,
          -1.1624146536875253,
          -1.1553396804636744,
          -1.1480806163674888,
          -1.1409147301589955,
          -1.1337009454365294,
          -1.1264373230773337,
          -1.1191219024292534,
          -1.1116076565356368,
          -1.1041815593476085,
          -1.0966976172022536,
          -1.0891537876929798,
          -1.08154800971819,
          -1.073727161905602,
          -1.0659899157957893,
          -1.0581843935198596,
          -1.0503084689147957,
          -1.042360002848236,
          -1.0341787668425986,
          -1.0260772282229078,
          -1.0178966273044385,
          -1.0096347908852945,
          -1.001289542780355,
          -0.992692525743714,
          -0.9841721846371507,
          -0.9755618704576939,
          -0.9668594240567864,
          -0.9580626990460895,
          -0.9489942126454743,
          -0.9400006097270981,
          -0.930906366044436,
          -0.9217094294153672,
          -0.9124077833180488,
          -0.9028138958246626,
          -0.8932948031364706,
          -0.8836651858941579,
          -0.8739232297875096,
          -0.8640671870844738,
          -0.8538986901688893,
          -0.8438072168772704,
          -0.8335968573446747,
          -0.8232662061938221,
          -0.8128139631829199,
          -0.802030353575421,
          -0.7913290508750904,
          -0.7805029545351685,
          -0.7695512734995763,
          -0.7584733655218435,
          -0.7470477785809118,
          -0.7357136368050251,
          -0.7242523217092752,
          -0.7126638778809915,
          -0.700948542000219,
          -0.6888732986311851,
          -0.6769032369019767,
          -0.6648082410652866,
          -0.6525893943507244,
          -0.6402480062310939,
          -0.6275400586347883,
          -0.6149561256424945,
          -0.6022550221547661,
          -0.589439005706745,
          -0.5765105741853475,
          -0.5632157393829628,
          -0.5500688679672021,
          -0.5368185707012221,
          -0.5234682928950221,
          -0.510021704073815,
          -0.4962163230303632,
          -0.48258728937256395,
          -0.4688743032130857,
          -0.45508184591083034,
          -0.44121457145765614,
          -0.4270033454730224,
          -0.4129997911154064,
          -0.3989363685576343,
          -0.3848182690231655,
          -0.37065077311886,
          -0.3561601698416512,
          -0.3419092799059806,
          -0.3276252825370782,
          -0.31331361777704375,
          -0.2989797139494467,
          -0.28434744762975245,
          -0.26998502882964553,
          -0.2556164842776106,
          -0.24124699161629515,
          -0.2268816180921955,
          -0.21224392969680547,
          -0.1979017863681444,
          -0.1835782204332248,
          -0.1692776892921084,
          -0.15500446326451112,
          -0.14048370221961265,
          -0.12627782150071884,
          -0.1121108965109313,
          -0.09798634483456349,
          -0.08390735409739458,
          -0.06960227397459985,
          -0.05562405837975907,
          -0.041699597348307936,
          -0.02783112480484089,
          -0.014020636356656535,
          -0.022304605740628362
        ],
        "amplitude_tangent": [
          -0.425779291565057,
          -0.3900516791430223,
          -0.35373476510674634,
          -0.31687811138637545,
          -0.2795380440867606,
          -0.24102723728257203,
          -0.20288554834777858,
          -0.16443466507558502,
          -0.12573335759363882,
          -0.0868407811407749,
          -0.04705028507777808,
          -0.007952907200667603,
          0.03115569589928502,
          0.07021573593997,
          0.10916749613969179,
          0.14870981438684389,
          0.18726156254521037,
          0.2255260691525527,
          0.26344482272979536,
          0.30095983780026936,
          0.3387352988843183,
          0.3752607134599708,
          0.4112113844638079,
          0.44653232579827307,
          0.48116951204143,
          0.5157269604147396,
          0.548822841897714,
          0.5810784945884309,
          0.6124445723634186,
          0.6428730877089889,
          0.6728846832341924,
          0.7012792912701502,
          0.7286004135999964,
          0.7548062425251719,
          0.7798566747247286,
          0.8041689695569332,
          0.8267709454343377,
          0.8481073817795644,
          0.8681456181333349,
          0.8868549786593602,
          0.9045332990810703,
          0.9204736604654212,
          0.9350050226717259,
          0.9481051295929293,
          0.9597539136779664,
          0.9701183321762713,
          0.9787839187204999,
          0.9859511632503007,
          0.9916090710870479,
          0.9957489559067975,
          0.9984004683465648,
          0.9994575511862401,
          0.9989845081093822,
          0.996982030087591,
          0.9934531475430602,
          0.9882890511049337,
          0.9816962012243475,
          0.973600230600498,
          0.9640134911320338,
          0.9529506154166436,
          0.9401685008683275,
          0.926178226692503,
          0.9107695980975444,
          0.8939661554585202,
          0.8757935735655499,
          0.8558837847875407,
          0.8350328825322534,
          0.8129029082371313,
          0.7895276890135682,
          0.7649429582437429,
          0.7386698159206971,
          0.7117588105309208,
          0.6837571953045676,
          0.654707787931609,
          0.6246550111628196,
          0.5930275285746954,
          0.5610900011374018,
          0.5282922843621829,
          0.49468454577143767,
          0.46031819520771805,
          0.4245514142039162,
          0.38881439597789547,
          0.3524807372266927,
          0.3156060326040906,
          0.27824670859089967,
          0.23971513559840343,
          0.20155208231076902,
          0.16307896305529807,
          0.12435466769116336,
          0.08543847509083168,
          0.04562338475806234,
          0.00650151290847913,
          -0.03263181923475374,
          -0.07171668794350854,
          -0.11069323912128946,
          -0.15026065190023194,
          -0.18883669113389664,
          -0.22712503033572728,
          -0.265067018579504,
          -0.3026045319862571,
          -0.3404020328437671,
          -0.3769480447122149,
          -0.4129181727912932,
          -0.4482573046787061,
          -0.482911293862677,
          -0.5174843268952078,
          -0.5505938658851998,
          -0.5828614642828023,
          -0.6142376856501123,
          -0.64467446227937,
          -0.6746924714557974,
          -0.703091340835215,
          -0.73041467073507,
          -0.7566206228311017,
          -0.7816690773370616,
          -0.8059771908601796,
          -0.8285729562695222,
          -0.8499011220322955,
          -0.869929071917665,
          -0.8886261895932049,
          -0.906290090106943,
          -0.9222144998300007,
          -0.9367282228085185,
          -0.9498091194312387,
          -0.9614372508819333,
          -0.9717792717843046,
          -0.9804217296031292,
          -0.9875648544458628,
          -0.9931978174234254,
          -0.9973121036850899,
          -0.9999370245955298,
          -1.0009677268179922,
          -1.0004681859532634,
          -0.9984392716110891,
          -0.9948841907757517,
          -0.9896938067357235,
          -0.9830757618588746,
          -0.9749553405685767,
          -0.9653450492883251,
          -0.9542596667604399,
          -0.941455821797276,
          -0.9274455581399921,
          -0.9120183669115328,
          -0.89519789309499,
          -0.8770099044897333,
          -0.8570861635387881,
          -0.8362233705720726,
          -0.8140833389565798,
          -0.7906999414332415,
          -0.766108945874449,
          -0.739831410975979,
          -0.7129180690783695,
          -0.6849160768672412,
          -0.6558682540668994,
          -0.6258190246843971,
          -0.5941971875207008,
          -0.562267211404822,
          -0.5294791019958557,
          -0.4958831557804648,
          -0.4615310343655587,
          -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": 1.471084340623987,
      "exact_objective": 1.4711984603913526,
      "gradient": [
        -0.14460688629112892,
        0.08535205425494716,
        -0.00012143195981049336
      ],
      "tangent_gradient": [
        -0.14460688629069987,
        0.0853520542557761,
        -0.00012143195981096203
      ],
      "reverse_gradient": [
        -0.14460688629112695,
        0.08535205425494174,
        -0.00012143195981084709
      ],
      "exact_gradient": [
        -0.14400769804323674,
        0.08515585831301455,
        0.0
      ],
      "gradient_error_inf": 0.0005991882478921795,
      "amplitude_gradient_error": 0.0005991882478921795,
      "phase_gradient_error": 0.00019619594193261147,
      "viscosity_gradient_error": 0.00012143195981049336,
      "gradient_duality_error": 8.289480213363731e-13,
      "gradient_reverse_error": 5.412337245047638e-15,
      "reverse_state_adjoint_error": 1.780966189411301e-13,
      "transpose_relative_error": 4.280709266070512e-13,
      "state_l1_error": 7.285118344976472e-05,
      "state_linf_error": 0.00015339453248919277,
      "primal_residual_inf": 6.972200594645983e-14,
      "primal_residual_density_inf": 1.1423253454267979e-09,
      "newton_correction_inf": 1.7670718245952836e-16,
      "tangent_residual_inf": 9.464526601679624e-13,
      "adjoint_residual_inf": 1.5688858090272262e-13,
      "jacobian_nonzeros": 81915,
      "psi_0": -1.4266713073864135,
      "psi_N": -0.022169881145825573,
      "exact_nodal_residual_inf": 5.058458644041641e-05,
      "exact_nodal_residual_boundary_rows_inf": 5.058458644041641e-05,
      "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": -0.119001269993646,
        "adjoint_directional_gradient": -0.11900127001464478,
        "absolute_error": 2.099877216554802e-11,
        "perturbed_primal_residuals_inf": [
          7.260858581048524e-14,
          7.061018436615996e-14
        ],
        "axis_central_differences": [
          -0.1446068863097949,
          0.08535205419102353,
          -0.00012143199779046653
        ],
        "axis_absolute_errors": [
          1.8665985423993448e-11,
          6.392363027796222e-11,
          3.7979973170360753e-11
        ]
      },
      "adjoint_l1_reference_error": 0.00012749085547082427,
      "adjoint_linf_reference_error": 0.003371360394208156,
      "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": 0.00010334199552830547,
      "psi_N_boundary_flux_error": 0.00013532968850885063,
      "elapsed_seconds": 0.26592345800600015,
      "cells": 16384,
      "nu": 0.01,
      "amplitude": 0.2,
      "phase": 0.07,
      "reconstruction": "smooth",
      "epsilon": 0.01,
      "newton_history": [
        {
          "iteration": 0,
          "residual_inf": 5.058458644041641e-05,
          "correction_inf": 0.0001533819063881701,
          "step": 1.0
        },
        {
          "iteration": 1,
          "residual_inf": 3.677835813675756e-12,
          "correction_inf": 1.268849183247193e-08,
          "step": 1.0
        },
        {
          "iteration": 2,
          "residual_inf": 6.916689443414725e-14,
          "correction_inf": 1.7670718245952836e-16,
          "step": 1.0
        }
      ],
      "state_l1_observed_order": 0.995422810877366,
      "state_linf_observed_order": 0.9968709930530528,
      "gradient_observed_order": 0.9938826289382788,
      "amplitude_gradient_observed_order": 0.9938826289382788,
      "phase_gradient_observed_order": 0.9815216270792002,
      "viscosity_gradient_observed_order": 1.4299409539449017,
      "adjoint_l1_observed_order": 0.9930898791317463,
      "psi_0_observed_order": 0.9978269621219856,
      "psi_N_observed_order": 0.9967710597402599,
      "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,
          0.9219876132789125,
          0.929250000009445,
          0.9366932589817987,
          0.9441614945060839,
          0.9517894754460856,
          0.9594174371297901,
          0.9671073713437349,
          0.9749236090870501,
          0.982702442541894,
          0.9905842451812773,
          0.9984039357814993,
          1.0062259664353697,
          1.0141148774578113,
          1.021905438424335,
          1.0297382339032004,
          1.0374492085510858,
          1.0451027982798744,
          1.052761272770849,
          1.0602642273957792,
          1.067747056086603,
          1.0750530328017205,
          1.0822441014102826,
          1.0893778682325062,
          1.0963049178401936,
          1.1031502510517148,
          1.1097704933529597,
          1.116222716410107,
          1.12255764957999,
          1.128642608194709,
          1.1345873966004683,
          1.1402675014004462,
          1.145732929022606,
          1.1510255824237368,
          1.1560346067336889,
          1.1608503901586504,
          1.1653720655958206,
          1.1696406525826388,
          1.1736876173145203,
          1.1774281952206016,
          1.1809298845674803,
          1.1841193413522724,
          1.1870270218029753,
          1.1896727459642138,
          1.1920010977290303,
          1.1940540910336557,
          1.1957887243517176,
          1.1972237200157942,
          1.198366490002784,
          1.1991930972103353,
          1.1997184560256204,
          1.1999315609202936,
          1.19983868059334,
          1.1994345338232315,
          1.1987275834733808,
          1.1977050704815733,
          1.196388409358904,
          1.1947711739767557,
          1.1928355925680454,
          1.1906222038685936,
          1.188091064921901,
          1.1852951884595657,
          1.1822157001858902,
          1.1788230204802985,
          1.1751882071701156,
          1.1712456676891532,
          1.167077976801845,
          1.1626545371240875,
          1.157935097721443,
          1.153018505775302,
          1.1478160392508212,
          1.1424366625395583,
          1.1368392308415838,
          1.130974368658898,
          1.1249649146305056,
          1.1187024264864491,
          1.1123180714267256,
          1.1057617383537333,
          1.0989768247545715,
          1.0921054405074908,
          1.0850235904867591,
          1.077879604249853,
          1.070616330220113,
          1.0631721143022976,
          1.0557028763518166,
          1.0480738337993705,
          1.0404447780637822,
          1.0327537135918436,
          1.0249363043964828,
          1.01715628777382,
          1.009273274010669,
          1.001452374822294,
          0.9936291334147922,
          0.9857390047260086,
          0.9779472499139247,
          0.9701132681522832,
          0.9624011448101581,
          0.9547464391850434,
          0.9470868779516657,
          0.9395828934073326,
          0.9320990778583405,
          0.9247921826018229,
          0.9176002596715342,
          0.9104657008378,
          0.9035379420019438,
          0.8966919731855812,
          0.8900711854843059,
          0.8836185043933781,
          0.8772832006338794,
          0.871197968775046,
          0.8652530012751021,
          0.859572816546969,
          0.8541074068677329,
          0.8488148711937942,
          0.8438060617560308,
          0.8389905935423009,
          0.8344693258740128,
          0.8302012395080948,
          0.8261548715446321,
          0.8224149713865461,
          0.8189140498134131,
          0.8157254311496676,
          0.8128186609483221,
          0.8101739232622311,
          0.8078466087387383,
          0.805794716960534,
          0.8040612209580311,
          0.8026274014738538,
          0.801485850865699,
          0.8006604746576318,
          0.800136374446771,
          0.7999245231897295,
          0.8000186562549525,
          0.8004240589338001,
          0.8011322359543351,
          0.8021559624617384,
          0.8034737927265224,
          0.8050921574628781,
          0.8070288317765855,
          0.8092432489926842,
          0.8117753658364326,
          0.8145721447121631,
          0.8176524643538909,
          0.8210459065336643,
          0.8246813942391844,
          0.8286245293729857,
          0.832792722323239,
          0.8372165739781612,
          0.8419363358019551,
          0.8468531527440831,
          0.852055750157327,
          0.8574351605154749,
          0.8630325301765397,
          0.8688972327229771,
          0.8749064327846232,
          0.8811685675039651,
          0.8875524754151831,
          0.8941082613875553,
          0.9008925134620096,
          0.9077631190061851,
          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": [
          -1.4266713073864135,
          -0.6720806298289376,
          -1.0490679855961522,
          -1.2597722277721526,
          -1.373319876954974,
          -1.4340670035841245,
          -1.4643383306544258,
          -1.478048046830498,
          -1.482575482702887,
          -1.4819728386294615,
          -1.4785552243844986,
          -1.4736565765170144,
          -1.4679448468250706,
          -1.4617366918046026,
          -1.4553600107351077,
          -1.4488032955613683,
          -1.4422539846986868,
          -1.4356805648347746,
          -1.429035208713426,
          -1.4224555913064747,
          -1.4158169954006348,
          -1.4092502025248566,
          -1.4026913280555513,
          -1.396076098125173,
          -1.3895324914768306,
          -1.3829314973235138,
          -1.3764004575611313,
          -1.3698743370622946,
          -1.3632882269694628,
          -1.3567689700400358,
          -1.350187635535678,
          -1.3436708881264776,
          -1.3371536683450391,
          -1.3305708628490562,
          -1.324049059649267,
          -1.3174590983972052,
          -1.3109276435861048,
          -1.3043894227456214,
          -1.2977788684792835,
          -1.2912229591989777,
          -1.2845917202315804,
          -1.278012478032598,
          -1.2714194578521114,
          -1.264746317612396,
          -1.2581211211203438,
          -1.2514124060458536,
          -1.2447488779319649,
          -1.2380639238222957,
          -1.2312900643163487,
          -1.2245571982299062,
          -1.2177316308441635,
          -1.210944217882005,
          -1.204127134206201,
          -1.1972113646799176,
          -1.1903294465447194,
          -1.183344644223893,
          -1.1763907889637668,
          -1.1693984368077022,
          -1.1622966071502816,
          -1.1552213346241713,
          -1.14803197590721,
          -1.1408662197994897,
          -1.1336525687292063,
          -1.1263176199312295,
          -1.119001822950837,
          -1.1115597065755805,
          -1.104133758939267,
          -1.0966499707229282,
          -1.0890320388956132,
          -1.0814258065813187,
          -1.0736800085965628,
          -1.065942935818595,
          -1.0581375921707326,
          -1.0501842829940167,
          -1.0422352849739966,
          -1.0341325390183806,
          -1.0260312023170972,
          -1.0178508096270003,
          -1.0095077823675316,
          -1.001161927279346,
          -0.9926473772943705,
          -0.9841272719445002,
          -0.9755172009193909,
          -0.9667292265006441,
          -0.9579318253099398,
          -0.9489503244841102,
          -0.9399569966906318,
          -0.9308630366381417,
          -0.9215757141730976,
          -0.9122733330330477,
          -0.9027714766495809,
          -0.893252703902471,
          -0.8836234161333393,
          -0.8737857312820585,
          -0.8639289108442215,
          -0.8538579749413274,
          -0.8437668711730617,
          -0.8335568914960805,
          -0.823124753787291,
          -0.8126717135909617,
          -0.8019915985461052,
          -0.7912907182322352,
          -0.7804650550114561,
          -0.7694058289254876,
          -0.7583271354855355,
          -0.7470112521049173,
          -0.7356775865342705,
          -0.7242167582305635,
          -0.7125145757464103,
          -0.7007985053945568,
          -0.6888392681777546,
          -0.6768697345406993,
          -0.6647752766458197,
          -0.6524365814033075,
          -0.6400945562265978,
          -0.6275087761442353,
          -0.6149254183993407,
          -0.6022248987996128,
          -0.5892832724967335,
          -0.5763543524431243,
          -0.5631874287570204,
          -0.5500411731388112,
          -0.5367914988967367,
          -0.523310489277118,
          -0.5098636118280901,
          -0.4961911735614226,
          -0.4825627892182683,
          -0.46885045826418714,
          -0.4549230700670281,
          -0.4410557520061443,
          -0.42698151231385756,
          -0.41297863446711847,
          -0.3989158931591002,
          -0.3846598201940713,
          -0.37049255650854346,
          -0.3561417780714592,
          -0.34189158618756543,
          -0.3276082904575486,
          -0.31315690821739395,
          -0.298823521179815,
          -0.28433259324783383,
          -0.2699708876772848,
          -0.25560305842698067,
          -0.2410934246344365,
          -0.22672883447827136,
          -0.2122326724307754,
          -0.19789124870438882,
          -0.18356840231061264,
          -0.1691285242545605,
          -0.1548563043097228,
          -0.14047605132416777,
          -0.12627088472709502,
          -0.11210467116998417,
          -0.09784257914499413,
          -0.08376475453025667,
          -0.0695981752904265,
          -0.055620655275322124,
          -0.041696884929848264,
          -0.0276934233338775,
          -0.013884193392484928,
          -0.022169881145825573
        ],
        "amplitude_tangent": [
          -0.4257792915650648,
          -0.39006173955867224,
          -0.3537496773171767,
          -0.31653334788041604,
          -0.27919221390903304,
          -0.24105241555842666,
          -0.20291275836271616,
          -0.16446326902380615,
          -0.1253822799907567,
          -0.08648831251299241,
          -0.047079489755715104,
          -0.007981201726712402,
          0.031128821588637827,
          0.07057329180790275,
          0.10952606825657928,
          0.1486900822233006,
          0.18724506425079993,
          0.22551320091957314,
          0.26380584985276745,
          0.3013209877887552,
          0.3387355959640051,
          0.3752660386524548,
          0.41122204188662653,
          0.4468916471089996,
          0.4815277632841417,
          0.5157554118564566,
          0.5488577007813005,
          0.581119996339558,
          0.6127959566437612,
          0.6432221308509668,
          0.6729475647707769,
          0.7013496589226972,
          0.7286784554386059,
          0.7551434820550228,
          0.7801904252161084,
          0.8042712561136046,
          0.8268815961666962,
          0.8482265550429396,
          0.8684634777260087,
          0.8871684935853552,
          0.9046791282064387,
          0.9206286114434266,
          0.9351692376266345,
          0.9484001208685926,
          0.9600441282619983,
          0.9703113647941314,
          0.9789867698746259,
          0.9861639682214526,
          0.9918800318693712,
          0.9960152229088939,
          0.998644145848023,
          0.9997117220213966,
          0.9992493061182371,
          0.9972305005362366,
          0.99369757218099,
          0.9885867513348654,
          0.9820050666209976,
          0.9739203948128756,
          0.9642438799435528,
          0.9531781786073105,
          0.9405235902479976,
          0.9265451471225868,
          0.9111484794977639,
          0.8941856846565335,
          0.876012030526223,
          0.8562995529693034,
          0.8354611125230434,
          0.8133437167206345,
          0.7897460973826355,
          0.7651624906419096,
          0.7391492660155947,
          0.712251255767055,
          0.6842627220082353,
          0.6549367642299598,
          0.6248876024942259,
          0.5935729839685073,
          0.5616487834543701,
          0.5288644230817857,
          0.49493685831629225,
          0.4605766962740518,
          0.42516389849968406,
          0.38944018363533817,
          0.3531197639646806,
          0.3158943301675745,
          0.2785435723044175,
          0.240393495879133,
          0.20224316189935718,
          0.16378255767854671,
          0.12468996124772275,
          0.08578418164551113,
          0.046363175465321656,
          0.0072526350835346275,
          -0.031869760026438106,
          -0.07132677550089878,
          -0.11029195776036814,
          -0.14946841042608855,
          -0.18803555208749229,
          -0.2263156206518644,
          -0.2646200163083257,
          -0.30214641787387303,
          -0.3395719576152655,
          -0.3761127199251372,
          -0.41207847386296487,
          -0.44775728372963675,
          -0.4824018186770393,
          -0.5166372065095904,
          -0.5497463505736847,
          -0.5820146462622245,
          -0.6136957518586899,
          -0.6441260761245824,
          -0.6738547108934564,
          -0.7022589656849362,
          -0.729588896337485,
          -0.7560540108434458,
          -0.7810999855156909,
          -0.805178771537758,
          -0.8277860366438315,
          -0.8491268900235692,
          -0.8693586435188625,
          -0.8880575566763789,
          -0.9055610733112078,
          -0.9215026062664929,
          -0.9360344367357188,
          -0.94925563920267,
          -0.9608893334286173,
          -0.9711454934539763,
          -0.9798093491625617,
          -0.9869744999358654,
          -0.9926779765793458,
          -0.9968003719033315,
          -0.9994161291102647,
          -1.0004705149405615,
          -0.9999948468538877,
          -0.9979626873304506,
          -0.994416651593747,
          -0.9892928013247768,
          -0.9826985029596625,
          -0.9746015866890261,
          -0.9649131607527826,
          -0.9538361868575962,
          -0.9411708134646126,
          -0.9271823463033524,
          -0.911776366091078,
          -0.894804942788866,
          -0.87662355896262,
          -0.8569041405358354,
          -0.836059717832914,
          -0.8139372554706432,
          -0.7903354722957937,
          -0.765748702421108,
          -0.7397332650091435,
          -0.7128340415468708,
          -0.6848452694110645,
          -0.655520057669771,
          -0.625472606668038,
          -0.5941606908654385,
          -0.5622401284693431,
          -0.5294603660327677,
          -0.49553843673024656,
          -0.46118488625844345,
          -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
        ]
      }
    }
  ]
}