RANS CRM wing 2-D data set

import numpy as np


raw = np.array(
    [
        [
            2.000000000000000000e00,
            4.500000000000000111e-01,
            1.536799999999999972e-02,
            3.674239999999999728e-01,
            5.592279999999999474e-01,
            -1.258039999999999992e-01,
            -1.248699999999999984e-02,
        ],
        [
            3.500000000000000000e00,
            4.500000000000000111e-01,
            1.985100000000000059e-02,
            4.904470000000000218e-01,
            7.574600000000000222e-01,
            -1.615260000000000029e-01,
            8.987000000000000197e-03,
        ],
        [
            5.000000000000000000e00,
            4.500000000000000111e-01,
            2.571000000000000021e-02,
            6.109189999999999898e-01,
            9.497949999999999449e-01,
            -1.954619999999999969e-01,
            4.090900000000000092e-02,
        ],
        [
            6.500000000000000000e00,
            4.500000000000000111e-01,
            3.304200000000000192e-02,
            7.266120000000000356e-01,
            1.131138999999999895e00,
            -2.255890000000000117e-01,
            8.185399999999999621e-02,
        ],
        [
            8.000000000000000000e00,
            4.500000000000000111e-01,
            4.318999999999999923e-02,
            8.247250000000000414e-01,
            1.271487000000000034e00,
            -2.397040000000000004e-01,
            1.217659999999999992e-01,
        ],
        [
            0.000000000000000000e00,
            5.799999999999999600e-01,
            1.136200000000000057e-02,
            2.048760000000000026e-01,
            2.950280000000000125e-01,
            -7.882100000000000217e-02,
            -2.280099999999999835e-02,
        ],
        [
            1.500000000000000000e00,
            5.799999999999999600e-01,
            1.426000000000000011e-02,
            3.375619999999999732e-01,
            5.114130000000000065e-01,
            -1.189420000000000061e-01,
            -1.588200000000000028e-02,
        ],
        [
            3.000000000000000000e00,
            5.799999999999999600e-01,
            1.866400000000000003e-02,
            4.687450000000000228e-01,
            7.240400000000000169e-01,
            -1.577669999999999906e-01,
            3.099999999999999891e-03,
        ],
        [
            4.500000000000000000e00,
            5.799999999999999600e-01,
            2.461999999999999952e-02,
            5.976639999999999731e-01,
            9.311709999999999710e-01,
            -1.944160000000000055e-01,
            3.357500000000000068e-02,
        ],
        [
            6.000000000000000000e00,
            5.799999999999999600e-01,
            3.280700000000000283e-02,
            7.142249999999999988e-01,
            1.111707999999999918e00,
            -2.205870000000000053e-01,
            7.151699999999999724e-02,
        ],
        [
            0.000000000000000000e00,
            6.800000000000000488e-01,
            1.138800000000000055e-02,
            2.099310000000000065e-01,
            3.032230000000000203e-01,
            -8.187899999999999345e-02,
            -2.172699999999999979e-02,
        ],
        [
            1.500000000000000000e00,
            6.800000000000000488e-01,
            1.458699999999999927e-02,
            3.518569999999999753e-01,
            5.356630000000000003e-01,
            -1.257649999999999879e-01,
            -1.444800000000000077e-02,
        ],
        [
            3.000000000000000000e00,
            6.800000000000000488e-01,
            1.952800000000000022e-02,
            4.924879999999999813e-01,
            7.644769999999999621e-01,
            -1.678040000000000087e-01,
            6.023999999999999841e-03,
        ],
        [
            4.500000000000000000e00,
            6.800000000000000488e-01,
            2.666699999999999973e-02,
            6.270339999999999803e-01,
            9.801630000000000065e-01,
            -2.035240000000000105e-01,
            3.810000000000000192e-02,
        ],
        [
            6.000000000000000000e00,
            6.800000000000000488e-01,
            3.891800000000000120e-02,
            7.172730000000000494e-01,
            1.097855999999999943e00,
            -2.014620000000000022e-01,
            6.640000000000000069e-02,
        ],
        [
            0.000000000000000000e00,
            7.500000000000000000e-01,
            1.150699999999999987e-02,
            2.149069999999999869e-01,
            3.115740000000000176e-01,
            -8.498999999999999611e-02,
            -2.057700000000000154e-02,
        ],
        [
            1.250000000000000000e00,
            7.500000000000000000e-01,
            1.432600000000000019e-02,
            3.415969999999999840e-01,
            5.199390000000000400e-01,
            -1.251009999999999900e-01,
            -1.515400000000000080e-02,
        ],
        [
            2.500000000000000000e00,
            7.500000000000000000e-01,
            1.856000000000000011e-02,
            4.677589999999999804e-01,
            7.262499999999999512e-01,
            -1.635169999999999957e-01,
            3.989999999999999949e-04,
        ],
        [
            3.750000000000000000e00,
            7.500000000000000000e-01,
            2.472399999999999945e-02,
            5.911459999999999493e-01,
            9.254930000000000101e-01,
            -1.966150000000000120e-01,
            2.524900000000000061e-02,
        ],
        [
            5.000000000000000000e00,
            7.500000000000000000e-01,
            3.506800000000000195e-02,
            7.047809999999999908e-01,
            1.097736000000000045e00,
            -2.143069999999999975e-01,
            5.321300000000000335e-02,
        ],
        [
            0.000000000000000000e00,
            8.000000000000000444e-01,
            1.168499999999999921e-02,
            2.196390000000000009e-01,
            3.197160000000000002e-01,
            -8.798200000000000465e-02,
            -1.926999999999999894e-02,
        ],
        [
            1.250000000000000000e00,
            8.000000000000000444e-01,
            1.481599999999999931e-02,
            3.553939999999999877e-01,
            5.435950000000000504e-01,
            -1.317419999999999980e-01,
            -1.345599999999999921e-02,
        ],
        [
            2.500000000000000000e00,
            8.000000000000000444e-01,
            1.968999999999999917e-02,
            4.918299999999999894e-01,
            7.669930000000000359e-01,
            -1.728079999999999894e-01,
            3.756999999999999923e-03,
        ],
        [
            3.750000000000000000e00,
            8.000000000000000444e-01,
            2.785599999999999882e-02,
            6.324319999999999942e-01,
            9.919249999999999456e-01,
            -2.077100000000000057e-01,
            3.159800000000000109e-02,
        ],
        [
            5.000000000000000000e00,
            8.000000000000000444e-01,
            4.394300000000000289e-02,
            7.650689999999999991e-01,
            1.188355999999999968e00,
            -2.332680000000000031e-01,
            5.645000000000000018e-02,
        ],
        [
            0.000000000000000000e00,
            8.299999999999999600e-01,
            1.186100000000000002e-02,
            2.232899999999999885e-01,
            3.261100000000000110e-01,
            -9.028400000000000314e-02,
            -1.806500000000000120e-02,
        ],
        [
            1.000000000000000000e00,
            8.299999999999999600e-01,
            1.444900000000000004e-02,
            3.383419999999999761e-01,
            5.161710000000000464e-01,
            -1.279530000000000112e-01,
            -1.402400000000000001e-02,
        ],
        [
            2.000000000000000000e00,
            8.299999999999999600e-01,
            1.836799999999999891e-02,
            4.554270000000000262e-01,
            7.082190000000000429e-01,
            -1.642339999999999911e-01,
            -1.793000000000000106e-03,
        ],
        [
            3.000000000000000000e00,
            8.299999999999999600e-01,
            2.466899999999999996e-02,
            5.798410000000000508e-01,
            9.088819999999999677e-01,
            -2.004589999999999983e-01,
            1.892900000000000138e-02,
        ],
        [
            4.000000000000000000e00,
            8.299999999999999600e-01,
            3.700400000000000217e-02,
            7.012720000000000065e-01,
            1.097366000000000064e00,
            -2.362420000000000075e-01,
            3.750699999999999867e-02,
        ],
        [
            0.000000000000000000e00,
            8.599999999999999867e-01,
            1.224300000000000041e-02,
            2.278100000000000125e-01,
            3.342720000000000136e-01,
            -9.307600000000000595e-02,
            -1.608400000000000107e-02,
        ],
        [
            1.000000000000000000e00,
            8.599999999999999867e-01,
            1.540700000000000056e-02,
            3.551839999999999997e-01,
            5.433130000000000459e-01,
            -1.364730000000000110e-01,
            -1.162200000000000039e-02,
        ],
        [
            2.000000000000000000e00,
            8.599999999999999867e-01,
            2.122699999999999934e-02,
            4.854620000000000046e-01,
            7.552919999999999634e-01,
            -1.817850000000000021e-01,
            1.070999999999999903e-03,
        ],
        [
            3.000000000000000000e00,
            8.599999999999999867e-01,
            3.178899999999999781e-02,
            6.081849999999999756e-01,
            9.510380000000000500e-01,
            -2.252020000000000133e-01,
            1.540799999999999982e-02,
        ],
        [
            4.000000000000000000e00,
            8.599999999999999867e-01,
            4.744199999999999806e-02,
            6.846989999999999466e-01,
            1.042564000000000046e00,
            -2.333600000000000119e-01,
            2.035400000000000056e-02,
        ],
    ]
)


def get_rans_crm_wing():
    # data structure:
    # alpha, mach, cd, cl, cmx, cmy, cmz

    deg2rad = np.pi / 180.0

    xt = np.array(raw[:, 0:2])
    yt = np.array(raw[:, 2:4])
    xlimits = np.array([[-3.0, 10.0], [0.4, 0.90]])

    xt[:, 0] *= deg2rad
    xlimits[0, :] *= deg2rad

    return xt, yt, xlimits


def plot_rans_crm_wing(xt, yt, limits, interp):
    import numpy as np
    import matplotlib

    matplotlib.use("Agg")
    import matplotlib.pyplot as plt

    rad2deg = 180.0 / np.pi

    num = 500
    num_a = 50
    num_M = 50

    x = np.zeros((num, 2))
    colors = ["b", "g", "r", "c", "m", "k", "y"]

    nrow = 3
    ncol = 2
    plt.close()
    fig, axs = plt.subplots(nrow, ncol, figsize=(15, 15))

    # -----------------------------------------------------------------------------

    mach_numbers = [0.45, 0.68, 0.80, 0.86]
    legend_entries = []

    alpha_sweep = np.linspace(0.0, 8.0, num)

    for ind, mach in enumerate(mach_numbers):
        x[:, 0] = alpha_sweep / rad2deg
        x[:, 1] = mach
        CD = interp.predict_values(x)[:, 0]
        CL = interp.predict_values(x)[:, 1]

        mask = np.abs(xt[:, 1] - mach) < 1e-10
        axs[0, 0].plot(xt[mask, 0] * rad2deg, yt[mask, 0], "o" + colors[ind])
        axs[0, 0].plot(alpha_sweep, CD, colors[ind])

        mask = np.abs(xt[:, 1] - mach) < 1e-10
        axs[0, 1].plot(xt[mask, 0] * rad2deg, yt[mask, 1], "o" + colors[ind])
        axs[0, 1].plot(alpha_sweep, CL, colors[ind])

        legend_entries.append("M={}".format(mach))
        legend_entries.append("exact")

    axs[0, 0].set(xlabel="alpha (deg)", ylabel="CD")
    axs[0, 0].legend(legend_entries)

    axs[0, 1].set(xlabel="alpha (deg)", ylabel="CL")
    axs[0, 1].legend(legend_entries)

    # -----------------------------------------------------------------------------

    alphas = [2.0, 4.0, 6.0]
    legend_entries = []

    mach_sweep = np.linspace(0.45, 0.86, num)

    for ind, alpha in enumerate(alphas):
        x[:, 0] = alpha / rad2deg
        x[:, 1] = mach_sweep
        CD = interp.predict_values(x)[:, 0]
        CL = interp.predict_values(x)[:, 1]

        axs[1, 0].plot(mach_sweep, CD, colors[ind])
        axs[1, 1].plot(mach_sweep, CL, colors[ind])

        legend_entries.append("alpha={}".format(alpha))

    axs[1, 0].set(xlabel="Mach number", ylabel="CD")
    axs[1, 0].legend(legend_entries)

    axs[1, 1].set(xlabel="Mach number", ylabel="CL")
    axs[1, 1].legend(legend_entries)

    # -----------------------------------------------------------------------------

    x = np.zeros((num_a, num_M, 2))
    x[:, :, 0] = np.outer(np.linspace(0.0, 8.0, num_a), np.ones(num_M)) / rad2deg
    x[:, :, 1] = np.outer(np.ones(num_a), np.linspace(0.45, 0.86, num_M))
    CD = interp.predict_values(x.reshape((num_a * num_M, 2)))[:, 0].reshape(
        (num_a, num_M)
    )
    CL = interp.predict_values(x.reshape((num_a * num_M, 2)))[:, 1].reshape(
        (num_a, num_M)
    )

    axs[2, 0].plot(xt[:, 1], xt[:, 0] * rad2deg, "o")
    axs[2, 0].contour(x[:, :, 1], x[:, :, 0] * rad2deg, CD, 20)
    pcm1 = axs[2, 0].pcolormesh(
        x[:, :, 1],
        x[:, :, 0] * rad2deg,
        CD,
        cmap=plt.get_cmap("rainbow"),
        shading="auto",
    )
    fig.colorbar(pcm1, ax=axs[2, 0])
    axs[2, 0].set(xlabel="Mach number", ylabel="alpha (deg)")
    axs[2, 0].set_title("CD")

    axs[2, 1].plot(xt[:, 1], xt[:, 0] * rad2deg, "o")
    axs[2, 1].contour(x[:, :, 1], x[:, :, 0] * rad2deg, CL, 20)
    pcm2 = axs[2, 1].pcolormesh(
        x[:, :, 1],
        x[:, :, 0] * rad2deg,
        CL,
        cmap=plt.get_cmap("rainbow"),
        shading="auto",
    )
    fig.colorbar(pcm2, ax=axs[2, 1])
    axs[2, 1].set(xlabel="Mach number", ylabel="alpha (deg)")
    axs[2, 1].set_title("CL")

    plt.show()

RMTB

from smt.surrogate_models import RMTB
from smt.examples.rans_crm_wing.rans_crm_wing import (
    get_rans_crm_wing,
    plot_rans_crm_wing,
)

xt, yt, xlimits = get_rans_crm_wing()

interp = RMTB(
    num_ctrl_pts=20, xlimits=xlimits, nonlinear_maxiter=100, energy_weight=1e-12
)
interp.set_training_values(xt, yt)
interp.train()

plot_rans_crm_wing(xt, yt, xlimits, interp)
___________________________________________________________________________

                                   RMTB
___________________________________________________________________________

 Problem size

      # training points.        : 35

___________________________________________________________________________

 Training

   Training ...
      Pre-computing matrices ...
         Computing dof2coeff ...
         Computing dof2coeff - done. Time (sec):  0.0000010
         Initializing Hessian ...
         Initializing Hessian - done. Time (sec):  0.0001640
         Computing energy terms ...
         Computing energy terms - done. Time (sec):  0.0015941
         Computing approximation terms ...
         Computing approximation terms - done. Time (sec):  0.0001333
      Pre-computing matrices - done. Time (sec):  0.0019090
      Solving for degrees of freedom ...
         Solving initial startup problem (n=400) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 9.429150220e-02 1.114942861e-02
               Iteration (num., iy, grad. norm, func.) :   0   0 5.411685665e-09 1.793038265e-10
            Solving for output 0 - done. Time (sec):  0.0034111
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 1.955493282e+00 4.799845498e+00
               Iteration (num., iy, grad. norm, func.) :   0   1 1.152882116e-06 4.567837893e-08
            Solving for output 1 - done. Time (sec):  0.0032072
         Solving initial startup problem (n=400) - done. Time (sec):  0.0066359
         Solving nonlinear problem (n=400) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 6.652710113e-09 1.793037477e-10
               Iteration (num., iy, grad. norm, func.) :   0   0 5.849768196e-09 1.703944261e-10
               Iteration (num., iy, grad. norm, func.) :   1   0 3.016454001e-08 1.031027582e-10
               Iteration (num., iy, grad. norm, func.) :   2   0 1.124710921e-08 2.503452196e-11
               Iteration (num., iy, grad. norm, func.) :   3   0 3.558936270e-09 1.052011492e-11
               Iteration (num., iy, grad. norm, func.) :   4   0 2.498908321e-09 9.513167500e-12
               Iteration (num., iy, grad. norm, func.) :   5   0 7.337648484e-10 7.423057662e-12
               Iteration (num., iy, grad. norm, func.) :   6   0 2.035878919e-10 6.536207916e-12
               Iteration (num., iy, grad. norm, func.) :   7   0 4.339677721e-11 6.262717357e-12
               Iteration (num., iy, grad. norm, func.) :   8   0 2.610301695e-11 6.261662965e-12
               Iteration (num., iy, grad. norm, func.) :   9   0 1.543232359e-11 6.260740582e-12
               Iteration (num., iy, grad. norm, func.) :  10   0 1.329544861e-11 6.260413869e-12
               Iteration (num., iy, grad. norm, func.) :  11   0 3.816926844e-12 6.256688224e-12
               Iteration (num., iy, grad. norm, func.) :  12   0 5.374725819e-13 6.255690501e-12
            Solving for output 0 - done. Time (sec):  0.0417490
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 9.727807753e-08 4.567646553e-08
               Iteration (num., iy, grad. norm, func.) :   0   1 9.336806869e-08 4.538213478e-08
               Iteration (num., iy, grad. norm, func.) :   1   1 2.895998969e-06 3.242270961e-08
               Iteration (num., iy, grad. norm, func.) :   2   1 8.585632456e-07 4.646623688e-09
               Iteration (num., iy, grad. norm, func.) :   3   1 2.739253784e-07 2.027009051e-09
               Iteration (num., iy, grad. norm, func.) :   4   1 2.525438576e-07 1.844466417e-09
               Iteration (num., iy, grad. norm, func.) :   5   1 7.493959631e-08 5.722361822e-10
               Iteration (num., iy, grad. norm, func.) :   6   1 8.096618492e-08 5.722012169e-10
               Iteration (num., iy, grad. norm, func.) :   7   1 2.391970442e-08 4.570786542e-10
               Iteration (num., iy, grad. norm, func.) :   8   1 4.025741805e-08 4.502724092e-10
               Iteration (num., iy, grad. norm, func.) :   9   1 1.205755219e-08 3.321741389e-10
               Iteration (num., iy, grad. norm, func.) :  10   1 5.915127060e-09 2.852783181e-10
               Iteration (num., iy, grad. norm, func.) :  11   1 1.748395965e-09 2.745189928e-10
               Iteration (num., iy, grad. norm, func.) :  12   1 1.020332111e-09 2.737098068e-10
               Iteration (num., iy, grad. norm, func.) :  13   1 2.958281615e-10 2.718558829e-10
               Iteration (num., iy, grad. norm, func.) :  14   1 1.244706534e-10 2.716147626e-10
               Iteration (num., iy, grad. norm, func.) :  15   1 9.612939394e-11 2.715864299e-10
               Iteration (num., iy, grad. norm, func.) :  16   1 4.817932290e-11 2.715105634e-10
               Iteration (num., iy, grad. norm, func.) :  17   1 5.807039247e-11 2.713914627e-10
               Iteration (num., iy, grad. norm, func.) :  18   1 1.172706159e-11 2.713663434e-10
               Iteration (num., iy, grad. norm, func.) :  19   1 1.038579664e-11 2.713659144e-10
               Iteration (num., iy, grad. norm, func.) :  20   1 1.441052598e-11 2.713605352e-10
               Iteration (num., iy, grad. norm, func.) :  21   1 1.183446666e-11 2.713500816e-10
               Iteration (num., iy, grad. norm, func.) :  22   1 7.124663001e-12 2.713459092e-10
               Iteration (num., iy, grad. norm, func.) :  23   1 4.711945231e-12 2.713455589e-10
               Iteration (num., iy, grad. norm, func.) :  24   1 6.028427248e-12 2.713455455e-10
               Iteration (num., iy, grad. norm, func.) :  25   1 2.445826614e-12 2.713453556e-10
               Iteration (num., iy, grad. norm, func.) :  26   1 2.370128840e-12 2.713452445e-10
               Iteration (num., iy, grad. norm, func.) :  27   1 1.338409467e-12 2.713451003e-10
               Iteration (num., iy, grad. norm, func.) :  28   1 1.406364883e-12 2.713450026e-10
               Iteration (num., iy, grad. norm, func.) :  29   1 5.971131896e-13 2.713449643e-10
            Solving for output 1 - done. Time (sec):  0.0959361
         Solving nonlinear problem (n=400) - done. Time (sec):  0.1377010
      Solving for degrees of freedom - done. Time (sec):  0.1443558
   Training - done. Time (sec):  0.1464341
___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001869

   Prediction time/pt. (sec) :  0.0000004

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001459

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001600

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001431

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001538

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001421

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001521

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001428

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001850

   Prediction time/pt. (sec) :  0.0000004

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001442

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001619

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001411

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001600

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0001409

   Prediction time/pt. (sec) :  0.0000003

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0004799

   Prediction time/pt. (sec) :  0.0000002

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0011289

   Prediction time/pt. (sec) :  0.0000005
../../../_images/rans_crm_wing.png

RMTC

from smt.surrogate_models import RMTC
from smt.examples.rans_crm_wing.rans_crm_wing import (
    get_rans_crm_wing,
    plot_rans_crm_wing,
)

xt, yt, xlimits = get_rans_crm_wing()

interp = RMTC(
    num_elements=20, xlimits=xlimits, nonlinear_maxiter=100, energy_weight=1e-10
)
interp.set_training_values(xt, yt)
interp.train()

plot_rans_crm_wing(xt, yt, xlimits, interp)
___________________________________________________________________________

                                   RMTC
___________________________________________________________________________

 Problem size

      # training points.        : 35

___________________________________________________________________________

 Training

   Training ...
      Pre-computing matrices ...
         Computing dof2coeff ...
         Computing dof2coeff - done. Time (sec):  0.0019720
         Initializing Hessian ...
         Initializing Hessian - done. Time (sec):  0.0001159
         Computing energy terms ...
         Computing energy terms - done. Time (sec):  0.0067520
         Computing approximation terms ...
         Computing approximation terms - done. Time (sec):  0.0003111
      Pre-computing matrices - done. Time (sec):  0.0091741
      Solving for degrees of freedom ...
         Solving initial startup problem (n=1764) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 1.279175539e-01 1.114942861e-02
               Iteration (num., iy, grad. norm, func.) :   0   0 1.259282070e-05 2.109789960e-08
            Solving for output 0 - done. Time (sec):  0.0191290
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 2.653045755e+00 4.799845498e+00
               Iteration (num., iy, grad. norm, func.) :   0   1 1.761847844e-04 6.478283527e-06
            Solving for output 1 - done. Time (sec):  0.0228369
         Solving initial startup problem (n=1764) - done. Time (sec):  0.0419991
         Solving nonlinear problem (n=1764) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 8.276687703e-07 2.096801653e-08
               Iteration (num., iy, grad. norm, func.) :   0   0 8.884396364e-07 1.662418478e-08
               Iteration (num., iy, grad. norm, func.) :   1   0 3.441659572e-07 3.191045347e-09
               Iteration (num., iy, grad. norm, func.) :   2   0 1.140278790e-07 1.028877472e-09
               Iteration (num., iy, grad. norm, func.) :   3   0 6.030827518e-08 5.275940591e-10
               Iteration (num., iy, grad. norm, func.) :   4   0 3.583981959e-08 4.129899689e-10
               Iteration (num., iy, grad. norm, func.) :   5   0 2.344765464e-08 3.785491285e-10
               Iteration (num., iy, grad. norm, func.) :   6   0 2.061895441e-08 3.748079064e-10
               Iteration (num., iy, grad. norm, func.) :   7   0 2.042895792e-08 3.737771607e-10
               Iteration (num., iy, grad. norm, func.) :   8   0 1.357907469e-08 3.613254590e-10
               Iteration (num., iy, grad. norm, func.) :   9   0 1.767294044e-08 3.411338356e-10
               Iteration (num., iy, grad. norm, func.) :  10   0 5.748755700e-09 3.049820275e-10
               Iteration (num., iy, grad. norm, func.) :  11   0 2.156169312e-09 2.891117507e-10
               Iteration (num., iy, grad. norm, func.) :  12   0 1.772786849e-09 2.876566274e-10
               Iteration (num., iy, grad. norm, func.) :  13   0 2.160274001e-09 2.876190655e-10
               Iteration (num., iy, grad. norm, func.) :  14   0 1.490064700e-09 2.874904937e-10
               Iteration (num., iy, grad. norm, func.) :  15   0 3.400329977e-09 2.872663534e-10
               Iteration (num., iy, grad. norm, func.) :  16   0 4.316611682e-10 2.867323229e-10
               Iteration (num., iy, grad. norm, func.) :  17   0 2.489681985e-10 2.867302148e-10
               Iteration (num., iy, grad. norm, func.) :  18   0 6.291419172e-10 2.866941738e-10
               Iteration (num., iy, grad. norm, func.) :  19   0 4.837469835e-10 2.866369249e-10
               Iteration (num., iy, grad. norm, func.) :  20   0 9.283861527e-10 2.865862017e-10
               Iteration (num., iy, grad. norm, func.) :  21   0 2.382079194e-10 2.865391052e-10
               Iteration (num., iy, grad. norm, func.) :  22   0 1.894975509e-10 2.865387665e-10
               Iteration (num., iy, grad. norm, func.) :  23   0 2.405852922e-10 2.865336296e-10
               Iteration (num., iy, grad. norm, func.) :  24   0 3.070573255e-10 2.865218301e-10
               Iteration (num., iy, grad. norm, func.) :  25   0 2.613049980e-10 2.865083846e-10
               Iteration (num., iy, grad. norm, func.) :  26   0 1.308482667e-10 2.865009386e-10
               Iteration (num., iy, grad. norm, func.) :  27   0 1.220979706e-10 2.865007984e-10
               Iteration (num., iy, grad. norm, func.) :  28   0 1.122777786e-10 2.865001450e-10
               Iteration (num., iy, grad. norm, func.) :  29   0 1.726789770e-10 2.864981347e-10
               Iteration (num., iy, grad. norm, func.) :  30   0 1.123446546e-10 2.864961197e-10
               Iteration (num., iy, grad. norm, func.) :  31   0 5.980430076e-11 2.864952870e-10
               Iteration (num., iy, grad. norm, func.) :  32   0 8.090859615e-11 2.864949463e-10
               Iteration (num., iy, grad. norm, func.) :  33   0 5.936596229e-11 2.864944374e-10
               Iteration (num., iy, grad. norm, func.) :  34   0 7.832680381e-11 2.864939276e-10
               Iteration (num., iy, grad. norm, func.) :  35   0 5.663067016e-11 2.864936254e-10
               Iteration (num., iy, grad. norm, func.) :  36   0 6.548138612e-11 2.864934878e-10
               Iteration (num., iy, grad. norm, func.) :  37   0 4.248302932e-11 2.864932808e-10
               Iteration (num., iy, grad. norm, func.) :  38   0 5.706961646e-11 2.864928701e-10
               Iteration (num., iy, grad. norm, func.) :  39   0 1.205490677e-11 2.864925499e-10
               Iteration (num., iy, grad. norm, func.) :  40   0 9.779697544e-12 2.864925497e-10
               Iteration (num., iy, grad. norm, func.) :  41   0 1.505135051e-11 2.864925379e-10
               Iteration (num., iy, grad. norm, func.) :  42   0 1.750117773e-11 2.864925219e-10
               Iteration (num., iy, grad. norm, func.) :  43   0 2.276253977e-11 2.864925175e-10
               Iteration (num., iy, grad. norm, func.) :  44   0 1.242486043e-11 2.864925038e-10
               Iteration (num., iy, grad. norm, func.) :  45   0 1.277909442e-11 2.864924940e-10
               Iteration (num., iy, grad. norm, func.) :  46   0 9.270563472e-12 2.864924721e-10
               Iteration (num., iy, grad. norm, func.) :  47   0 1.423173424e-11 2.864924524e-10
               Iteration (num., iy, grad. norm, func.) :  48   0 6.618598844e-12 2.864924381e-10
               Iteration (num., iy, grad. norm, func.) :  49   0 8.612779828e-12 2.864924362e-10
               Iteration (num., iy, grad. norm, func.) :  50   0 8.016201180e-12 2.864924360e-10
               Iteration (num., iy, grad. norm, func.) :  51   0 9.905043751e-12 2.864924334e-10
               Iteration (num., iy, grad. norm, func.) :  52   0 5.314899333e-12 2.864924283e-10
               Iteration (num., iy, grad. norm, func.) :  53   0 7.643978239e-12 2.864924247e-10
               Iteration (num., iy, grad. norm, func.) :  54   0 3.062729209e-12 2.864924217e-10
               Iteration (num., iy, grad. norm, func.) :  55   0 5.222165609e-12 2.864924204e-10
               Iteration (num., iy, grad. norm, func.) :  56   0 2.729961166e-12 2.864924193e-10
               Iteration (num., iy, grad. norm, func.) :  57   0 4.296941506e-12 2.864924190e-10
               Iteration (num., iy, grad. norm, func.) :  58   0 2.253107949e-12 2.864924181e-10
               Iteration (num., iy, grad. norm, func.) :  59   0 2.888295706e-12 2.864924176e-10
               Iteration (num., iy, grad. norm, func.) :  60   0 1.474836055e-12 2.864924169e-10
               Iteration (num., iy, grad. norm, func.) :  61   0 2.005862349e-12 2.864924165e-10
               Iteration (num., iy, grad. norm, func.) :  62   0 1.072143325e-12 2.864924162e-10
               Iteration (num., iy, grad. norm, func.) :  63   0 1.293356797e-12 2.864924161e-10
               Iteration (num., iy, grad. norm, func.) :  64   0 8.918332384e-13 2.864924160e-10
            Solving for output 0 - done. Time (sec):  0.7125902
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 1.384935414e-05 6.453687706e-06
               Iteration (num., iy, grad. norm, func.) :   0   1 1.388050335e-05 6.210060496e-06
               Iteration (num., iy, grad. norm, func.) :   1   1 1.452494640e-05 8.014959585e-07
               Iteration (num., iy, grad. norm, func.) :   2   1 1.903208528e-05 3.734712156e-07
               Iteration (num., iy, grad. norm, func.) :   3   1 5.737186337e-06 1.281344686e-07
               Iteration (num., iy, grad. norm, func.) :   4   1 4.457389321e-06 9.689222211e-08
               Iteration (num., iy, grad. norm, func.) :   5   1 1.372969382e-06 3.543782462e-08
               Iteration (num., iy, grad. norm, func.) :   6   1 7.024568652e-07 2.906732291e-08
               Iteration (num., iy, grad. norm, func.) :   7   1 5.433786024e-07 2.860360694e-08
               Iteration (num., iy, grad. norm, func.) :   8   1 4.358777169e-07 2.801530768e-08
               Iteration (num., iy, grad. norm, func.) :   9   1 1.955146494e-07 2.256768273e-08
               Iteration (num., iy, grad. norm, func.) :  10   1 8.458938107e-08 1.740128028e-08
               Iteration (num., iy, grad. norm, func.) :  11   1 3.373930461e-08 1.493369323e-08
               Iteration (num., iy, grad. norm, func.) :  12   1 3.979022494e-08 1.482361019e-08
               Iteration (num., iy, grad. norm, func.) :  13   1 3.979022494e-08 1.482361019e-08
               Iteration (num., iy, grad. norm, func.) :  14   1 3.979022493e-08 1.482361019e-08
               Iteration (num., iy, grad. norm, func.) :  15   1 3.641259638e-08 1.472420600e-08
               Iteration (num., iy, grad. norm, func.) :  16   1 1.311420547e-08 1.457626468e-08
               Iteration (num., iy, grad. norm, func.) :  17   1 1.398441040e-08 1.453051901e-08
               Iteration (num., iy, grad. norm, func.) :  18   1 9.613776414e-09 1.450298372e-08
               Iteration (num., iy, grad. norm, func.) :  19   1 1.370861978e-08 1.449297649e-08
               Iteration (num., iy, grad. norm, func.) :  20   1 8.446713182e-09 1.448755140e-08
               Iteration (num., iy, grad. norm, func.) :  21   1 1.196851879e-08 1.448503531e-08
               Iteration (num., iy, grad. norm, func.) :  22   1 4.054368625e-09 1.447561126e-08
               Iteration (num., iy, grad. norm, func.) :  23   1 4.621687218e-09 1.447331134e-08
               Iteration (num., iy, grad. norm, func.) :  24   1 3.765764979e-09 1.447105093e-08
               Iteration (num., iy, grad. norm, func.) :  25   1 5.334804460e-09 1.446881592e-08
               Iteration (num., iy, grad. norm, func.) :  26   1 2.010772855e-09 1.446749825e-08
               Iteration (num., iy, grad. norm, func.) :  27   1 3.671998661e-09 1.446677921e-08
               Iteration (num., iy, grad. norm, func.) :  28   1 1.631139985e-09 1.446604962e-08
               Iteration (num., iy, grad. norm, func.) :  29   1 3.542826070e-09 1.446549400e-08
               Iteration (num., iy, grad. norm, func.) :  30   1 9.542027933e-10 1.446452047e-08
               Iteration (num., iy, grad. norm, func.) :  31   1 1.188067935e-09 1.446436111e-08
               Iteration (num., iy, grad. norm, func.) :  32   1 1.345782379e-09 1.446432277e-08
               Iteration (num., iy, grad. norm, func.) :  33   1 1.748189914e-09 1.446430390e-08
               Iteration (num., iy, grad. norm, func.) :  34   1 1.263414936e-09 1.446415024e-08
               Iteration (num., iy, grad. norm, func.) :  35   1 8.260416831e-10 1.446392531e-08
               Iteration (num., iy, grad. norm, func.) :  36   1 6.993097536e-10 1.446379220e-08
               Iteration (num., iy, grad. norm, func.) :  37   1 6.442625198e-10 1.446372212e-08
               Iteration (num., iy, grad. norm, func.) :  38   1 6.900070799e-10 1.446366233e-08
               Iteration (num., iy, grad. norm, func.) :  39   1 3.517489876e-10 1.446362519e-08
               Iteration (num., iy, grad. norm, func.) :  40   1 3.111249598e-10 1.446362319e-08
               Iteration (num., iy, grad. norm, func.) :  41   1 4.331118092e-10 1.446361597e-08
               Iteration (num., iy, grad. norm, func.) :  42   1 2.862868503e-10 1.446359627e-08
               Iteration (num., iy, grad. norm, func.) :  43   1 2.555239059e-10 1.446358032e-08
               Iteration (num., iy, grad. norm, func.) :  44   1 1.656608986e-10 1.446357153e-08
               Iteration (num., iy, grad. norm, func.) :  45   1 1.302415697e-10 1.446357078e-08
               Iteration (num., iy, grad. norm, func.) :  46   1 1.384920680e-10 1.446356968e-08
               Iteration (num., iy, grad. norm, func.) :  47   1 1.983734872e-10 1.446356687e-08
               Iteration (num., iy, grad. norm, func.) :  48   1 1.033395890e-10 1.446356410e-08
               Iteration (num., iy, grad. norm, func.) :  49   1 1.783105827e-10 1.446356267e-08
               Iteration (num., iy, grad. norm, func.) :  50   1 8.504372891e-11 1.446356183e-08
               Iteration (num., iy, grad. norm, func.) :  51   1 4.706446360e-11 1.446356146e-08
               Iteration (num., iy, grad. norm, func.) :  52   1 1.055612475e-10 1.446356060e-08
               Iteration (num., iy, grad. norm, func.) :  53   1 3.539377179e-11 1.446355980e-08
               Iteration (num., iy, grad. norm, func.) :  54   1 3.138627807e-11 1.446355979e-08
               Iteration (num., iy, grad. norm, func.) :  55   1 3.353947687e-11 1.446355973e-08
               Iteration (num., iy, grad. norm, func.) :  56   1 3.904821974e-11 1.446355954e-08
               Iteration (num., iy, grad. norm, func.) :  57   1 4.319046220e-11 1.446355931e-08
               Iteration (num., iy, grad. norm, func.) :  58   1 9.981051857e-12 1.446355926e-08
               Iteration (num., iy, grad. norm, func.) :  59   1 8.556448373e-12 1.446355926e-08
               Iteration (num., iy, grad. norm, func.) :  60   1 1.737515758e-11 1.446355925e-08
               Iteration (num., iy, grad. norm, func.) :  61   1 1.143123402e-11 1.446355921e-08
               Iteration (num., iy, grad. norm, func.) :  62   1 8.719484755e-12 1.446355918e-08
               Iteration (num., iy, grad. norm, func.) :  63   1 8.366045083e-12 1.446355918e-08
               Iteration (num., iy, grad. norm, func.) :  64   1 1.213927390e-11 1.446355916e-08
               Iteration (num., iy, grad. norm, func.) :  65   1 2.851868503e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  66   1 2.414465887e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  67   1 2.642020366e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  68   1 4.353645960e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  69   1 2.143032098e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  70   1 4.317214961e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  71   1 1.333262874e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  72   1 1.528597611e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  73   1 1.096969027e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  74   1 1.952531148e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  75   1 6.879998230e-13 1.446355915e-08
            Solving for output 1 - done. Time (sec):  0.7740831
         Solving nonlinear problem (n=1764) - done. Time (sec):  1.4867001
      Solving for degrees of freedom - done. Time (sec):  1.5287228
   Training - done. Time (sec):  1.5381517
___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002968

   Prediction time/pt. (sec) :  0.0000006

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002151

   Prediction time/pt. (sec) :  0.0000004

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002499

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002351

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002551

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002429

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002470

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002298

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002649

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002458

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002518

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002520

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002513

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0002391

   Prediction time/pt. (sec) :  0.0000005

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0008912

   Prediction time/pt. (sec) :  0.0000004

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0008621

   Prediction time/pt. (sec) :  0.0000003
../../../_images/rans_crm_wing.png