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 matplotlib
    import numpy as np

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

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):  0.0000000
         Initializing Hessian ...
         Initializing Hessian - done. Time (sec):  0.0000000
         Computing energy terms ...
         Computing energy terms - done. Time (sec):  0.0039933
         Computing approximation terms ...
         Computing approximation terms - done. Time (sec):  0.0000000
      Pre-computing matrices - done. Time (sec):  0.0039933
      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 6.229432982e-09 1.793038469e-10
            Solving for output 0 - done. Time (sec):  0.0055189
            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 2.880003477e-07 4.567660731e-08
            Solving for output 1 - done. Time (sec):  0.0049999
         Solving initial startup problem (n=400) - done. Time (sec):  0.0105188
         Solving nonlinear problem (n=400) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 6.652713506e-09 1.793037943e-10
               Iteration (num., iy, grad. norm, func.) :   0   0 5.849717047e-09 1.703954640e-10
               Iteration (num., iy, grad. norm, func.) :   1   0 3.028427146e-08 1.034023971e-10
               Iteration (num., iy, grad. norm, func.) :   2   0 1.125871064e-08 2.505156303e-11
               Iteration (num., iy, grad. norm, func.) :   3   0 3.657654439e-09 1.062711951e-11
               Iteration (num., iy, grad. norm, func.) :   4   0 2.384395507e-09 9.420573075e-12
               Iteration (num., iy, grad. norm, func.) :   5   0 6.795760320e-10 7.398469916e-12
               Iteration (num., iy, grad. norm, func.) :   6   0 1.893580345e-10 6.530836833e-12
               Iteration (num., iy, grad. norm, func.) :   7   0 3.914693345e-11 6.262121148e-12
               Iteration (num., iy, grad. norm, func.) :   8   0 2.607684883e-11 6.261389686e-12
               Iteration (num., iy, grad. norm, func.) :   9   0 1.596473148e-11 6.260468564e-12
               Iteration (num., iy, grad. norm, func.) :  10   0 8.775713015e-12 6.260124667e-12
               Iteration (num., iy, grad. norm, func.) :  11   0 3.358656828e-12 6.256629410e-12
               Iteration (num., iy, grad. norm, func.) :  12   0 5.210392100e-13 6.255688670e-12
            Solving for output 0 - done. Time (sec):  0.0631311
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 9.729377248e-08 4.567642993e-08
               Iteration (num., iy, grad. norm, func.) :   0   1 9.338363991e-08 4.538219456e-08
               Iteration (num., iy, grad. norm, func.) :   1   1 2.891391770e-06 3.242337200e-08
               Iteration (num., iy, grad. norm, func.) :   2   1 8.605107278e-07 4.652778039e-09
               Iteration (num., iy, grad. norm, func.) :   3   1 5.067375622e-07 2.745465684e-09
               Iteration (num., iy, grad. norm, func.) :   4   1 4.513840269e-07 2.455226693e-09
               Iteration (num., iy, grad. norm, func.) :   5   1 1.339167789e-07 6.881109113e-10
               Iteration (num., iy, grad. norm, func.) :   6   1 6.591489027e-08 5.500475184e-10
               Iteration (num., iy, grad. norm, func.) :   7   1 3.839790426e-08 4.862409238e-10
               Iteration (num., iy, grad. norm, func.) :   8   1 1.327787768e-08 4.053646260e-10
               Iteration (num., iy, grad. norm, func.) :   9   1 4.178809432e-09 3.129533457e-10
               Iteration (num., iy, grad. norm, func.) :  10   1 1.162280444e-09 2.724104537e-10
               Iteration (num., iy, grad. norm, func.) :  11   1 9.071092861e-10 2.722854123e-10
               Iteration (num., iy, grad. norm, func.) :  12   1 5.267790369e-10 2.722199641e-10
               Iteration (num., iy, grad. norm, func.) :  13   1 3.128933500e-10 2.721466104e-10
               Iteration (num., iy, grad. norm, func.) :  14   1 1.223449033e-10 2.716612344e-10
               Iteration (num., iy, grad. norm, func.) :  15   1 3.662769998e-11 2.714261096e-10
               Iteration (num., iy, grad. norm, func.) :  16   1 1.874681541e-11 2.713872039e-10
               Iteration (num., iy, grad. norm, func.) :  17   1 4.264650696e-11 2.713834397e-10
               Iteration (num., iy, grad. norm, func.) :  18   1 9.492032166e-12 2.713607454e-10
               Iteration (num., iy, grad. norm, func.) :  19   1 1.706167514e-11 2.713578816e-10
               Iteration (num., iy, grad. norm, func.) :  20   1 7.138581938e-12 2.713509077e-10
               Iteration (num., iy, grad. norm, func.) :  21   1 8.869098799e-12 2.713470556e-10
               Iteration (num., iy, grad. norm, func.) :  22   1 7.413215243e-12 2.713459004e-10
               Iteration (num., iy, grad. norm, func.) :  23   1 2.698341151e-12 2.713454840e-10
               Iteration (num., iy, grad. norm, func.) :  24   1 2.260359199e-12 2.713454159e-10
               Iteration (num., iy, grad. norm, func.) :  25   1 2.987484747e-12 2.713452000e-10
               Iteration (num., iy, grad. norm, func.) :  26   1 9.299976611e-13 2.713450184e-10
            Solving for output 1 - done. Time (sec):  0.1322930
         Solving nonlinear problem (n=400) - done. Time (sec):  0.1954241
      Solving for degrees of freedom - done. Time (sec):  0.2059429
   Training - done. Time (sec):  0.2109408
___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0010037

   Prediction time/pt. (sec) :  0.0000020

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0010016

   Prediction time/pt. (sec) :  0.0000020

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0010087

   Prediction time/pt. (sec) :  0.0000020

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0009997

   Prediction time/pt. (sec) :  0.0000004

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0009985

   Prediction time/pt. (sec) :  0.0000004
../../../_images/rans_crm_wing.png

RMTC

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

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):  0.0025086
         Initializing Hessian ...
         Initializing Hessian - done. Time (sec):  0.0000000
         Computing energy terms ...
         Computing energy terms - done. Time (sec):  0.0080247
         Computing approximation terms ...
         Computing approximation terms - done. Time (sec):  0.0010026
      Pre-computing matrices - done. Time (sec):  0.0115359
      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 2.575575620e-06 2.207577304e-08
            Solving for output 0 - done. Time (sec):  0.0190427
            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 5.806995269e-05 6.501953946e-06
            Solving for output 1 - done. Time (sec):  0.0120237
         Solving initial startup problem (n=1764) - done. Time (sec):  0.0310664
         Solving nonlinear problem (n=1764) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 8.737858409e-07 2.207058354e-08
               Iteration (num., iy, grad. norm, func.) :   0   0 9.583937937e-07 1.752349703e-08
               Iteration (num., iy, grad. norm, func.) :   1   0 3.546737468e-07 3.273320789e-09
               Iteration (num., iy, grad. norm, func.) :   2   0 1.183236974e-07 1.053100246e-09
               Iteration (num., iy, grad. norm, func.) :   3   0 6.339993507e-08 5.347470320e-10
               Iteration (num., iy, grad. norm, func.) :   4   0 3.374476763e-08 4.103939213e-10
               Iteration (num., iy, grad. norm, func.) :   5   0 2.244269022e-08 3.752837377e-10
               Iteration (num., iy, grad. norm, func.) :   6   0 1.965616160e-08 3.750955278e-10
               Iteration (num., iy, grad. norm, func.) :   7   0 1.527792816e-08 3.661190229e-10
               Iteration (num., iy, grad. norm, func.) :   8   0 1.694107204e-08 3.641575713e-10
               Iteration (num., iy, grad. norm, func.) :   9   0 1.400350042e-08 3.400159769e-10
               Iteration (num., iy, grad. norm, func.) :  10   0 8.618937187e-09 3.088359753e-10
               Iteration (num., iy, grad. norm, func.) :  11   0 2.752861021e-09 2.905779707e-10
               Iteration (num., iy, grad. norm, func.) :  12   0 2.459715986e-09 2.894122635e-10
               Iteration (num., iy, grad. norm, func.) :  13   0 2.459715986e-09 2.894122635e-10
               Iteration (num., iy, grad. norm, func.) :  14   0 2.459715986e-09 2.894122635e-10
               Iteration (num., iy, grad. norm, func.) :  15   0 3.790841098e-09 2.884227179e-10
               Iteration (num., iy, grad. norm, func.) :  16   0 7.660403189e-10 2.872925091e-10
               Iteration (num., iy, grad. norm, func.) :  17   0 1.462954522e-09 2.870607852e-10
               Iteration (num., iy, grad. norm, func.) :  18   0 9.736562709e-10 2.869808466e-10
               Iteration (num., iy, grad. norm, func.) :  19   0 9.254952451e-10 2.869603286e-10
               Iteration (num., iy, grad. norm, func.) :  20   0 8.664460782e-10 2.869027351e-10
               Iteration (num., iy, grad. norm, func.) :  21   0 1.082182834e-09 2.867531901e-10
               Iteration (num., iy, grad. norm, func.) :  22   0 7.203857332e-10 2.866272767e-10
               Iteration (num., iy, grad. norm, func.) :  23   0 3.764133529e-10 2.865649123e-10
               Iteration (num., iy, grad. norm, func.) :  24   0 3.282663853e-10 2.865624972e-10
               Iteration (num., iy, grad. norm, func.) :  25   0 4.358374191e-10 2.865622292e-10
               Iteration (num., iy, grad. norm, func.) :  26   0 4.203829589e-10 2.865539364e-10
               Iteration (num., iy, grad. norm, func.) :  27   0 4.236541716e-10 2.865430468e-10
               Iteration (num., iy, grad. norm, func.) :  28   0 2.549813945e-10 2.865278740e-10
               Iteration (num., iy, grad. norm, func.) :  29   0 3.175902813e-10 2.865200228e-10
               Iteration (num., iy, grad. norm, func.) :  30   0 1.818129781e-10 2.865131410e-10
               Iteration (num., iy, grad. norm, func.) :  31   0 2.432582109e-10 2.865037093e-10
               Iteration (num., iy, grad. norm, func.) :  32   0 8.721803489e-11 2.864965834e-10
               Iteration (num., iy, grad. norm, func.) :  33   0 7.322984911e-11 2.864965493e-10
               Iteration (num., iy, grad. norm, func.) :  34   0 8.732258237e-11 2.864961378e-10
               Iteration (num., iy, grad. norm, func.) :  35   0 8.804680263e-11 2.864954282e-10
               Iteration (num., iy, grad. norm, func.) :  36   0 8.914333813e-11 2.864951327e-10
               Iteration (num., iy, grad. norm, func.) :  37   0 8.038605550e-11 2.864948918e-10
               Iteration (num., iy, grad. norm, func.) :  38   0 1.211396047e-10 2.864945162e-10
               Iteration (num., iy, grad. norm, func.) :  39   0 4.409752418e-11 2.864938221e-10
               Iteration (num., iy, grad. norm, func.) :  40   0 5.330912907e-11 2.864934684e-10
               Iteration (num., iy, grad. norm, func.) :  41   0 3.762907472e-11 2.864932279e-10
               Iteration (num., iy, grad. norm, func.) :  42   0 5.711461398e-11 2.864930324e-10
               Iteration (num., iy, grad. norm, func.) :  43   0 2.453269461e-11 2.864928261e-10
               Iteration (num., iy, grad. norm, func.) :  44   0 3.736869281e-11 2.864928135e-10
               Iteration (num., iy, grad. norm, func.) :  45   0 2.321967355e-11 2.864927721e-10
               Iteration (num., iy, grad. norm, func.) :  46   0 3.910640430e-11 2.864927177e-10
               Iteration (num., iy, grad. norm, func.) :  47   0 1.788968560e-11 2.864926239e-10
               Iteration (num., iy, grad. norm, func.) :  48   0 2.002815893e-11 2.864925521e-10
               Iteration (num., iy, grad. norm, func.) :  49   0 1.180675297e-11 2.864925052e-10
               Iteration (num., iy, grad. norm, func.) :  50   0 1.941442472e-11 2.864925043e-10
               Iteration (num., iy, grad. norm, func.) :  51   0 1.146499516e-11 2.864925028e-10
               Iteration (num., iy, grad. norm, func.) :  52   0 1.650029728e-11 2.864924929e-10
               Iteration (num., iy, grad. norm, func.) :  53   0 1.070168524e-11 2.864924715e-10
               Iteration (num., iy, grad. norm, func.) :  54   0 1.177117044e-11 2.864924480e-10
               Iteration (num., iy, grad. norm, func.) :  55   0 4.190805945e-12 2.864924309e-10
               Iteration (num., iy, grad. norm, func.) :  56   0 3.466624617e-12 2.864924292e-10
               Iteration (num., iy, grad. norm, func.) :  57   0 4.187491808e-12 2.864924274e-10
               Iteration (num., iy, grad. norm, func.) :  58   0 4.908088917e-12 2.864924250e-10
               Iteration (num., iy, grad. norm, func.) :  59   0 6.094730716e-12 2.864924232e-10
               Iteration (num., iy, grad. norm, func.) :  60   0 3.555167666e-12 2.864924217e-10
               Iteration (num., iy, grad. norm, func.) :  61   0 4.667159382e-12 2.864924216e-10
               Iteration (num., iy, grad. norm, func.) :  62   0 2.758935157e-12 2.864924203e-10
               Iteration (num., iy, grad. norm, func.) :  63   0 4.025897384e-12 2.864924191e-10
               Iteration (num., iy, grad. norm, func.) :  64   0 1.886632298e-12 2.864924177e-10
               Iteration (num., iy, grad. norm, func.) :  65   0 2.858509935e-12 2.864924172e-10
               Iteration (num., iy, grad. norm, func.) :  66   0 1.505715565e-12 2.864924169e-10
               Iteration (num., iy, grad. norm, func.) :  67   0 2.664590083e-12 2.864924165e-10
               Iteration (num., iy, grad. norm, func.) :  68   0 8.712580952e-13 2.864924159e-10
            Solving for output 0 - done. Time (sec):  0.9173832
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 1.434042246e-05 6.499348875e-06
               Iteration (num., iy, grad. norm, func.) :   0   1 1.434144082e-05 6.252435785e-06
               Iteration (num., iy, grad. norm, func.) :   1   1 1.476589235e-05 8.057263488e-07
               Iteration (num., iy, grad. norm, func.) :   2   1 1.795902459e-05 3.606941390e-07
               Iteration (num., iy, grad. norm, func.) :   3   1 5.530739183e-06 1.259947411e-07
               Iteration (num., iy, grad. norm, func.) :   4   1 4.450520917e-06 9.727596048e-08
               Iteration (num., iy, grad. norm, func.) :   5   1 1.368980438e-06 3.501563197e-08
               Iteration (num., iy, grad. norm, func.) :   6   1 1.020853131e-06 3.008202531e-08
               Iteration (num., iy, grad. norm, func.) :   7   1 7.823302514e-07 2.972410388e-08
               Iteration (num., iy, grad. norm, func.) :   8   1 5.069636419e-07 2.921779973e-08
               Iteration (num., iy, grad. norm, func.) :   9   1 1.871226190e-07 2.355740343e-08
               Iteration (num., iy, grad. norm, func.) :  10   1 8.846817742e-08 1.806067121e-08
               Iteration (num., iy, grad. norm, func.) :  11   1 4.191727220e-08 1.505842598e-08
               Iteration (num., iy, grad. norm, func.) :  12   1 3.298523058e-08 1.477470833e-08
               Iteration (num., iy, grad. norm, func.) :  13   1 3.298523058e-08 1.477470833e-08
               Iteration (num., iy, grad. norm, func.) :  14   1 3.298523058e-08 1.477470833e-08
               Iteration (num., iy, grad. norm, func.) :  15   1 3.527910738e-08 1.467890057e-08
               Iteration (num., iy, grad. norm, func.) :  16   1 1.052194537e-08 1.453974951e-08
               Iteration (num., iy, grad. norm, func.) :  17   1 1.462841687e-08 1.451934915e-08
               Iteration (num., iy, grad. norm, func.) :  18   1 1.106621818e-08 1.450927248e-08
               Iteration (num., iy, grad. norm, func.) :  19   1 1.458451265e-08 1.449957379e-08
               Iteration (num., iy, grad. norm, func.) :  20   1 7.422220754e-09 1.449817301e-08
               Iteration (num., iy, grad. norm, func.) :  21   1 1.266731481e-08 1.449629744e-08
               Iteration (num., iy, grad. norm, func.) :  22   1 4.873470821e-09 1.448291296e-08
               Iteration (num., iy, grad. norm, func.) :  23   1 5.830688146e-09 1.447443516e-08
               Iteration (num., iy, grad. norm, func.) :  24   1 2.702817368e-09 1.446930180e-08
               Iteration (num., iy, grad. norm, func.) :  25   1 3.482517704e-09 1.446853284e-08
               Iteration (num., iy, grad. norm, func.) :  26   1 2.425197299e-09 1.446779033e-08
               Iteration (num., iy, grad. norm, func.) :  27   1 4.384364765e-09 1.446656530e-08
               Iteration (num., iy, grad. norm, func.) :  28   1 1.666807655e-09 1.446520269e-08
               Iteration (num., iy, grad. norm, func.) :  29   1 1.146121195e-09 1.446505644e-08
               Iteration (num., iy, grad. norm, func.) :  30   1 1.957016230e-09 1.446485007e-08
               Iteration (num., iy, grad. norm, func.) :  31   1 1.400902411e-09 1.446446069e-08
               Iteration (num., iy, grad. norm, func.) :  32   1 2.024876704e-09 1.446420260e-08
               Iteration (num., iy, grad. norm, func.) :  33   1 7.392307757e-10 1.446402715e-08
               Iteration (num., iy, grad. norm, func.) :  34   1 6.113871401e-10 1.446396613e-08
               Iteration (num., iy, grad. norm, func.) :  35   1 8.897950108e-10 1.446387799e-08
               Iteration (num., iy, grad. norm, func.) :  36   1 8.435572508e-10 1.446376880e-08
               Iteration (num., iy, grad. norm, func.) :  37   1 6.781034056e-10 1.446369127e-08
               Iteration (num., iy, grad. norm, func.) :  38   1 4.359785203e-10 1.446365605e-08
               Iteration (num., iy, grad. norm, func.) :  39   1 3.604168165e-10 1.446364595e-08
               Iteration (num., iy, grad. norm, func.) :  40   1 4.714920931e-10 1.446363720e-08
               Iteration (num., iy, grad. norm, func.) :  41   1 4.111309595e-10 1.446361859e-08
               Iteration (num., iy, grad. norm, func.) :  42   1 2.935425518e-10 1.446360051e-08
               Iteration (num., iy, grad. norm, func.) :  43   1 4.007380257e-10 1.446358478e-08
               Iteration (num., iy, grad. norm, func.) :  44   1 1.363139815e-10 1.446357223e-08
               Iteration (num., iy, grad. norm, func.) :  45   1 9.870853160e-11 1.446357135e-08
               Iteration (num., iy, grad. norm, func.) :  46   1 1.398078199e-10 1.446357010e-08
               Iteration (num., iy, grad. norm, func.) :  47   1 1.301007213e-10 1.446356763e-08
               Iteration (num., iy, grad. norm, func.) :  48   1 1.641898408e-10 1.446356566e-08
               Iteration (num., iy, grad. norm, func.) :  49   1 1.162937331e-10 1.446356439e-08
               Iteration (num., iy, grad. norm, func.) :  50   1 1.192123410e-10 1.446356022e-08
               Iteration (num., iy, grad. norm, func.) :  51   1 6.556032628e-11 1.446355959e-08
               Iteration (num., iy, grad. norm, func.) :  52   1 6.137545986e-11 1.446355959e-08
               Iteration (num., iy, grad. norm, func.) :  53   1 4.468566796e-11 1.446355957e-08
               Iteration (num., iy, grad. norm, func.) :  54   1 2.996918496e-11 1.446355952e-08
               Iteration (num., iy, grad. norm, func.) :  55   1 1.980844385e-11 1.446355940e-08
               Iteration (num., iy, grad. norm, func.) :  56   1 1.794802120e-11 1.446355928e-08
               Iteration (num., iy, grad. norm, func.) :  57   1 9.147072506e-12 1.446355920e-08
               Iteration (num., iy, grad. norm, func.) :  58   1 1.229585725e-11 1.446355919e-08
               Iteration (num., iy, grad. norm, func.) :  59   1 9.365521643e-12 1.446355919e-08
               Iteration (num., iy, grad. norm, func.) :  60   1 1.406243787e-11 1.446355918e-08
               Iteration (num., iy, grad. norm, func.) :  61   1 5.522603866e-12 1.446355916e-08
               Iteration (num., iy, grad. norm, func.) :  62   1 6.529863254e-12 1.446355916e-08
               Iteration (num., iy, grad. norm, func.) :  63   1 4.754418096e-12 1.446355916e-08
               Iteration (num., iy, grad. norm, func.) :  64   1 6.124393750e-12 1.446355916e-08
               Iteration (num., iy, grad. norm, func.) :  65   1 6.089857348e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  66   1 1.636095665e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  67   1 1.518616253e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  68   1 2.823435682e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  69   1 1.718325361e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  70   1 1.805099003e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  71   1 1.353303475e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  72   1 1.740106987e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  73   1 4.164410037e-13 1.446355915e-08
            Solving for output 1 - done. Time (sec):  0.9746635
         Solving nonlinear problem (n=1764) - done. Time (sec):  1.8920467
      Solving for degrees of freedom - done. Time (sec):  1.9231131
   Training - done. Time (sec):  1.9346490
___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0009995

   Prediction time/pt. (sec) :  0.0000020

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0009997

   Prediction time/pt. (sec) :  0.0000020

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0009987

   Prediction time/pt. (sec) :  0.0000020

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0000000

   Prediction time/pt. (sec) :  0.0000000

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0019970

   Prediction time/pt. (sec) :  0.0000008

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0020299

   Prediction time/pt. (sec) :  0.0000008
../../../_images/rans_crm_wing.png