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):  0.0000000
         Computing approximation terms ...
         Computing approximation terms - done. Time (sec):  0.0000000
      Pre-computing matrices - done. Time (sec):  0.0000000
      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 6.361608377e-09 1.793038202e-10
            Solving for output 0 - done. Time (sec):  0.0157151
            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 1.413882548e-07 4.567643574e-08
            Solving for output 1 - done. Time (sec):  0.0000000
         Solving initial startup problem (n=400) - done. Time (sec):  0.0157151
         Solving nonlinear problem (n=400) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 6.652712074e-09 1.793037678e-10
               Iteration (num., iy, grad. norm, func.) :   0   0 5.849628222e-09 1.703954128e-10
               Iteration (num., iy, grad. norm, func.) :   1   0 3.027427470e-08 1.033861402e-10
               Iteration (num., iy, grad. norm, func.) :   2   0 1.125798382e-08 2.504937528e-11
               Iteration (num., iy, grad. norm, func.) :   3   0 3.573484541e-09 1.053192602e-11
               Iteration (num., iy, grad. norm, func.) :   4   0 2.491313135e-09 9.521725888e-12
               Iteration (num., iy, grad. norm, func.) :   5   0 7.373265568e-10 7.437104352e-12
               Iteration (num., iy, grad. norm, func.) :   6   0 2.127610441e-10 6.541104844e-12
               Iteration (num., iy, grad. norm, func.) :   7   0 4.491224738e-11 6.262749389e-12
               Iteration (num., iy, grad. norm, func.) :   8   0 2.678528584e-11 6.262036113e-12
               Iteration (num., iy, grad. norm, func.) :   9   0 1.890458725e-11 6.260921588e-12
               Iteration (num., iy, grad. norm, func.) :  10   0 1.026127463e-11 6.260205674e-12
               Iteration (num., iy, grad. norm, func.) :  11   0 3.073950306e-12 6.256593531e-12
               Iteration (num., iy, grad. norm, func.) :  12   0 6.628206941e-13 6.255688696e-12
            Solving for output 0 - done. Time (sec):  0.0844629
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 9.729512355e-08 4.567641548e-08
               Iteration (num., iy, grad. norm, func.) :   0   1 9.338535090e-08 4.538218375e-08
               Iteration (num., iy, grad. norm, func.) :   1   1 2.793660470e-06 3.158625636e-08
               Iteration (num., iy, grad. norm, func.) :   2   1 8.280829537e-07 4.467205623e-09
               Iteration (num., iy, grad. norm, func.) :   3   1 2.471585317e-07 1.754067656e-09
               Iteration (num., iy, grad. norm, func.) :   4   1 7.360944708e-08 7.514442525e-10
               Iteration (num., iy, grad. norm, func.) :   5   1 6.382088695e-08 6.202555675e-10
               Iteration (num., iy, grad. norm, func.) :   6   1 1.975747825e-08 5.727770136e-10
               Iteration (num., iy, grad. norm, func.) :   7   1 6.305403118e-09 4.470752571e-10
               Iteration (num., iy, grad. norm, func.) :   8   1 6.539592945e-09 3.117262610e-10
               Iteration (num., iy, grad. norm, func.) :   9   1 1.800710465e-09 2.765831061e-10
               Iteration (num., iy, grad. norm, func.) :  10   1 1.432583667e-09 2.762228885e-10
               Iteration (num., iy, grad. norm, func.) :  11   1 3.459281962e-10 2.734946089e-10
               Iteration (num., iy, grad. norm, func.) :  12   1 1.937089163e-10 2.719093375e-10
               Iteration (num., iy, grad. norm, func.) :  13   1 4.191227557e-11 2.714583258e-10
               Iteration (num., iy, grad. norm, func.) :  14   1 5.379716328e-11 2.714249977e-10
               Iteration (num., iy, grad. norm, func.) :  15   1 3.735608154e-11 2.714059840e-10
               Iteration (num., iy, grad. norm, func.) :  16   1 5.074917089e-11 2.713945463e-10
               Iteration (num., iy, grad. norm, func.) :  17   1 1.135494957e-11 2.713592113e-10
               Iteration (num., iy, grad. norm, func.) :  18   1 1.866777371e-11 2.713567409e-10
               Iteration (num., iy, grad. norm, func.) :  19   1 1.365618643e-11 2.713544120e-10
               Iteration (num., iy, grad. norm, func.) :  20   1 2.196197154e-11 2.713503041e-10
               Iteration (num., iy, grad. norm, func.) :  21   1 4.703269102e-12 2.713473057e-10
               Iteration (num., iy, grad. norm, func.) :  22   1 1.577064311e-11 2.713464813e-10
               Iteration (num., iy, grad. norm, func.) :  23   1 3.126100067e-12 2.713459142e-10
               Iteration (num., iy, grad. norm, func.) :  24   1 4.329925240e-12 2.713456898e-10
               Iteration (num., iy, grad. norm, func.) :  25   1 4.760702705e-12 2.713452984e-10
               Iteration (num., iy, grad. norm, func.) :  26   1 2.186298077e-12 2.713451820e-10
               Iteration (num., iy, grad. norm, func.) :  27   1 1.090371663e-12 2.713450690e-10
               Iteration (num., iy, grad. norm, func.) :  28   1 1.643853117e-12 2.713449846e-10
               Iteration (num., iy, grad. norm, func.) :  29   1 9.754974651e-13 2.713449617e-10
            Solving for output 1 - done. Time (sec):  0.2075577
         Solving nonlinear problem (n=400) - done. Time (sec):  0.2920206
      Solving for degrees of freedom - done. Time (sec):  0.3077357
   Training - done. Time (sec):  0.3077357
___________________________________________________________________________

 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):  0.0000000

   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):  0.0084314

   Prediction time/pt. (sec) :  0.0000034

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

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

   Prediction time/pt. (sec) :  0.0000000
../../../_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):  0.0000000
         Initializing Hessian ...
         Initializing Hessian - done. Time (sec):  0.0000000
         Computing energy terms ...
         Computing energy terms - done. Time (sec):  0.0159726
         Computing approximation terms ...
         Computing approximation terms - done. Time (sec):  0.0000000
      Pre-computing matrices - done. Time (sec):  0.0159726
      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 1.040702505e-05 2.104565751e-08
            Solving for output 0 - done. Time (sec):  0.0156188
            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 1.009043784e-04 6.496775939e-06
            Solving for output 1 - done. Time (sec):  0.0156209
         Solving initial startup problem (n=1764) - done. Time (sec):  0.0312397
         Solving nonlinear problem (n=1764) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 8.424965568e-07 2.095596418e-08
               Iteration (num., iy, grad. norm, func.) :   0   0 8.937561990e-07 1.660200956e-08
               Iteration (num., iy, grad. norm, func.) :   1   0 3.417439495e-07 3.185554201e-09
               Iteration (num., iy, grad. norm, func.) :   2   0 1.135240095e-07 1.027663890e-09
               Iteration (num., iy, grad. norm, func.) :   3   0 6.040725703e-08 5.273037477e-10
               Iteration (num., iy, grad. norm, func.) :   4   0 3.589817049e-08 4.130921956e-10
               Iteration (num., iy, grad. norm, func.) :   5   0 2.367069222e-08 3.787308651e-10
               Iteration (num., iy, grad. norm, func.) :   6   0 2.073063682e-08 3.750425098e-10
               Iteration (num., iy, grad. norm, func.) :   7   0 2.151639102e-08 3.738627774e-10
               Iteration (num., iy, grad. norm, func.) :   8   0 1.387810346e-08 3.612029122e-10
               Iteration (num., iy, grad. norm, func.) :   9   0 1.599147620e-08 3.410626872e-10
               Iteration (num., iy, grad. norm, func.) :  10   0 5.969921818e-09 3.050205235e-10
               Iteration (num., iy, grad. norm, func.) :  11   0 2.143674691e-09 2.891346316e-10
               Iteration (num., iy, grad. norm, func.) :  12   0 1.704740268e-09 2.876659596e-10
               Iteration (num., iy, grad. norm, func.) :  13   0 2.247790649e-09 2.876207868e-10
               Iteration (num., iy, grad. norm, func.) :  14   0 1.512050677e-09 2.874786667e-10
               Iteration (num., iy, grad. norm, func.) :  15   0 3.609275143e-09 2.872620463e-10
               Iteration (num., iy, grad. norm, func.) :  16   0 4.433709820e-10 2.867396778e-10
               Iteration (num., iy, grad. norm, func.) :  17   0 2.496800518e-10 2.867367691e-10
               Iteration (num., iy, grad. norm, func.) :  18   0 1.248267600e-09 2.867322407e-10
               Iteration (num., iy, grad. norm, func.) :  19   0 4.542676797e-10 2.866856880e-10
               Iteration (num., iy, grad. norm, func.) :  20   0 1.142461233e-09 2.866768805e-10
               Iteration (num., iy, grad. norm, func.) :  21   0 3.518825494e-10 2.866050691e-10
               Iteration (num., iy, grad. norm, func.) :  22   0 5.728450541e-10 2.865809700e-10
               Iteration (num., iy, grad. norm, func.) :  23   0 3.010375451e-10 2.865582760e-10
               Iteration (num., iy, grad. norm, func.) :  24   0 4.646038054e-10 2.865505543e-10
               Iteration (num., iy, grad. norm, func.) :  25   0 2.741412951e-10 2.865409788e-10
               Iteration (num., iy, grad. norm, func.) :  26   0 3.916274212e-10 2.865294244e-10
               Iteration (num., iy, grad. norm, func.) :  27   0 2.548934938e-10 2.865167624e-10
               Iteration (num., iy, grad. norm, func.) :  28   0 1.866884307e-10 2.865097019e-10
               Iteration (num., iy, grad. norm, func.) :  29   0 2.863664727e-10 2.865073043e-10
               Iteration (num., iy, grad. norm, func.) :  30   0 1.744332186e-10 2.865050504e-10
               Iteration (num., iy, grad. norm, func.) :  31   0 2.167504214e-10 2.865034390e-10
               Iteration (num., iy, grad. norm, func.) :  32   0 1.134260875e-10 2.865006839e-10
               Iteration (num., iy, grad. norm, func.) :  33   0 1.574862995e-10 2.864975544e-10
               Iteration (num., iy, grad. norm, func.) :  34   0 4.824600446e-11 2.864946039e-10
               Iteration (num., iy, grad. norm, func.) :  35   0 4.451682046e-11 2.864944625e-10
               Iteration (num., iy, grad. norm, func.) :  36   0 5.588069321e-11 2.864942826e-10
               Iteration (num., iy, grad. norm, func.) :  37   0 6.154401521e-11 2.864940091e-10
               Iteration (num., iy, grad. norm, func.) :  38   0 6.823581622e-11 2.864935946e-10
               Iteration (num., iy, grad. norm, func.) :  39   0 4.174059514e-11 2.864931933e-10
               Iteration (num., iy, grad. norm, func.) :  40   0 2.893931426e-11 2.864931009e-10
               Iteration (num., iy, grad. norm, func.) :  41   0 4.539814138e-11 2.864929669e-10
               Iteration (num., iy, grad. norm, func.) :  42   0 2.466568434e-11 2.864928406e-10
               Iteration (num., iy, grad. norm, func.) :  43   0 4.529576874e-11 2.864927539e-10
               Iteration (num., iy, grad. norm, func.) :  44   0 1.548376023e-11 2.864926735e-10
               Iteration (num., iy, grad. norm, func.) :  45   0 2.508731202e-11 2.864926446e-10
               Iteration (num., iy, grad. norm, func.) :  46   0 1.420495919e-11 2.864925940e-10
               Iteration (num., iy, grad. norm, func.) :  47   0 2.205651344e-11 2.864925596e-10
               Iteration (num., iy, grad. norm, func.) :  48   0 9.679171011e-12 2.864925115e-10
               Iteration (num., iy, grad. norm, func.) :  49   0 1.423642822e-11 2.864924974e-10
               Iteration (num., iy, grad. norm, func.) :  50   0 1.150310283e-11 2.864924858e-10
               Iteration (num., iy, grad. norm, func.) :  51   0 9.985115673e-12 2.864924436e-10
               Iteration (num., iy, grad. norm, func.) :  52   0 4.325538797e-12 2.864924246e-10
               Iteration (num., iy, grad. norm, func.) :  53   0 4.324044881e-12 2.864924246e-10
               Iteration (num., iy, grad. norm, func.) :  54   0 4.304543184e-12 2.864924246e-10
               Iteration (num., iy, grad. norm, func.) :  55   0 4.641764688e-12 2.864924217e-10
               Iteration (num., iy, grad. norm, func.) :  56   0 1.388374801e-12 2.864924185e-10
               Iteration (num., iy, grad. norm, func.) :  57   0 2.007280330e-12 2.864924183e-10
               Iteration (num., iy, grad. norm, func.) :  58   0 2.152823589e-12 2.864924178e-10
               Iteration (num., iy, grad. norm, func.) :  59   0 2.792847949e-12 2.864924174e-10
               Iteration (num., iy, grad. norm, func.) :  60   0 1.549756182e-12 2.864924172e-10
               Iteration (num., iy, grad. norm, func.) :  61   0 2.660765151e-12 2.864924166e-10
               Iteration (num., iy, grad. norm, func.) :  62   0 9.058260844e-13 2.864924158e-10
            Solving for output 0 - done. Time (sec):  1.1510787
            Solving for output 1 ...
               Iteration (num., iy, grad. norm, func.) :   0   1 1.422938883e-05 6.489189054e-06
               Iteration (num., iy, grad. norm, func.) :   0   1 1.422426134e-05 6.242643394e-06
               Iteration (num., iy, grad. norm, func.) :   1   1 1.468644644e-05 8.046322464e-07
               Iteration (num., iy, grad. norm, func.) :   2   1 1.980829934e-05 3.853967070e-07
               Iteration (num., iy, grad. norm, func.) :   3   1 6.149803188e-06 1.326901223e-07
               Iteration (num., iy, grad. norm, func.) :   4   1 5.514652283e-06 1.083596434e-07
               Iteration (num., iy, grad. norm, func.) :   5   1 1.681671136e-06 3.942980521e-08
               Iteration (num., iy, grad. norm, func.) :   6   1 1.311263507e-06 3.188700938e-08
               Iteration (num., iy, grad. norm, func.) :   7   1 1.042778091e-06 3.098470569e-08
               Iteration (num., iy, grad. norm, func.) :   8   1 5.949946674e-07 2.935838506e-08
               Iteration (num., iy, grad. norm, func.) :   9   1 1.837095130e-07 2.336750770e-08
               Iteration (num., iy, grad. norm, func.) :  10   1 1.024120702e-07 1.803239328e-08
               Iteration (num., iy, grad. norm, func.) :  11   1 4.560016252e-08 1.512381840e-08
               Iteration (num., iy, grad. norm, func.) :  12   1 4.069079267e-08 1.484797776e-08
               Iteration (num., iy, grad. norm, func.) :  13   1 4.069079267e-08 1.484797776e-08
               Iteration (num., iy, grad. norm, func.) :  14   1 4.069079267e-08 1.484797776e-08
               Iteration (num., iy, grad. norm, func.) :  15   1 3.533011076e-08 1.478206340e-08
               Iteration (num., iy, grad. norm, func.) :  16   1 2.307870255e-08 1.465456167e-08
               Iteration (num., iy, grad. norm, func.) :  17   1 2.093728910e-08 1.458023846e-08
               Iteration (num., iy, grad. norm, func.) :  18   1 1.150417427e-08 1.451706578e-08
               Iteration (num., iy, grad. norm, func.) :  19   1 7.998452099e-09 1.449203218e-08
               Iteration (num., iy, grad. norm, func.) :  20   1 8.061749901e-09 1.449008606e-08
               Iteration (num., iy, grad. norm, func.) :  21   1 7.541915802e-09 1.448862605e-08
               Iteration (num., iy, grad. norm, func.) :  22   1 1.063867707e-08 1.448377094e-08
               Iteration (num., iy, grad. norm, func.) :  23   1 4.857018607e-09 1.447702314e-08
               Iteration (num., iy, grad. norm, func.) :  24   1 6.341357316e-09 1.447401552e-08
               Iteration (num., iy, grad. norm, func.) :  25   1 3.561692708e-09 1.447090211e-08
               Iteration (num., iy, grad. norm, func.) :  26   1 6.731711790e-09 1.446900010e-08
               Iteration (num., iy, grad. norm, func.) :  27   1 1.571562669e-09 1.446712148e-08
               Iteration (num., iy, grad. norm, func.) :  28   1 2.944549357e-09 1.446709230e-08
               Iteration (num., iy, grad. norm, func.) :  29   1 2.230547757e-09 1.446658757e-08
               Iteration (num., iy, grad. norm, func.) :  30   1 3.389783471e-09 1.446606337e-08
               Iteration (num., iy, grad. norm, func.) :  31   1 1.702346016e-09 1.446509203e-08
               Iteration (num., iy, grad. norm, func.) :  32   1 1.801538274e-09 1.446446791e-08
               Iteration (num., iy, grad. norm, func.) :  33   1 8.220960597e-10 1.446415726e-08
               Iteration (num., iy, grad. norm, func.) :  34   1 7.967134401e-10 1.446407546e-08
               Iteration (num., iy, grad. norm, func.) :  35   1 9.007869020e-10 1.446401984e-08
               Iteration (num., iy, grad. norm, func.) :  36   1 1.398823471e-09 1.446393572e-08
               Iteration (num., iy, grad. norm, func.) :  37   1 6.179297314e-10 1.446384093e-08
               Iteration (num., iy, grad. norm, func.) :  38   1 9.792102584e-10 1.446373558e-08
               Iteration (num., iy, grad. norm, func.) :  39   1 3.124943095e-10 1.446364015e-08
               Iteration (num., iy, grad. norm, func.) :  40   1 3.122610001e-10 1.446363327e-08
               Iteration (num., iy, grad. norm, func.) :  41   1 2.906225035e-10 1.446362445e-08
               Iteration (num., iy, grad. norm, func.) :  42   1 4.498402993e-10 1.446360941e-08
               Iteration (num., iy, grad. norm, func.) :  43   1 3.504886327e-10 1.446358012e-08
               Iteration (num., iy, grad. norm, func.) :  44   1 1.051533071e-10 1.446356658e-08
               Iteration (num., iy, grad. norm, func.) :  45   1 1.029088597e-10 1.446356657e-08
               Iteration (num., iy, grad. norm, func.) :  46   1 9.760858285e-11 1.446356650e-08
               Iteration (num., iy, grad. norm, func.) :  47   1 1.653862000e-10 1.446356537e-08
               Iteration (num., iy, grad. norm, func.) :  48   1 7.269692555e-11 1.446356368e-08
               Iteration (num., iy, grad. norm, func.) :  49   1 1.835035106e-10 1.446356308e-08
               Iteration (num., iy, grad. norm, func.) :  50   1 7.017414129e-11 1.446356177e-08
               Iteration (num., iy, grad. norm, func.) :  51   1 5.674642093e-11 1.446356064e-08
               Iteration (num., iy, grad. norm, func.) :  52   1 6.385672542e-11 1.446356051e-08
               Iteration (num., iy, grad. norm, func.) :  53   1 4.403979266e-11 1.446356033e-08
               Iteration (num., iy, grad. norm, func.) :  54   1 6.103719588e-11 1.446356003e-08
               Iteration (num., iy, grad. norm, func.) :  55   1 2.598341540e-11 1.446355963e-08
               Iteration (num., iy, grad. norm, func.) :  56   1 3.749284045e-11 1.446355958e-08
               Iteration (num., iy, grad. norm, func.) :  57   1 2.948894440e-11 1.446355958e-08
               Iteration (num., iy, grad. norm, func.) :  58   1 4.349011114e-11 1.446355945e-08
               Iteration (num., iy, grad. norm, func.) :  59   1 1.150489306e-11 1.446355931e-08
               Iteration (num., iy, grad. norm, func.) :  60   1 2.030175252e-11 1.446355930e-08
               Iteration (num., iy, grad. norm, func.) :  61   1 1.505670170e-11 1.446355928e-08
               Iteration (num., iy, grad. norm, func.) :  62   1 2.500274676e-11 1.446355926e-08
               Iteration (num., iy, grad. norm, func.) :  63   1 9.998184321e-12 1.446355922e-08
               Iteration (num., iy, grad. norm, func.) :  64   1 1.174683169e-11 1.446355920e-08
               Iteration (num., iy, grad. norm, func.) :  65   1 7.818126211e-12 1.446355918e-08
               Iteration (num., iy, grad. norm, func.) :  66   1 1.344365437e-11 1.446355918e-08
               Iteration (num., iy, grad. norm, func.) :  67   1 6.259601480e-12 1.446355918e-08
               Iteration (num., iy, grad. norm, func.) :  68   1 8.863962464e-12 1.446355916e-08
               Iteration (num., iy, grad. norm, func.) :  69   1 2.095663893e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  70   1 1.682008437e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  71   1 1.904057340e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  72   1 1.849606450e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  73   1 2.252138274e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  74   1 1.900456942e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  75   1 2.022349276e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  76   1 2.369216629e-12 1.446355915e-08
               Iteration (num., iy, grad. norm, func.) :  77   1 7.696623094e-13 1.446355915e-08
            Solving for output 1 - done. Time (sec):  1.3746848
         Solving nonlinear problem (n=1764) - done. Time (sec):  2.5257635
      Solving for degrees of freedom - done. Time (sec):  2.5570033
   Training - done. Time (sec):  2.5729759
___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0021315

   Prediction time/pt. (sec) :  0.0000043

___________________________________________________________________________

 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):  0.0084257

   Prediction time/pt. (sec) :  0.0000169

___________________________________________________________________________

 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):  0.0084097

   Prediction time/pt. (sec) :  0.0000168

___________________________________________________________________________

 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):  0.0024054

   Prediction time/pt. (sec) :  0.0000048

___________________________________________________________________________

 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):  0.0084326

   Prediction time/pt. (sec) :  0.0000034

___________________________________________________________________________

 Evaluation

      # eval points. : 2500

   Predicting ...
   Predicting - done. Time (sec):  0.0024102

   Prediction time/pt. (sec) :  0.0000010
../../../_images/rans_crm_wing.png