1-D step-like data set

import numpy as np


def get_one_d_step():
    xt = np.array(
        [
            0.0000,
            0.4000,
            0.6000,
            0.7000,
            0.7500,
            0.7750,
            0.8000,
            0.8500,
            0.8750,
            0.9000,
            0.9250,
            0.9500,
            0.9750,
            1.0000,
            1.0250,
            1.0500,
            1.1000,
            1.2000,
            1.3000,
            1.4000,
            1.6000,
            1.8000,
            2.0000,
        ],
        dtype=np.float64,
    )
    yt = np.array(
        [
            0.0130,
            0.0130,
            0.0130,
            0.0130,
            0.0130,
            0.0130,
            0.0130,
            0.0132,
            0.0135,
            0.0140,
            0.0162,
            0.0230,
            0.0275,
            0.0310,
            0.0344,
            0.0366,
            0.0396,
            0.0410,
            0.0403,
            0.0390,
            0.0360,
            0.0350,
            0.0345,
        ],
        dtype=np.float64,
    )

    xlimits = np.array([[0.0, 2.0]])

    return xt, yt, xlimits


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

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

    num = 500
    x = np.linspace(0.0, 2.0, num)
    y = interp.predict_values(x)[:, 0]

    plt.plot(x, y)
    plt.plot(xt, yt, "o")
    plt.xlabel("x")
    plt.ylabel("y")
    plt.show()

RMTB

from smt.examples.one_D_step.one_D_step import get_one_d_step, plot_one_d_step
from smt.surrogate_models import RMTB

xt, yt, xlimits = get_one_d_step()

interp = RMTB(
    num_ctrl_pts=100,
    xlimits=xlimits,
    nonlinear_maxiter=20,
    solver_tolerance=1e-16,
    energy_weight=1e-14,
    regularization_weight=0.0,
)
interp.set_training_values(xt, yt)
interp.train()

plot_one_d_step(xt, yt, xlimits, interp)
___________________________________________________________________________

                                   RMTB
___________________________________________________________________________

 Problem size

      # training points.        : 23

___________________________________________________________________________

 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=100) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 1.032652876e-01 8.436300000e-03
               Iteration (num., iy, grad. norm, func.) :   0   0 5.558767804e-08 2.270128086e-13
            Solving for output 0 - done. Time (sec):  0.0159578
         Solving initial startup problem (n=100) - done. Time (sec):  0.0159578
         Solving nonlinear problem (n=100) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 1.442278272e-11 2.234025428e-13
               Iteration (num., iy, grad. norm, func.) :   0   0 1.276932427e-11 2.206468481e-13
               Iteration (num., iy, grad. norm, func.) :   1   0 4.604333797e-10 1.412945915e-13
               Iteration (num., iy, grad. norm, func.) :   2   0 3.274195007e-10 9.555539967e-14
               Iteration (num., iy, grad. norm, func.) :   3   0 9.638115965e-11 2.479560025e-14
               Iteration (num., iy, grad. norm, func.) :   4   0 2.789323778e-11 1.138389897e-14
               Iteration (num., iy, grad. norm, func.) :   5   0 2.205371728e-11 1.075389070e-14
               Iteration (num., iy, grad. norm, func.) :   6   0 6.005987821e-12 8.818284843e-15
               Iteration (num., iy, grad. norm, func.) :   7   0 4.105104107e-12 8.682287242e-15
               Iteration (num., iy, grad. norm, func.) :   8   0 1.166159130e-12 8.497521242e-15
               Iteration (num., iy, grad. norm, func.) :   9   0 3.907475214e-13 8.466958190e-15
               Iteration (num., iy, grad. norm, func.) :  10   0 1.123639852e-13 8.455386478e-15
               Iteration (num., iy, grad. norm, func.) :  11   0 6.687210306e-14 8.454404117e-15
               Iteration (num., iy, grad. norm, func.) :  12   0 3.060099646e-14 8.453844993e-15
               Iteration (num., iy, grad. norm, func.) :  13   0 9.013685289e-15 8.453413582e-15
               Iteration (num., iy, grad. norm, func.) :  14   0 3.568462456e-15 8.453316548e-15
               Iteration (num., iy, grad. norm, func.) :  15   0 7.068428651e-16 8.453277203e-15
               Iteration (num., iy, grad. norm, func.) :  16   0 5.357685654e-16 8.453272016e-15
               Iteration (num., iy, grad. norm, func.) :  17   0 4.395170225e-16 8.453271767e-15
               Iteration (num., iy, grad. norm, func.) :  18   0 3.694965901e-16 8.453271676e-15
               Iteration (num., iy, grad. norm, func.) :  19   0 1.772757574e-16 8.453270829e-15
            Solving for output 0 - done. Time (sec):  0.0848029
         Solving nonlinear problem (n=100) - done. Time (sec):  0.0848029
      Solving for degrees of freedom - done. Time (sec):  0.1007607
   Training - done. Time (sec):  0.1007607
___________________________________________________________________________

 Evaluation

      # eval points. : 500

   Predicting ...
   Predicting - done. Time (sec):  0.0156202

   Prediction time/pt. (sec) :  0.0000312
../../../_images/ex_1d_step.png

RMTC

from smt.examples.one_D_step.one_D_step import get_one_d_step, plot_one_d_step
from smt.surrogate_models import RMTC

xt, yt, xlimits = get_one_d_step()

interp = RMTC(
    num_elements=40,
    xlimits=xlimits,
    nonlinear_maxiter=20,
    solver_tolerance=1e-16,
    energy_weight=1e-14,
    regularization_weight=0.0,
)
interp.set_training_values(xt, yt)
interp.train()

plot_one_d_step(xt, yt, xlimits, interp)
___________________________________________________________________________

                                   RMTC
___________________________________________________________________________

 Problem size

      # training points.        : 23

___________________________________________________________________________

 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=82) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 1.470849329e-01 8.436300000e-03
               Iteration (num., iy, grad. norm, func.) :   0   0 5.814481774e-10 2.493602350e-14
            Solving for output 0 - done. Time (sec):  0.0159605
         Solving initial startup problem (n=82) - done. Time (sec):  0.0159605
         Solving nonlinear problem (n=82) ...
            Solving for output 0 ...
               Iteration (num., iy, grad. norm, func.) :   0   0 7.483954478e-12 2.493518683e-14
               Iteration (num., iy, grad. norm, func.) :   0   0 9.032369145e-12 2.483155071e-14
               Iteration (num., iy, grad. norm, func.) :   1   0 8.718452192e-11 2.392752964e-14
               Iteration (num., iy, grad. norm, func.) :   2   0 4.131175954e-11 1.658086360e-14
               Iteration (num., iy, grad. norm, func.) :   3   0 3.955373996e-11 1.636785165e-14
               Iteration (num., iy, grad. norm, func.) :   4   0 1.291670646e-11 1.192880996e-14
               Iteration (num., iy, grad. norm, func.) :   5   0 3.378763717e-12 1.116775902e-14
               Iteration (num., iy, grad. norm, func.) :   6   0 4.769319870e-13 1.109480428e-14
               Iteration (num., iy, grad. norm, func.) :   7   0 9.630933570e-14 1.109039946e-14
               Iteration (num., iy, grad. norm, func.) :   8   0 5.380254088e-14 1.108982132e-14
               Iteration (num., iy, grad. norm, func.) :   9   0 1.228166919e-14 1.108945934e-14
               Iteration (num., iy, grad. norm, func.) :  10   0 3.096828107e-15 1.108941229e-14
               Iteration (num., iy, grad. norm, func.) :  11   0 8.923711312e-16 1.108940503e-14
               Iteration (num., iy, grad. norm, func.) :  12   0 2.580481756e-16 1.108940368e-14
               Iteration (num., iy, grad. norm, func.) :  13   0 7.019512501e-17 1.108940343e-14
            Solving for output 0 - done. Time (sec):  0.0844636
         Solving nonlinear problem (n=82) - done. Time (sec):  0.0844636
      Solving for degrees of freedom - done. Time (sec):  0.1004241
   Training - done. Time (sec):  0.1004241
___________________________________________________________________________

 Evaluation

      # eval points. : 500

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

   Prediction time/pt. (sec) :  0.0000000
../../../_images/ex_1d_step.png