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 numpy as np
import matplotlib
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.surrogate_models import RMTB
from smt.examples.one_D_step.one_D_step import get_one_d_step, plot_one_d_step
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 8.879126107e-10 2.217748918e-13
Solving for output 0 - done. Time (sec): 0.0000000
Solving initial startup problem (n=100) - done. Time (sec): 0.0000000
Solving nonlinear problem (n=100) ...
Solving for output 0 ...
Iteration (num., iy, grad. norm, func.) : 0 0 1.552681635e-11 2.217739998e-13
Iteration (num., iy, grad. norm, func.) : 0 0 1.400336329e-11 2.190101681e-13
Iteration (num., iy, grad. norm, func.) : 1 0 4.614334315e-10 1.420996036e-13
Iteration (num., iy, grad. norm, func.) : 2 0 3.386385427e-10 9.957696091e-14
Iteration (num., iy, grad. norm, func.) : 3 0 9.965548477e-11 2.559472351e-14
Iteration (num., iy, grad. norm, func.) : 4 0 3.028292057e-11 1.206316456e-14
Iteration (num., iy, grad. norm, func.) : 5 0 8.399776244e-12 9.089294075e-15
Iteration (num., iy, grad. norm, func.) : 6 0 2.074830115e-12 8.557170853e-15
Iteration (num., iy, grad. norm, func.) : 7 0 3.817538099e-13 8.464326104e-15
Iteration (num., iy, grad. norm, func.) : 8 0 2.920095323e-13 8.459776827e-15
Iteration (num., iy, grad. norm, func.) : 9 0 7.721236909e-14 8.454758697e-15
Iteration (num., iy, grad. norm, func.) : 10 0 2.417042968e-14 8.453876676e-15
Iteration (num., iy, grad. norm, func.) : 11 0 2.213769117e-14 8.453844066e-15
Iteration (num., iy, grad. norm, func.) : 12 0 7.168882034e-15 8.453415843e-15
Iteration (num., iy, grad. norm, func.) : 13 0 1.322758762e-15 8.453276708e-15
Iteration (num., iy, grad. norm, func.) : 14 0 1.086918935e-15 8.453275361e-15
Iteration (num., iy, grad. norm, func.) : 15 0 9.562581577e-16 8.453275241e-15
Iteration (num., iy, grad. norm, func.) : 16 0 8.144965006e-16 8.453273757e-15
Iteration (num., iy, grad. norm, func.) : 17 0 6.113930019e-16 8.453272411e-15
Iteration (num., iy, grad. norm, func.) : 18 0 1.911917523e-16 8.453270747e-15
Iteration (num., iy, grad. norm, func.) : 19 0 1.931585657e-16 8.453270703e-15
Solving for output 0 - done. Time (sec): 0.0999222
Solving nonlinear problem (n=100) - done. Time (sec): 0.0999222
Solving for degrees of freedom - done. Time (sec): 0.0999222
Training - done. Time (sec): 0.0999222
___________________________________________________________________________
Evaluation
# eval points. : 500
Predicting ...
Predicting - done. Time (sec): 0.0000000
Prediction time/pt. (sec) : 0.0000000
RMTC¶
from smt.surrogate_models import RMTC
from smt.examples.one_D_step.one_D_step import get_one_d_step, plot_one_d_step
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 4.031960886e-12 2.493686471e-14
Solving for output 0 - done. Time (sec): 0.0156379
Solving initial startup problem (n=82) - done. Time (sec): 0.0156379
Solving nonlinear problem (n=82) ...
Solving for output 0 ...
Iteration (num., iy, grad. norm, func.) : 0 0 7.484146480e-12 2.493686331e-14
Iteration (num., iy, grad. norm, func.) : 0 0 9.032461435e-12 2.483319871e-14
Iteration (num., iy, grad. norm, func.) : 1 0 8.676384412e-11 2.388494401e-14
Iteration (num., iy, grad. norm, func.) : 2 0 6.755496606e-11 1.951826538e-14
Iteration (num., iy, grad. norm, func.) : 3 0 4.611359154e-11 1.521578957e-14
Iteration (num., iy, grad. norm, func.) : 4 0 9.560517650e-12 1.149409997e-14
Iteration (num., iy, grad. norm, func.) : 5 0 5.356117813e-12 1.129031598e-14
Iteration (num., iy, grad. norm, func.) : 6 0 8.365028192e-13 1.110518657e-14
Iteration (num., iy, grad. norm, func.) : 7 0 1.740075688e-13 1.109155907e-14
Iteration (num., iy, grad. norm, func.) : 8 0 1.554156778e-13 1.109124706e-14
Iteration (num., iy, grad. norm, func.) : 9 0 1.497358635e-13 1.109091009e-14
Iteration (num., iy, grad. norm, func.) : 10 0 3.279226021e-14 1.108962650e-14
Iteration (num., iy, grad. norm, func.) : 11 0 1.384472847e-14 1.108945872e-14
Iteration (num., iy, grad. norm, func.) : 12 0 2.898607110e-15 1.108940698e-14
Iteration (num., iy, grad. norm, func.) : 13 0 3.214675952e-16 1.108940346e-14
Iteration (num., iy, grad. norm, func.) : 14 0 1.039690103e-17 1.108940340e-14
Solving for output 0 - done. Time (sec): 0.0624967
Solving nonlinear problem (n=82) - done. Time (sec): 0.0624967
Solving for degrees of freedom - done. Time (sec): 0.0781345
Training - done. Time (sec): 0.0781345
___________________________________________________________________________
Evaluation
# eval points. : 500
Predicting ...
Predicting - done. Time (sec): 0.0156255
Prediction time/pt. (sec) : 0.0000313
