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 1.127974095e-08 2.219243982e-13
Solving for output 0 - done. Time (sec): 0.0035331
Solving initial startup problem (n=100) - done. Time (sec): 0.0035331
Solving nonlinear problem (n=100) ...
Solving for output 0 ...
Iteration (num., iy, grad. norm, func.) : 0 0 1.548191750e-11 2.217751325e-13
Iteration (num., iy, grad. norm, func.) : 0 0 1.394278805e-11 2.190097980e-13
Iteration (num., iy, grad. norm, func.) : 1 0 4.584836663e-10 1.413359358e-13
Iteration (num., iy, grad. norm, func.) : 2 0 3.608388849e-10 1.074624094e-13
Iteration (num., iy, grad. norm, func.) : 3 0 1.062566066e-10 2.714188761e-14
Iteration (num., iy, grad. norm, func.) : 4 0 3.110030538e-11 1.186730380e-14
Iteration (num., iy, grad. norm, func.) : 5 0 8.637889286e-12 8.985747510e-15
Iteration (num., iy, grad. norm, func.) : 6 0 2.113680400e-12 8.519465166e-15
Iteration (num., iy, grad. norm, func.) : 7 0 2.080738024e-12 8.518276630e-15
Iteration (num., iy, grad. norm, func.) : 8 0 3.841507903e-13 8.471580148e-15
Iteration (num., iy, grad. norm, func.) : 9 0 3.112306577e-13 8.467274773e-15
Iteration (num., iy, grad. norm, func.) : 10 0 5.070566370e-14 8.454548297e-15
Iteration (num., iy, grad. norm, func.) : 11 0 1.666762121e-14 8.453802707e-15
Iteration (num., iy, grad. norm, func.) : 12 0 1.727503879e-14 8.453801200e-15
Iteration (num., iy, grad. norm, func.) : 13 0 1.466105530e-14 8.453708354e-15
Iteration (num., iy, grad. norm, func.) : 14 0 9.493520089e-15 8.453377554e-15
Iteration (num., iy, grad. norm, func.) : 15 0 6.800282381e-15 8.453310106e-15
Iteration (num., iy, grad. norm, func.) : 16 0 8.753012817e-16 8.453274195e-15
Iteration (num., iy, grad. norm, func.) : 17 0 8.861540187e-16 8.453274132e-15
Iteration (num., iy, grad. norm, func.) : 18 0 5.330033187e-16 8.453273264e-15
Iteration (num., iy, grad. norm, func.) : 19 0 5.785118903e-16 8.453271091e-15
Solving for output 0 - done. Time (sec): 0.0601628
Solving nonlinear problem (n=100) - done. Time (sec): 0.0601628
Solving for degrees of freedom - done. Time (sec): 0.0636959
Training - done. Time (sec): 0.0636959
___________________________________________________________________________
Evaluation
# eval points. : 500
Predicting ...
Predicting - done. Time (sec): 0.0000000
Prediction time/pt. (sec) : 0.0000000
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 1.807875749e-12 2.493686470e-14
Solving for output 0 - done. Time (sec): 0.0000000
Solving initial startup problem (n=82) - done. Time (sec): 0.0000000
Solving nonlinear problem (n=82) ...
Solving for output 0 ...
Iteration (num., iy, grad. norm, func.) : 0 0 7.484146522e-12 2.493686350e-14
Iteration (num., iy, grad. norm, func.) : 0 0 9.032461792e-12 2.483319895e-14
Iteration (num., iy, grad. norm, func.) : 1 0 8.726294577e-11 2.394210072e-14
Iteration (num., iy, grad. norm, func.) : 2 0 6.860390512e-11 1.978091449e-14
Iteration (num., iy, grad. norm, func.) : 3 0 4.691798616e-11 1.537297203e-14
Iteration (num., iy, grad. norm, func.) : 4 0 9.922338291e-12 1.153328544e-14
Iteration (num., iy, grad. norm, func.) : 5 0 5.460856036e-12 1.130225803e-14
Iteration (num., iy, grad. norm, func.) : 6 0 8.530617619e-13 1.110676984e-14
Iteration (num., iy, grad. norm, func.) : 7 0 1.870453869e-13 1.109190883e-14
Iteration (num., iy, grad. norm, func.) : 8 0 1.151673802e-13 1.109065775e-14
Iteration (num., iy, grad. norm, func.) : 9 0 3.661383211e-14 1.108964365e-14
Iteration (num., iy, grad. norm, func.) : 10 0 9.092762497e-15 1.108943182e-14
Iteration (num., iy, grad. norm, func.) : 11 0 1.449202696e-15 1.108940466e-14
Iteration (num., iy, grad. norm, func.) : 12 0 1.011249189e-16 1.108940343e-14
Iteration (num., iy, grad. norm, func.) : 13 0 1.154891849e-17 1.108940340e-14
Solving for output 0 - done. Time (sec): 0.0400596
Solving nonlinear problem (n=82) - done. Time (sec): 0.0400596
Solving for degrees of freedom - done. Time (sec): 0.0400596
Training - done. Time (sec): 0.0400596
___________________________________________________________________________
Evaluation
# eval points. : 500
Predicting ...
Predicting - done. Time (sec): 0.0000000
Prediction time/pt. (sec) : 0.0000000
